rowid,Castle 1,Castle 2,Castle 3,Castle 4,Castle 5,Castle 6,Castle 7,Castle 8,Castle 9,Castle 10,Why did you choose your troop deployment?
1,0,1,2,16,21,3,2,1,32,22,Good against the last round; great against everyone who optimized against the last round.
2,0,3,4,14,15,5,5,5,33,16,"I figure most people will use strategies that are either close to the winning submission, would outperform that submission head-to-head, follow your advice from the column after the last time this challenge was submitted, or follow a pretty similar strategy as they did last time. Goal is to get to 28 points, though in general you also want to keep in mind that you want to win the castles you win by just a little, and lose the ones you lose big time. This deployment looks to probably get to that 28 point margin by winning 4,5,9, and 10 most often. But the scout size of 3-5 is designed to try to be a couple steps ahead of the adjusters who are presenting 2-3 scouts after the previous run. I also wanted to watch out for people loading on 8,9,10, and 1, which was a reasonable strategy last time, which is why I loaded pretty heavily into 9 (which I still expect to be less contested than 10).

As a final note, I also think it would be interesting to look at which strategies do best in terms of total differential to opponents, and how that differs from the actual winners of the contest as published."
3,0,0,0,15,19,1,1,1,32,31,"Previous winner won 84%. Took the 90%ile of the previous distribution and subtracted the optimal even distribution of 100 soldiers/28 points. Found best values of 4/5/9/10, and matched those number. Added a couple to the lower numbers.  Used the rest to spread between the others with 1 soldier
"
4,3,3,3,17,17,3,4,4,23,23,"10+9+5+4=28 for the win.  Plus, if you put 0 in any castle, you have a 0% chance of winning.  So many put 0's that even 3 or 4 troops can win you several castles."
5,0,0,0,16,21,0,0,0,36,27,Near optimal integer program vs previous round: beats 1068 of them.
6,1,1,2,16,19,4,4,4,22,27,"10,9,5,4 gives a win, so almost all in on those"
7,0,0,0,16,21,0,0,0,31,32,"28 to win. Looked like castles 4,5,9,10 got less troops allocated to them per value than other spots last go around. Didn't bother putting troops anywhere else. Also wanted to be one greater than round numbers like 15 or 30."
8,0,8,0,0,0,1,28,1,33,29,"My approach: let `S` be all the strategies available, initialized to the strategies posted on github. Use simulated annealing to find the strategy that ~maximises `P(winning | S)`, and then add that strategy to `S` and repeat. Eventually we will find a strategy that is ""good"" against the empirical strategies and other optimal strategies."
9,1,1,12,1,1,24,1,1,28,30,"28 victory points is the minimum threshold to win any war since there are 55 total victory points available. Therefore, it's unnecessary to win every castle. The top three castles alone aren't enough to get 28 victory points, as it falls short by just one point. So lower valued castles could be surprisingly competitive. Based on this, there's an inherent tradeoff between allocating troops in lower valued castles and allocating lots of troops in just a few of the high valued castles. So this set up focuses on the top two castles, the six point castle and the three point castle, which if captured would yield a majority of the victory points. In the event that someone neglects any of the castles, one troop is deployed to the remainder to ensure a victory in case certain strategies solely focus on a few castles."
10,6,0,0,0,0,1,2,33,33,25,"Against most opponents, I am trying to win the 10/9/8/1 castles. But there are some strategies that try to do the same, and I attack them on a different front. I don't compete against them for the 10, but trump their assumed zeros on the 7 and 6 (also trumping the guy with my idea with a 2 on the 7). Even if I lose the 9 vs such a strategy I get 28 points if I win the 876 and 1 (tying the rest with 0)."
11,1,1,2,18,18,2,3,3,26,26,"Primarily trying to win 10-9-5-4, while leaving some troops to capture other castles if needed. I'm hoping that even with a shifting metagame, this won't be an approach that people will expect."
12,0,0,12,0,1,22,1,1,32,31,"Found a strategy that beat the previous 5 winners, assuming that most people would copy the winning strategies, then I tweaked it a bit to maximize the wins"
13,2,6,2,14,21,2,6,5,21,21,"I'm hoping people will mimic the winning strategy of focusing on castles 8 and 7, so I'm going for 10, 9, 5, and 4, which would give the 28 required to win. I'm also keeping a few soldiers everywhere else in the hopes I'll pick up a few cheap wins from others completely abandoning castles."
14,0,0,0,16,16,2,2,2,31,31,"Focus on 4/5/9/10 to reach 28 points and avoiding the likely heavy competition at 6-8. 31 creeps above the round 30s, 16 creeps above the round 15s and beats out those who are evenly spreading troops out amongst 1-7 and ignoring 8-10. 2 in 6-8 for possible ties or wins over 0s and 1s."
15,1,1,1,15,20,1,1,1,30,29,"I only need 28 points to win. All I need to do is divide my resources so that I am able to try to get that many points. So I focus most of my forces on the castles that have the most value to me and then get two other mid-range castles to supplement the points. I devote 1 to each of the castles that are not main targets because I figure that if someone is going to beat me on 9 or 10 that they may not have any covering 8, 7 etc. Instead of dividing the points, I think I can win them in these situations."
16,1,2,3,5,16,21,5,5,21,21,"Most of prior winners focused on 7 & 8. So I focused on 5, 6, and 10"
17,1,1,1,6,17,17,6,6,22,23,"I tried to accomplish some middle ground between concentrating and even distribution.  Since 4 would be sufficient last time to win on the low castles most of the time, I jumped it to 6.  Enough people put 1, so I dropped 1 troop on each of those because why not?"
18,0,0,0,17,17,0,0,0,30,36,"Variation on the heavily commit to undervalued top castles, try to steal two smaller ones, and ignore everywhere else.  Went for 4 and 5 rather than 6 and 3 or 7 and 2, because people during last battle really committed to 6, 7, and 8"
19,0,8,0,0,0,0,28,0,32,32,"Gambit strategy that preys on anyone who uses balanced troop distribution. This would have failed in the first iteration of the game, but I predict the metagame shifts towards more normal-looking strategies which will get beaten by this one."
20,6,0,0,0,0,0,0,38,32,24,"Out of 55 total points, you only need 28 to win, so let's go all in and see what happens! The way to do this with the fewest number of castles is by winning castles 10, 9, 8,and 1. We'll start by doubling the mean allocation from the previous battle, giving 22 soldiers to castle #10, 32 to #9, 38 to #8, and 6 to #1. This leaves 2 soldiers left, which I'll additionally allocate to castle #10 (because I randomly feel people will be more aggressive on that number based on past results)."
21,0,0,0,0,22,23,28,0,0,27,This setup beat 1071 of the 1387 past strategies (found by integer programming)
22,1,3,3,20,20,3,5,5,20,20,Concentrate deployment to attain 28 points needing the fewest castles without conceding any.
23,4,7,10,13,4,4,4,4,23,27,We battle hard for 9 and 10 and 1-4. Leaving 4 at every other location
24,9,0,0,0,0,0,0,32,32,27,10+9+8+1=28
25,3,7,7,13,17,3,3,3,22,22,"Put at least some troops to all castles, go for weaker targets according to previous round results."
26,9,1,1,1,1,1,1,35,25,25,"Ideally, this will beat out many more balanced strategies, as it captures exactly 28 points if all 1,8,9, and 10 (with more than one troop) are captured. The values are all well above the mean and winning strategy for these castles, so people trying to mimic that will lose to me as well. The other castles have one each to pick up any open points in case I lose a main castle."
27,0,0,15,15,15,20,5,5,5,20,Focus soldiers on  castles that allow me to meet the minimum requirement to win
28,0,1,8,14,16,1,22,3,25,10,https://pastebin.com/LSXrjJJV
29,0,0,0,15,18,1,1,1,26,38,Mostly random
30,3,6,9,12,15,18,5,5,16,11,"Low prior deployments for the top couple castles indicates that one should be easily available. If I can get either the 10 or 9, the emphasis on the lower ranked castle's should push me over the edge."
31,1,4,4,4,16,21,22,4,11,13,"Previous data suggests 2 and 3 were good choices for your ""throw-off"" castles, as you beat the large swath of 0s and 1s.  I believe that 4 is the ""new 2"" as people will respond to this, being more likely to throw a 2 or 3 on a castle than a 0 or 1. There will be an arms race to grab the 10 and 9 on the cheap (the winner did so because he won something like 40% of the time on those castles for only 2 troop investment). Now people will be responding by putting 4 troops there, and then there will be people trying to next-level those people. I want to be near the top of the next-levelers, because these are key castles, but I still want to lose by a lot to the people that go huge on these to maintain an overwhelming advantage elsewhere.   On castle 8, I think people will respond in two ways, after seeing that people really fought over this castle last time. They will either not enter the fight, or they will enter the fray hard. I chose to throw off, but selected 4 to beat the other people who threw off with 2s and 3s."
32,3,6,6,14,14,14,6,6,15,16,"Try to get 10 and 9 and two of 4,5,6. Or get a few cheap ones."
33,0,0,9,13,13,23,3,3,4,32,Genetic Algorithm trained on the previous answers yielded this solution after running overnight - had a 78.73% win rate
34,1,2,4,7,14,22,3,3,23,21,"Starting with a geometric weighting of castles (SUM(castle#^2)), I then willingly all but abandoned castles #7 and #8 in favor of castles #5, #6, #9 and #10. (Over-weighted in the current data set, I expect a lingering approach to emphasizing these and ignoring castles #9 and #10) Next, I adjusted the castle values incrementally, depending on how many victories I gained or lost between adjustments when battling the initial data set. Min-max adjustments along similar-valued castles got me to this."
35,2,0,2,12,2,22,3,30,6,21,ryanmdraper@gmail.com
36,1,1,9,3,3,2,28,32,7,14,This is maddening! I want to know the answer! Ahhhhhhh!
37,2,2,8,11,17,17,8,11,12,12,Just guessing where the majority of players will land after reviewing the data from previous game.  Trying to figure out where I can get the most vps's (victory points per solider)
38,0,2,2,2,21,22,2,2,23,24,"Relies on information from first game: 7 and 8 were popular, 9 and 10 ignored, abandoned castles got 0 or 1."
39,0,1,1,12,21,2,1,1,29,32,I specified my deployment based on previous strategy but more concentrated.
40,2,3,15,15,15,15,5,5,5,20,"Sacrifice some higher castles (7-9) in the hopes of getting some of the more ignored lower castles (3-6).  Although when ""sacrificing"", still offering some chance and not completely giving them away for free."
41,0,0,3,3,20,16,3,20,24,11,not sure.
42,3,3,3,8,17,17,9,6,17,17,"I tried not to overreact to the winner from last time (and hopefully predict some of others overreactions) I decided to never completely give up free points so put no fewer than 3 troops at any location. However I concentrated my armies in such a way as to get over half the points with only 4 wins (5,6,9,10). I hoped that this 2 pronged strategy of picking up ""cheap"" points and a few strategic placements (along with some luck) might be enough to win."
43,5,1,8,13,12,23,3,2,25,8,https://pastebin.com/LSXrjJJV
44,0,0,0,0,19,24,27,0,0,30,Focus on smallest number of castles that can win. Also people seem to understaffed castle 10 so include this in lineup
45,0,2,2,15,5,25,3,31,5,12,"Scarborough, ME"
46,1,4,6,12,18,22,3,3,5,26,"Slight alteration of my other strategy, mostly reversing 9/10 and  6/7"
47,4,0,6,13,13,25,1,3,26,9,https://pastebin.com/LSXrjJJV
48,3,0,8,12,12,22,3,2,32,6,A variation on another strategy.
49,4,8,7,8,13,16,4,5,22,13,I estimated how many people I would beat at every number and multiplied that percentage by my points. My goal was more than 27.5 expected points.
50,2,5,10,10,18,18,3,3,23,8,"I don't really have a great answer, but this was fun to do."
51,6,8,8,12,17,17,6,7,9,10,"I took the average of the top 5 winners from round 1, and figured most people would do a version of that, and this answer beats them."
52,1,8,9,16,1,1,1,1,31,31,"Nothing flashy.  Tried to assemble 28 from the castles that didn't get enough love last time around (2+3+4+9+10).  Left a lone straggler at the others to punish the fools that leave castles naked.  This strategy is incapable of winning big, but it wins by a small margin an impressive amount of the time."
53,4,10,6,15,18,10,5,6,12,14,First valid set of 10 numbers a d20 gave me.
54,0,9,11,13,16,3,3,3,21,21,"Try to pick up 9 or 10, because I can probably get at least one of them. and then must win 5 through 2. Three in each of the rest except 1."
55,1,1,5,1,11,23,28,3,11,16,"The last group of winners focused on castle attacking castles 7&8; this is designed specifically to counter that strategy by dropping castle 8. Anticipating that a significant number of people are likely to pursue that strategy as well, we go somewhat hard at castles 9 and 10 as well, which allows us to beat equally distributed strategies."
56,0,0,2,5,14,22,29,0,6,22,I made an algorithm that weighted the placement 75% based on what would beat all submissions from last competition and 25% based on what would beat those placements.
57,2,6,11,16,16,21,3,3,11,11,"Looked at how troop placement was divided up in the previous run-through and tried to place an amount of troops in each castle which would win each one the majority of the time, while largely ignoring castle 7 and 8.  Also tried to stay above multiples of 5."
58,0,2,11,11,16,3,21,5,26,5,"Targeting 28 by way of castles 9, 7, 5, 4, and 3. Wanted each of those castles to get at least 10 troops (to beat anyone who submits a strategy of 10s across the board, which I imagine will be at least somewhat popular)."
59,3,8,10,12,12,22,11,7,7,8,"I focused exclusively on the top five performers of the previous competition.  I noted that among those competitors, the ordering was Brett>Jim>Ken>Lukas>Cyrus (ironically, Cyrus placed last among that group).  I then assumed that this round's strategies would include the following: Brett clones, anti-Brett strategies, Cyrus clones, anti-Cyrus strategies, ""7 and 8 avoiders"", and old, ineffective strategies.  Most of what followed was guesswork and I only spent about ten minutes actually dividing up my troops.  I quickly decided to devote five more troops than Brett's strategy to each of castles 8, 9, and 10 in the hopes of outmaneuvering all of the Brett, anti-Brett, Cyrus, and anti-Cyrus strategies.  I anticipated a flight from castle 7, which has a disproportionate number of troops but left a decent contingent there to mop up those who avoided the castle entirely.  Castles 1 through 6 remain mostly unchanged from the first battle."
60,0,5,6,8,12,22,3,31,6,7,"Just a variant of the strategy I did last time. This time I am fighting for castles 6 and 8 and hope to pick up others that are not well defended. I expect people to put fewer 0,1, & 2, for castles on 9 and 10 and more 3, 4 and 5."
61,6,5,0,0,0,0,0,37,32,20,"heavy investment in most valuable positions, with some investment in least competitive battlefields"
62,6,6,9,11,13,16,8,8,9,14,I assumed that the distribution would change a little from the previous round but not a whole lot. For the top castles I chose values a few more than what would have done well earlier. For 7 and 8 I went much lower than the winners of the previous round but still a reasonable amount. Then I went down from 6-1.
63,4,6,4,11,12,4,9,4,34,12,"My first strategy was similar to the winner, but not quite as good. Seeing the distributions this time, I went for a more uniform distribution. I started with 4 at each castle, which is enough to win a lot of battles since some castles will have few soldiers so others could be loaded up on. Then, I shifted my remaining 60 troops to ensure that A) I could beat a equally distributed soldier allotment, B) I could beat someone who loaded up on the top 3 or 4 by most likely winning castle 9, and C) I could beat the previous winner."
64,1,0,9,12,15,4,21,5,28,5,"Last round, many people who did not commit many troops to an attack sent fewer than four or five. My five each on castles ten and eight, and four on castle six could gain a large number of points against such players for a small price. The last winner committed most of his troops to castles totaling 30 points. I decided to try a similar number.  I tried to avoid overinvesting in large castles because the last winner's arrangement suggested that people did so last time."
65,2,2,2,8,13,22,3,3,23,22,"I used the approximate percentage distribution from the prior results. I chose to give up the tail end of each distribution, and always capturing the minimally defended towers. Ballpark for the distribution, my average score is about 31 against the prior game players."
66,3,2,9,10,12,23,3,2,29,7,"I assumed that most people would submit deployments that perform as well or better than the winner from round 1 (against round 1 submissions). So, I wrote an algorithm that generates a large number of winning deployments against round 1 submissions and then made those compete. The result is a deployment that beats the winner from round 1 and also performs well against other winning deployments."
67,3,6,11,16,16,21,3,3,10,11,"Beating bias towards multiples of 5 by adding 1 to each castle. People are afraid of 10 and 9 so they stack 8 and 7, so those are the ones I give up on. Always have >2 men per castle (usually beats 50% of lineups right there). Players that put ~20 on castles 9 and 10 will see they were basically better off putting 5 or 6 down, so I'm expecting a lot of high single digits there. This also beats straight 10's and the old champion, which could be popular lineups"
68,1,1,7,8,20,3,8,25,20,7,started filling out numbers and they happened to add to 100.  Similar to last winning submission.
69,1,5,7,12,12,3,21,21,7,11,Gut feeling
70,1,4,11,3,16,16,16,6,11,16,I tried to build a strategy that would beat strategies designed to beat the prior curves.  Truthfully it was just a guess.
71,0,2,3,3,12,22,3,26,21,8,I built a spreadsheet to test different strategies against last year's entries plus an equal number of randomly generated strategies.  Then lots of trial and error.  This was the best performing deployment I could find.
72,4,6,8,13,18,8,5,23,7,8,"This is an over-thought plan that is designed to defeat an optimization of the data from the first group of data.  It assumes that people will not try and win 7 or 6 because lots of people tried to win 7 or 6, but it doesn't just give up the space.  In most cases it adds 1 to 2 soldiers over what is optimal in the first contest and (mostly) does not over-commit.  The assumption is that people will mostly choose a plan that was optimal in the first contest, or optimal +1.  This plan will defeat most of the best plans from the first contest, but would be weaker against ""lesser"" plans then the leaders."
73,4,4,11,16,16,5,11,11,11,11,I chose my troop deployment with the hope that proper diversification could counter an opponent that put too much emphasis on any one castle.
74,4,4,5,16,21,26,4,4,8,8,Mostly wanted to ensure I sent at least 4 troops as looking at the data from last time it seemed many players sent 0-3 troops to many castles. After that I just kind of randomly chose some of the middle castles to make a serious stab at. I fully expect to lose given I suspect others will put a lot more analysis into their plans.
75,0,5,6,8,12,22,2,32,6,7,"Randomly generated troop deployment that both does great against the originally submitted answers (it would have won round 1 overall by a comfortable margin), and also does great against *other* randomly generated troop deployments that would have won overall in round 1. Slightly adjusted manually to get even better numbers."
76,0,6,2,11,4,16,6,21,8,26,"Focusing on the higher value of each paired number (1,2;3,4;5,6...)"
77,0,0,11,14,18,22,1,0,1,33,variant of first strat. Looking for 5 wins instead of 4 by focusing on 3 and 6 instead of the pricier 9. Gave a couple more to 10 as well. avoided 8.
78,1,6,9,16,5,15,9,12,15,12,"I chose it based on an intuition that a certain number of people would pick the winning strategy from last time, a certain number of people would pick a strategy which beats that one, a certain number would pick a strategy which beats THAT one, and so on and so forth.  Like with a Keynesian beauty contest game, you want to be exactly one step ahead of most other people; no more, no less.  And, in my experience, people usually go around 2-3 levels deep on these things.  So, I generated a data set which took the original strategy and added a lot of the winning strategy, and one which beats the winning strategy, and one which beats that, etc.  Then, I calculated the expected number of net points you can get, based on this dataset, for each number of people in each castle.  After that, it's a simple evolving function to find a strategy where taking away from any one castle would cause more harm than the good of adding someone to another castle.  The remainder of my answer is a copy of the R code which I made to find this answer:

library(foreign)

setwd(""~/Voting data"")

previousanswers <- read.csv(""castle-solutions.csv"")
previousanswers <- previousanswers[,-11]
#I'm not using the text comments, and they just make things harder to read.

#Need 28+ points to win.

previouswinner <- c(3,5,8,10,13,1,26,30,2,2)

#I'm going to make a ""predicted"" dataset, baesd on the previous answers, the previous winner, and winning strategies against the previous winner and so on

#The idea is that some people will copy the winner, some people will anticipate that and make a strategy which beats the winner
#some people will anticipate that and make a strategy which beats the winner beater, etc., etc.
#I'm going 4 layers deep on winner beating.  I'm guessing a peek around 2-3.

#Winning strategies should be able to soundly beat the strategy they are set against, while retaining
#2+ in each castle.
#There is some subjectivity going into these

winnerb1 <- c(4,6,9,11,14,5,5,31,6,9)
#This will beat the previous winner in castles 1,2,3,4,5,6,7,9,10, giving 47 points
winnerb2 <- c(6,8,11,13,16,10,8,7,10,11)
#This will beat b1 in all but castle 8 and beat the previous winner in all but 7 and 8.
winnerb3 <- c(2,2,13,15,4,12,12,9,12,15)
winnerb4 <- c(2,2,3,17,6,14,14,11,14,17)

#Now to combine them together into one big data matrix
previouswinnermatrix <-  t(matrix(rep(previouswinner),10,nrow(previousanswers) * 0.20))
winnerb1matrix <- t(matrix(rep(winnerb1),10,nrow(previousanswers) * 0.15))
winnerb2matrix <- t(matrix(rep(winnerb2),10,nrow(previousanswers) * 0.22))
winnerb3matrix <- t(matrix(rep(winnerb3),10,nrow(previousanswers) * 0.20))
winnerb4matrix <- t(matrix(rep(winnerb4),10,nrow(previousanswers) * 0.10))

colnames(previouswinnermatrix) <- colnames(previousanswers)
colnames(winnerb1matrix) <- colnames(previousanswers)
colnames(winnerb2matrix) <- colnames(previousanswers)
colnames(winnerb3matrix) <- colnames(previousanswers)
colnames(winnerb4matrix) <- colnames(previousanswers)

datamatrix <- rbind(previousanswers, previouswinnermatrix, winnerb1matrix, winnerb2matrix, winnerb3matrix, winnerb4matrix)

#Now that I have my data, it's time to figure out what the expected number of points I can expect
#from each castle, for each number of soldiars at that castle.

expectedmatrix <- matrix(0,100,10)
colnames(expectedmatrix) <- colnames(datamatrix)
#Only 100 rows.  I'm precluding strategies that include 0 people at any castle.

#Now, to go by for each castle...
for (i in 1:ncol(expectedmatrix))
{
  #...and go through each number of soldiers in that castle...
  for (j in 1:nrow(expectedmatrix))
  {
    #And replace that value with the expected number of net wins with that number of people
    #+1 if win, 0 if tie, -1 if lose.
    expectedmatrix[j,i] <- (length(datamatrix[(datamatrix[,i] < j),i]) - length(datamatrix[(datamatrix[,i] > j),i])) / length(datamatrix[,i])
  }
  #Multiple each column by the value of that castle, to get expected # of points
  expectedmatrix[,i] <- expectedmatrix[,i] * i
}


#Now, to make a looped function to continue taking away from the castle with the lowest expected loss
#And giving to the castle with the highest expected gain
#Until lowest loss > greatest gain
strategy <- c(10,10,10,10,10,10,10,10,10,10)
losses <- strategy
gains <- strategy
keepgoing <- TRUE
while (keepgoing)
{
  for (i in 1:10)
  {
    #calculte losses
    if (strategy[i] == 1)
    {
      losses[i] <- 10
    }
    else
    {
      losses[i] <- expectedmatrix[strategy[i],i] - expectedmatrix[strategy[i]-1,i]
    }
    
    #calculate gains
    if (strategy[i] == 100)
    {
      gains[i] <- 0
    }
    else
    {
      gains[i] <- expectedmatrix[strategy[i]+1,i] - expectedmatrix[strategy[i],i]
    }
    
  }
  #If the biggest gain and smallest loss are the same castle, break
  if (which.max(gains) == which.min(losses))
  {
    keepgoing <- FALSE
  }
  else
  {
    #If the biggest gain is less than the smallest loss, break
    if (max(gains) < min(losses))
    {
      keepgoing <- FALSE
    }
    else
    {
      #Otherwise, evolve the strategy.
      strategy[which.max(gains)] <- strategy[which.max(gains)] + 1
      strategy[which.min(losses)] <- strategy[which.min(losses)] - 1
    }
  }
}

#Cool, that was quick.
#How many expected points can we get?

expectednetpoints <- 0
for (i in 1:10)
{
  expectednetpoints <- expectednetpoints + expectedmatrix[strategy[i],i]
}
#Based on the datamatrix I generated (which is dubious), this strategy will get 8.18 points more than a given opponent, on average."
79,1,8,2,13,0,17,20,6,27,6,"a) Challenging hard for castles 9,7,6. (If someone outbid me on one of those, It's likely that they lowballed 10 and/or 8 and I can pick those up instead)
b) For the remaining ~6 points I need to win, I ignore 5 and try to pick up any combination of the lower castles with modest deployments in each one, focusing on 4 and 2
c) ""win by a little, lose by a lot""
d) My strategy loses against (10,10,10,..,10) but I don't think that is important. It also wins against last year's winner, but hopefully it beats everyone else who is trying to beat last year's winner."
80,6,6,6,0,0,21,21,4,26,10,"Based on previous distribution, wanted a decent chance to win 10, without sacrificing much, and also to win 9, 7, 6, which would give me a win. I also wanted to maybe steal a couple points with low castles, too, hence the couple armies in the low castles. This wasn't super scientific."
81,2,4,12,16,4,6,4,4,22,26,"People normally submit numbers that are multiples of five, so I added one to the soldier count."
82,1,1,1,2,21,21,5,21,21,6,"In order to win, I'll need 28 points. My strategy depends on winning castles 5, 6, 8 and 9, which sum to 28. Assuming a number of warlords will choose a round number like 20, I've put 21 at each. Then, I divided the remainder amongst the other six castles, using the scout strategy and weighting troops towards castles 10 and 7."
83,0,6,1,2,21,22,27,4,4,13,"Selected 10, 7, 6, 5 as a main win condition with extras placed on other castles to contest them against strategies with overlapping win conditions."
84,1,2,2,13,2,21,2,33,3,21,"This is my second entry, and it focuses on countering the most successful strategies from Round 1 along with some very basic strategies (10's all-around, simple progressive, mid-focus, high-focus, etc). I focus on castles 4, 6, 8, and 10, since winning all four yields a total of 28 points. I placed small forces in the remaining castles - enough to capture or tie with many other strategies that also neglect them. I focus heavily on castle 8 because it was so competitive in round 1, though I acknowledge this could backfire if a large number of entries shift forces away from castle 8. We'll see what happens!"
85,0,0,11,15,18,22,0,0,0,34,"You only need 28 points to win, so we will focus on winning 10, 6, 5, 4, and 3 (total 28), sending troops proportional to the point totals (rounding down for #10 since people doing complicated things are more likely to concede #10). Going all-in on a linear strategy is often good in a situation where a large part of the field is trying to out-metagame each other. This may be the situation this time since the data from the last challenge was posted!"
86,0,3,13,18,18,3,23,3,11,8,"Several months have passed since the battle of a thousand armies and a new general arrives on the battle torn lands with a sizeable army behind him. He believes that the practice of sending only one soldier to battle in the hope it would be abandoned, which was common in the first war is unethical and he vowed to send at least 3 fine soldiers to each battle, if one got wounded the plan was that one would stay behind and the other would return for help. With that in mind he still had 70 troops to send out. The general was greedy and decided he liked the look of the two largest castles, one as his home and the other as a guest house so he sent a sizeable platoon to those two. Expecting to secure at least one of the two palaces he admired most he set his 60 remaining loyal soldiers to fight for 4 other palaces. He decided to send some troops to the third outpost, a small group of buildings barley worth fighting over. The forth and fifth castles also looked inviting so he sent an larger group to them. He then had 20 soldiers left over, all eager for battle. He decided that they would be best suited to attacking the seventh fort, a fine set of buildings which were reasonably contested in previous battles. He decided that this would be where his stronghold would be and decided to command the army from there. The night before the attack a trio of soldier approached the general saying they were told to attack the smallest of the forts. They thought that their attack was pointless and against many enemies they wouldn't be needed so they requested to be promoted. The general considered this that night and in the morning he approached the three soldiers and told them he agreed with them and thought they would be more useful to him in the squadron fighting for his proposed guest house. Finally he was set for battle and gave the order to attack to his officers. The army crested the hill, ready for the fight. ""ATTACK"" the general screamed..."
87,2,1,2,11,16,2,2,2,31,31,This was one of the better performers in the simulations I ran.
88,0,0,0,0,16,22,0,0,28,34,need a total of 28 to win a battle.  concentration of forces into a few strong holds and abandon all others.  this will be clearly fail against a more balanced strategy if I loose castle 6 or 5 (assumption is I would win 10 and 9 against a balanced strategy).  a tie in castle 5 with wins in the other 3 leads to an overall tie.  I thought of adding more to 5 & 6 - even to the point of completely balancing across the 4 but I think that would be a risk against anyone using a strategy similar to mine.  it's really an all or nothing approach.  curious so see what happens.
89,2,2,12,13,16,2,20,5,23,5,I decided to focus on the (9+7+5+4+3=28) strategy. I hope that this configuration will give me the five castles that give a majority. I decided to send a few soldiers to castle 10 and 8 in order to take it in the event of my opponent taking those loosely too.
90,3,5,6,8,14,13,3,5,20,23,"It had to beat two strategies- one where every troop was deployed evenly in marginal value (so, castle 10 gets 18 troops, castle 5 gets 9 troops, etc) and it had to beat the winner last time (as that's a focal strategy that lots of people will adopt, or at least adopt a small variation on). Also, looking at the distributions from last time, many people went with 0,1, or 2 troops at some relatively high value castles, so I set a minimum of 3 troops per castle to round up some cheap points- that fits with a strategy where you want to win a castle by having just one more troop than your opponent at a given castle. Those conditions allocated over 80 of the troops. The remainder were allocated split across some of the high value castles, leaving castles 7 and 8 at low levels to provide extra troops at castles 5, 9 and 10."
91,1,2,7,13,14,16,5,24,9,9,"The equilibria of the previous tournament are almost ludicrously nonlinear. My approach is to start from the previous tournament's submissions (human nature hasn't changed much in the past few months) then add in the obvious strategies - a few dozen copycats of the top five and about a hundred copies of strategies tailored to beat the previous tournament (the best one I could find was 6-6-7-11-12-21-26-2-4-5). Once I found an optimal solution, I tweaked it some more. It's nothing like the Nash equilibrium strategy will look like; but a Nash equilibrium usually winds up in the middle of the pack and I want to win. Banzai!"
92,0,5,7,9,12,22,2,31,5,7,Modified basic data; optimalization.
93,5,6,11,12,12,16,4,4,4,26,"Punt on 7, 8, 9.  Try to win the rest."
94,0,0,3,9,12,22,6,32,8,8,"Tried to place the numbers to fall in the abandoned distribution points.  Either just ahead of the low end or just ahead of the high end.  And I want Castle 8, 6, & 5 with the hope to steal 9 or 10 or (7 + 3 or 4)."
95,2,3,4,11,14,22,26,5,6,7,Modified the winners strategy but gave up on 8 and put more resources elsewhere. Figured a lot of people would follow the old results.
96,1,7,8,11,13,2,28,3,13,14,"I expect the ""abandon 9 and 10"" strategy to not be as widespread this time, so substantial resources have to be deployed there this time. I chose to abandon 8 and 6 with half-effort in 10 and 9 - the goal is to beat the people who mostly abandon 10 and 9, and split with people who fight hard for just 1 of those two castles."
97,3,6,7,8,2,13,15,1,33,12,"I aimed for something that could do well against the naive strategies, the past results, and the people trying to learn from the last winner. I targeted castle 9, sacrificed castles 5 and 8, and had a good spread of the rest. I have a good chance of getting 19-25 points in the top 5 castles plus just enough of the lower 4 to give me over half the points."
98,3,5,10,12,15,17,12,12,7,7,next level
99,8,10,1,1,1,1,1,33,22,22,"The goal of the game is not to win as many castle as possible, its to get 28 points. The easy way (looking at the graphs) to do this it to win castles 10,9,8,and 1. The hardest of these is 8 so I invest enough to beat most people on 8 first. I then invest enough to win 1 and 2 as a back up for 1. This leaves me with 49 points. I place one on the castles I'm not going for because the ROI is ridiculously high. (Around 8% chance of getting the points for 1 troop) and split the final 22 between 10 and 9 which should be enough to win most of the time."
100,1,1,1,13,16,19,2,2,24,21,"This time we're aiming for a 10, 9, any 2 of <6, 5, 4> strategy."
101,4,4,4,4,14,14,14,8,26,8,Just tried to figure out where I would have put my troops as a level 0 strategy and then one-uped all the other castles while sacrificing one of them.
102,2,2,6,12,17,12,28,7,7,7,Increasing all biggish castles slightly from last winner except 8. Trying to end amounts in a 2 or 7; seems less common than 0/5 or 1/6.
103,10,0,10,0,20,0,0,0,30,30,Intuitiveness
104,5,6,6,14,6,23,22,6,6,6,"Given the previous troop deployment, this is the optimal strategy. Assuming your readers don't learn, this wins about 90% of battles. But it may be worse if they do in fact read and learn"
105,1,3,8,5,12,22,2,33,6,8,https://pastebin.com/LSXrjJJV
106,5,6,7,8,9,17,18,6,11,13,Let Castle 8 go.... Keep something on the lower numbers and not go overboard on 9 and 10!
107,0,5,9,14,5,15,8,3,9,32,not enough time to submit too.
108,2,6,9,9,12,5,5,5,14,33,Avi Mahajan
109,4,7,4,6,13,14,14,6,19,13,I assume the bulk of players aren't going to change their strategy. I then select levels that seem to be just to the right of a large area of the curve.
110,6,4,13,10,12,14,5,11,15,10,"This troop deployment was quasi-random with a slight bias towards low-value castles and a bigger bias towards high-value castles, mostly ignoring medium-value castles, since those will probably be hotly contested."
111,7,8,10,13,14,3,7,20,7,11,Totally random distribution
112,4,5,7,11,15,18,24,4,6,6,"You only need 28 points to win, so I know that 1-7 equals 28 and I went for it."
113,2,2,9,2,7,6,27,19,10,16,geddylee1717@yahoo.com
114,0,4,12,19,25,4,5,6,8,17,https://github.com/norvig/pytudes/blob/master/Riddler%20Battle%20Royale.ipynb
115,2,2,5,8,13,17,27,3,12,11,"win a decent amount of 9 and 10 because everyone will lowball them based on the data, forfeit 8 and try to win 4-7 at a decent clip"
116,7,2,4,20,23,4,2,12,12,14,"Ideally, I will win castles 10, 9, 8, and 1, giving me 27 points. Especially for 10 and 9, a majority of people put less than 10, and those who put more usually put 20 or more troops there. To defend against someone gaining the 9 or the 8, I have put many troops on the 4 and 5 castles to gain 9 points back. In addition, I have scattered a few troops on the rest of the towers in the hopes that some people put no (or very few) troops there."
117,5,5,10,10,5,5,5,25,5,25,Need 28 points to win the battle. So I go aggressive on small numbers (1-4) and super aggressive on 8 and 10. 1+2+3+4+8+10 = 28. Left 5 each for 5-7 and 9 for in case of a steal.
118,7,10,13,15,18,8,5,8,8,8,"I first redistributed to beat the original distribution, but assumed everyone else would do that. So I redistributed again to beat that distribution."
119,0,6,8,6,18,13,3,34,6,6,"Going for close wins and major losses. Hoping to win 7-9 and 3&4. Will lose to opponents who used more than placeholders anywhere, but hopefully get lots of wins in the two groups that can help reach 28."
120,0,8,11,15,4,25,4,4,6,23,"I programmed a solver in Python to find optimal solutions for a given field by evaluating all nearest neighbors, then stepping in the best direction until no step improves the strategy, i.e. gives it a better win-loss% for the given field. In the case of 10 castles, there are 81 nearest neighbors, which can be found by adding a single troop to one castle while subtracting one from another. This strategy finds locally optimal solutions (not better than any neighbor), but by re-starting the solver from different random entries, one can be relatively certain (~95%) of having found the global optima after around 100 random starts. I used this to find all locally optimal solutions greater than the 90th-percentile entry in the original field. Since some of those entries are very close to each other (but greater than one step obviously), I filtered those for only the top solutions more than 5 steps apart to avoid repeating similar strategies. This left me with 365 locally optimal entries, which I combined with the top 10% of entries from round 1 for a theoretical round 2 field. My submission is the globally optimal solution for this ""round 2"" field. Fingers crossed!"
121,0,0,1,13,2,4,30,31,13,6,"Based on how many folks de-emphasized going after Castles 9 and 10 last time, I figure there's a minor market inefficiency there, and increased my deployments. Others no doubt noticed the same thing, so I didn't go overboard; might be enough to steal them in a few showdowns, but without putting all my eggs in those baskets. As before, the majority of my efforts go towards Castles 7 and 8, with an additional over-deployment for Castle 4. The rest are essentially punted (I gave myself a chance to steal or split on 5 and 6, just in case). Generally speaking, I feel like this gives me a chance to steal either 9 or 10 in some battles, with 7 and 8 going to me in almost all. Making sure I can take #4 is all I need to reach 28 points if I do manage to catch 3 of the top 4. It'll come down how others adjust to the realization that 9 and 10 are ripe for the pickin's based on last time around, and if they choose to put even more of their resources into the top 2 castles. If they do, then I could be in trouble."
122,6,6,4,11,13,13,5,19,10,13,I chose numbers that were slightly larger than the key clusters shown in the prior results.  I generally bumped my troops up one or two from those clusters (anticipating that others might use this same strategy).
123,3,6,8,4,13,12,17,12,8,17,Science! And maths! With data! And computers!
124,0,1,6,10,15,18,2,2,23,23,"Looked for holes and inflections in prior troop deployment data.  Decided to commit at least a couple to almost all castles (except 1), to pick up cheap points, if opponent goes 0 on some."
125,1,4,9,16,25,16,9,6,4,10,"i counted up by perfect squares, then down to 7, then used the rest.  nothing brilliant bro."
126,7,0,0,0,0,0,0,31,31,31,"It's a simple all or nothing assault. The goal is to directly seize the 28 points needed to win. The 10, 9, 8, and 1 castles do just this. Contesting any other fortress distracts from this goal. The strategy is designed to overwhelm balanced assaults on the various castles."
127,7,0,0,0,0,0,0,31,31,31,"The total number of points is 55, so a player needs more than 27.5 points to win. From  there, I decided to minimize the number of castles that must be conquered (although that strategy runs contrary to what the previous winner did) in order to maximize the number of troops that can be sent to each one.

Using the previous contest's distribution, I (not very rigorously) determined that I would only send 7 troops to Castle 1. The resulting occurrence of sending 31 troops to each remaining castle was a happy accident (although, I wanted to divide them up as evenly as possible; if I lose one castle, I almost definitely lose, so in a sense they should all be weighted equally. However, the opponent might choose to send troops based more strictly on the proportion of points that each castle offers, in which case I would have to re-evaluate my divisions)."
128,7,0,0,0,0,0,0,31,31,31,Win all my castles with troops.
129,7,0,0,0,0,0,0,31,31,31,Win the fewest number of castles needed by loading them up with troops.
130,0,5,7,9,12,22,3,32,4,6,"This has the best record against the original batch, plus a smaller batch that all have the best record against all the aforementioned deployments, plus a smaller batch that all have the best record against all the aforementioned deployments, etc."
131,1,2,14,13,13,14,4,4,4,31,"This approach aims to win with castles 10, 6, 5, 4, and 3. I'm hoping people will either avoid castle 10 or try to win it cheaply, and give less support to castles 3-6."
132,4,5,4,16,11,16,16,16,6,6,Above 50% on previous plans
133,4,6,8,11,11,12,13,6,14,15,"Simple, balanced strategy, trying to beat players who attack the middle hard and sacrifice too much at the top and bottom."
134,13,9,5,16,14,4,9,5,14,11,Because you asked me to.
135,1,3,8,12,16,5,21,2,27,5,"DAW: Too many people cared about 8 last time. I'm aiming at a 9-7-5-4-3 combo most of the time, with some hedged soldiers at 10 and 6."
136,3,6,6,7,13,13,12,8,16,16,Higher point castles get more guys.  Go a few over the even 10's because that was the pattern last time
137,6,4,6,6,0,12,0,32,22,12,I banged my head on the keyboard until something added up to 100
138,0,0,0,6,6,8,32,8,32,8,Modify from one of the best sample
139,4,4,4,18,16,14,14,12,8,6,Trying to get the mid scores + probably 1 of the higher ones
140,1,4,9,16,11,11,8,13,5,22,Compared to previous winning distribution graph
141,3,3,4,18,24,24,6,6,6,6,Angery reacts only. Shoutout to UC Berkeley memes for edgey teens!
142,1,5,10,1,15,25,1,1,30,11,"Just kind of threw some troops at it,  no big crazy strategy"
143,2,3,3,16,11,6,16,16,16,11,"I avoided placing troops on multiples of 5 and aimed to create a strong 9,8,7,4 core to get the 28 points to win.  I left troops in 10 and 5 to try and cover up any losses in the main core."
144,6,0,0,0,0,0,0,31,31,32,This is sparta
145,6,0,0,0,0,0,0,31,31,32,Only need a few victories.
146,1,3,3,5,7,3,28,10,31,9,Trying to break the 'top 3/4 castles' approach while claiming some cheap ones down the order
147,0,5,7,9,18,16,3,31,6,5,Simulated annealing using total wins against prior entries as objective function
148,5,5,7,9,12,21,27,2,5,7,"I just did a ""natural selection"" process on random walks beginning with randomly chosen top-50 (in terms of wins) strategies and taking smallish (1-3 troops shifted at a time) steps. I also did a few more walks of the winning-est strategy from the first competition. This one does the best among those (including the newly generated 'good' models)"
149,2,4,8,11,16,2,27,4,21,5,I thought it might perform well?
150,2,5,6,10,13,7,10,11,18,18,"Created a strategy to beat Round 1 Median values, then assumed that would be most popular selection this Round and chose strategy to beat that."
151,0,0,15,15,15,4,15,1,15,20,"At 55 total possible points, my goal was to get to >27.5. I chose the 3/4/5/7/9-point castles as my route, and allotted enough points to each that I could reasonably expect to win most matchups. Then it was about maximizing the scenarios where I didn't win those five. Castles #1 and 2 are only useful if I win two of my ""unlikely to win"" castles. For example, winning both would make up for losing 3, or winning 1 and 6 would make up for losing 7. So I abandoned them and put a few extra in 6, thinking that winning this one would make up for losing either 3, 4 or 5. Without doing more complicated math, I'm assuming my odds of winning castle #6 with 4 points are greater than winning any two castle with only 1 or 2 points in them, which is why I left castles #1 and 2 with 0 points. I ended up putting more than initially expected into castle #10, but it's a useful safety net against losing any of the castles below it in VPs, or even combinations of two like 7/3 or 5/4. I should probably re-jigger the safe, ""base 10-ish"" totals on most of my castles, which at 15 and 20 for many seem liable to be slightly outbid by savvy 538 puzzlers. But I'm at work and this is already a long paragraph. Cheers!"
152,2,2,8,4,18,7,21,11,21,6,My strategy is to tie for half the castles 25% of the time and tie the other half 75% of the time therefore hoping for a 100% win.
153,3,3,8,8,11,18,3,3,23,20,Deliberate near-sacrifice of castles 8 and 7 as those were the most hotly-contested from last time around allows a significant number to be sent to Castle 10 and 9 without jeopardising strength at Castles 1-6. Setting a minimum number of 3 per castle covers off matchups where 0 are sent to those locations (which made up a significant number of deployments last time around)
154,2,8,12,4,4,4,10,16,24,16,Kind of randomly. I figure people will go for the middle. Doubt I'll win but I'll contribute to the curve!
155,3,4,11,14,18,21,1,1,1,26,"I put just 1 troop each at Castle 7, 8, and 9 so that I'd win against any zeroes, but otherwise ignore the castles that had the most troops deployed last time. Then, I tried to use the data to deploy my resources so as to beat as large of a population as possible (around 80%) from the previous data set."
156,3,6,10,16,9,10,13,14,11,8,Random
157,3,5,8,10,13,3,17,19,10,12,"The previous winner was onto something, so I took a mathematical average of that strategy and two default deployments that were either proportional to the pointed awarded or any even spread of 10 per castle.   Then I tweaked the result by drawing from deployments that were unlikely to win anyway and adding to deployments that were likely to be close calls.

Finally, I compared the result to all three strategies that I mentioned above.  When it proved to be victorious each time, I figured that was good enough and submitted!"
158,1,3,8,2,15,25,28,6,6,6,To be slightly more (and then some) from what the previous winner had on the bigger castles and forfeit some of the smaller castles.
159,2,7,12,16,21,23,4,3,6,6,Looked at which placements provided the best marginal value relative to the strategies submitted last time.
160,5,10,12,15,8,5,10,10,10,15,Whim
161,1,3,4,6,4,5,25,36,8,8,"I took the first round of 538 data and then added 29000 additional random data sets. Then ran 2000 random sets through  a round robin the the with the 30,000 sets, including the first set of data,  looking for the top 10 finishers. Then I picked the one of the top ten I liked the best trying to take into account the adjustments the other players would do."
162,5,6,9,11,4,8,26,8,12,11,"Just tried to imagine how people would recalibrate their strategies after seeing the results of Round One, and optimized my strategy to beat that."
163,1,1,1,17,17,13,20,5,5,20,"I want to win any battles where my opponent declared zero.  I want to find a likely way to achieve a majority of points.  If I lose a big battle, I still want a chance at winning the other big battles if my opponent had overloaded a certain castle."
164,4,4,4,13,5,11,5,22,25,7,No time for strategy
165,2,1,5,6,18,10,25,1,15,17,Don't know
166,6,6,6,6,7,20,2,32,8,7,I think enough people will use the winning strategy from last time as a focal point and I'd like to defeat that at the more valuable castles.
167,0,5,5,5,13,8,2,32,22,8,"Generated many random inputs that would mimic what other users would choose, merged them with the last round's data set, and ran all possible permutations to find the most frequent winner.

Code and writeup on GitHub here: https://github.com/mattdodge/538-riddler-nation"
168,0,7,7,9,16,15,3,33,5,5,My boyfriend said to.
169,5,5,7,9,12,22,26,2,6,6,"Found the best strategy against the previous data set, then completed multiple iterations of improvement assuming the new data set will include similar strategies."
170,6,11,11,16,16,16,6,6,6,6,"Expected value for each position based off of previous allocations, +1 to beat the human nature of choosing base 10 units."
171,2,5,6,12,12,23,4,26,4,6,best of many random tries against previous deployment data
172,7,9,12,12,11,12,11,7,12,7,"To win, obviously."
173,0,11,3,11,16,4,21,4,4,26,"I want to slightly beat my opponent on the ones I win, and lose by a lot on the ones I lose. What's more, I want to create a targeted approach rather than casting a wide net and hoping for the best. The 'easiest' way to get to 28 is with 4 numbers... which is why I chose to do it with 5 instead, to be less popular. My target points were 2, 4, 5, 7, and 10, summing to 28. I imagine a fair amount of people will submit a 10, 10, 10, ... 10 strategy, so I want to make sure my targeting beats that, which means all of my targeted numbers must get at least 11 troops. I also want my strategy to win against 0, 0, 0, 0, 0, 20, 20, 20, 20, 20, which means that I need at least 21 troops for castles 7 and 10. Finally, I don't want to simply ignore the castles I don't want, especially the higher ones, so I want to distribute at least 4 insurance troops to any castle on the higher end of the spectrum (I'm guessing that most people will choose 3 as their baseline). I can ignore the 1 castle altogether as it's not part of my path to victory."
174,2,3,5,8,10,18,7,7,28,12,Through a thorough selection process bounded by the restriction that I needed to pick all of the number in under a minute.
175,0,2,2,10,4,15,3,33,21,10,"Way too much data analysis (Clustering, gradient descent, etc) optimizing over previous submissions and some other objective functions."
176,1,3,7,11,16,20,24,6,6,6,This is basically Brett Seymour's strategy with a bit more focus on the top 3 castles.
177,3,6,3,11,12,7,12,12,17,17,"I tried to guess, how the average Player would react to the new Intel.
For instance: it turns out, that 10 sodiers would (surprisingly) be enough to almost always win No10. So I invested a Little bit more than 10 soldiers on No10. etc."
178,6,6,6,6,6,6,6,6,26,26,People choose round numbers. Many give up on 9 and 10
179,6,6,6,6,6,6,6,6,26,26,Trying to take castle's 9 and 10 and steal any lowly guarded other castles.
180,0,6,8,11,14,17,2,33,3,6,"7 and 8 are the battlegrounds. By focusing on only one of them, you can greatly strengthen your middle game. Completely abandon castle 1 to try and sneak castle 10 from some low bidders (also the reason you need to win castle 8 and not castle 7)."
181,2,3,7,10,13,16,19,10,10,10,"Based on people responding to the results last time, I expect people will send more soldiers to castles 9 and 10 and fewer to castle 8.  I sent 10 to each of these castles, which is the total number of soldiers divided by the number of castles.  I sent the soldiers to the remaining castles in a linearly increasing fashion.  I would note that if I lose castles 8-10 I would still win if I win all of the remaining castles."
182,6,14,6,16,4,16,4,14,6,14,"Winner from last time basically followed the prevailing trend: low deployments on either extreme, substantial deployments in the middle. My strategy beats that one by collecting the ""even"" castles. I still putting a token effort into the odds so I'm not assuming automatic zeroes anywhere. I split mostly evenly so every set of 11 points has 20 soldiers (10 and 1 have 20 soldiers, 5 and 6 have 20 soldiers) while still trying to favor the middle run (the only 16's I placed were in the middle).

I hope this split will grant me the extremes values of 10, 8, 2, 1 more often than not, while putting up a fight for the middle runs. I will lose if someone tries to sweep 10, 9, 8, but since that strategy loses to last Winner I think most people will shy from it. And the majority of people seem to avoid high values on 10 and 9 last time anyway."
183,6,8,11,15,19,23,3,3,6,6,"The aim here is to think precisely one move ahead everybody else. It is not enough to come up with a strategy which beats the previous winners because everybody will try to do that, but also to come up with a strategy which beats a strategy which beats the previous winners. Hence I have increased the number of troops on 9 and 10 to 6, to beat anybody who places 4 or 5 troops. I have also anticipated a shift to focusing on the lower-numbered castles, by putting 3 more troops on them than a proportionate strategy would do."
184,2,7,2,2,16,2,5,21,21,22,"I chose to count on other people going for the lower values and hedging my bets in the few large count ones I would need to win, plus a couple troops at each castle to beat anyone who chooses to put none or just one at places."
185,1,1,8,13,15,21,23,6,6,6,"Because I wanted to win. Also, a modified deployment of #3s strategy from the last round, as"
186,3,6,6,9,17,20,4,4,27,4,"I chose castles worth 30 points to focus on, since I need 28 points or more to win. I assigned 4 soldiers each to the castles I'm willing to sacrifice, since the distribution from last time indicates that 4 soldiers is enough to give me a good chance of winning if my opponent also chose to sacrifice the same castle. For each of the remaining castles I sampled a Gaussian distribution with mean value proportional to the square of the number of points the castle is worth."
187,2,3,8,10,15,8,6,36,6,6,jamesclowes@hotmail.co.uk
188,2,4,4,15,15,15,15,5,20,5,"Try to win 9, but give up 8 and 10"
189,0,5,7,12,12,22,3,3,32,4,try to get castle (2+3+4+5+6+9 [=29>27.5]) with some effort on 7+8+10
190,0,5,7,12,11,22,2,32,2,7,This beats 1250 of the previous 1387 matches :)
191,1,2,4,14,14,16,18,1,16,14,don't fight for 8
192,5,8,9,1,1,1,1,34,25,15,"Technically, this could perform well if the opponent goes for the middle. I genuinely have no idea if this will work, but if it does, that'll be pretty cool."
193,3,3,12,3,0,20,0,0,25,34,designed a plan that would beat the last winner hoping that lots of people would mindlessly copy him
194,0,5,6,8,13,23,3,32,5,5,Historical performance^2 * Performance against those who optimized against that.
195,0,1,1,14,14,14,14,14,14,14,"Based on the previous battles, an average deployment of 10 per castle would have won the game handily. I'm unlikely to be the only person to notice this, so I figured I can win an average of half of the castles. If those are 5 of the main castles I send troops to (or I could get lucky on castle 2 & 3 with the extras), I'm sitting perfect."
196,15,0,10,0,20,0,0,0,30,25,"You only need 28 points to win, so I tried to focus on getting specific castles and not bothering to protect other castles."
197,2,3,7,12,23,33,3,3,7,7,"There will be more contests in castle 7 and 8 after last round's winner used this strategy - I decided to give up those castles and focus on either sides - Castle 4, 5, 6 as well as 9 and 10. Numbers that are 2 or 3 mod 5 are chosen because of player tendency to pick numbers divisible by 5 or are 1 mod 5 in the last battle; we could see a rise of 2 mod 5 picks here."
198,2,3,7,12,23,33,3,3,7,7,"Correction to previous submit - I think I put 8 soldiers in castle 3 rather than 7, which was intended."
199,2,2,11,7,2,14,10,15,21,16,"Ignoring castles 1, 2, and 5 will not lose me very much. However, it's best to leave  them with some defenses. I prioritize 6, 8, 9, and 10, since those alone give me 33, more than enough for a majority, and I can still lose one of those and get lucky elsewhere and settle for a slight victory."
200,1,1,10,15,20,20,0,0,3,30,"Something of an ""all eggs in one basket"" strategy. Looking at how players split up their troops last time round, I invested enough troops to more-or-less guarantee winning the 10, 6, 5, 4 and 3 castles which give me 28 points, a bare majority of the 55 (I only need to win by one point!) Then I've distributed the left-over soldiers to try and pick up the odd nine-point castle (which oddly enough doesn't seem that keenly fought over), which in conjunction with taking the one or two-pointer means I don't need to win the ten-pointer."
201,2,4,8,11,13,13,13,13,13,10,Intuition
202,6,6,6,6,6,23,6,29,6,6,"The bar chart for each castle depicts a cluster of deployments from 0 to 4, and a cluster of higher deployments. As the castle numbers get lower, these clusters merge. 6 token troops to each castle should be enough to conquer it from most players; that combined with higher deployments to castles 6 and 8 could disrupt all-high or all-low strategies. This plan loses to those that distribute troops more evenly, and many plans that have higher deployments to castles 6 and 8, but otherwise it's pretty solid, I think."
203,2,2,2,3,3,3,5,32,27,21,"I went big on the larger values because if I can win 10+9+8 fairly often, all I need is one more point elsewhere. And chances are, somebody is putting a 0 or 1 somewhere in their allocation to maximize strategic values elsewhere, I figured I might as well try to rip off some points from them at the smaller castle, try to win some easy points."
204,0,1,10,13,9,11,21,21,7,7,"I tried to win the majority of the 9, 10 battles with as little troop effort as possible (based on the relatively high number of 1, 2, and 3's).  I figure more people will dedicate 5 (or 6 to not make it an obvious number 5) to win these so I went with 7.  Beyond that, I just followed the general trend of the benevolent Cyrus Hettle ... he seemed well liked so that's a good role model."
205,1,0,3,10,5,1,1,34,34,11,I think this beats any major strategy.
206,3,3,11,12,11,2,21,2,29,6,Tried to follow similar pattern as previous winner
207,2,1,3,16,3,11,10,15,19,20,Randomly generated
208,1,11,11,11,11,11,11,11,11,11,I think that most people will think too hard about countering strategies and leave themselves weak against a fairly naive deployment. I didn't go all 10's because I figure castle 1 wasn't going to make or break it anyway.
209,1,11,11,11,11,11,11,11,11,11,Numerical consistency is super important.
210,0,4,3,15,3,16,3,31,3,22,Best result of an alternate genetic algorithm including the given data set.
211,2,2,7,17,22,22,13,4,4,7,"Disrupt strategies that rely on winning 4, 5, 6, or 7."
212,0,0,4,15,17,5,22,25,5,7,"I figure many people will send slightly more troops than the winners sent to the high value castles last time at the expense of the low value castles, so I completely bailed on 1 and 2 and tried to snag 9 and 10 more often."
213,5,7,9,12,14,16,14,11,7,5,Weighted Gaussian
214,1,1,3,11,4,13,16,8,34,9,"(Please use this submission over the earlier one I submitted if only one submission is allowed per person) A correction to my earlier submission which ensures that I beat the winning distribution from the last competition (a likely choice for people who don't want to invest a lot of effort). Otherwise the main argument is the same - win at least one of top 3, spread out troops amongst all castles, try to capture a lot of the middle (4/5/6/7)."
215,0,7,8,6,13,9,6,35,11,5,Random solution meant to help my initial submission.
216,5,5,7,7,12,12,3,23,13,13,"I chose numbers like 13 and 12 in hopes of beating people who chose flat numbers, and beating people who went 1 over to beat flat numbers."
217,0,0,0,11,11,17,21,18,11,11,Fight for the big points.
218,1,7,5,4,17,8,2,13,8,35,GA battling itself. The top half is based on the best solutions and the bottom half of the population is random.
219,0,1,4,6,8,12,24,32,6,7,Arbitrary and malicious
220,1,4,6,12,18,2,24,2,26,5,"Round 1 plan was good (75th %-tile) but not great. I adjusted by choosing a strategy that would have (a) finished in the top 10 last time, (b) defeated all of the top 5 finishers last time (many might imitate those placements), and (c)  would defeat the approximate 70th %-tile of last times' consensus (which uses about 140 troops total); my thinking is that many will try to edge toward higher-than-median from round 1 for many of their placements, but lacking 140 troops, they will decrease somewhere. Also, many may try to put 3 or 4 in castle 10 since most gave that up, so I have 5 there, but I went big on castle 9."
221,3,8,12,13,20,25,4,4,5,6,"I saw that 9 and 10 were winnable towers after battle 1, so I wanted to allocate a few extra troops to each.  7 and 8 were the most hotly contested towers, so I wanted to steer clear, but not completely because I thought others would have the same strategy as me so I sent force that could defeat anyone just scouting.  I focused the majority of my troops on 5 and 6, hoping to lock down some mid range points while poaching enough of the high value targets to ensure victory."
222,2,3,7,4,5,5,21,21,9,23,Spread it out and tried to strategically have slightly more at each castle than a round number generator would deploy.
223,5,1,1,0,0,0,0,31,31,31,"One needs at least 28 points to win. My first thought was to focus on the middle range -- castles 4 through 8, but then realized this could easily fall to a strategy that focused only on castles 10, 9, 8, and 1. The goal isn't to maximize your expected score, it's to maximize the number of times you score 28 or more. Looking at the overall distribution, this distribution looks like it will win a good portion of the time. I throw a soldier to 2 and 3 in case somebody beats me out for castle 1."
224,0,2,2,14,3,2,22,31,19,5,Always leave the most number of doors open.
225,1,1,9,11,14,11,15,12,15,11,I ran 29 random and weighted-random scenarios and optimized for maximum wins.  This configuration along with some minor variations won 28 of 29.
226,2,6,7,11,2,2,2,2,33,33,"Based on everyone targeting the 6-8 range last time, I decided to go all in on 9 and 10. If you lock those 2 up, then you only need another 9 point to win. I decided to target 4-3-2 to get those points. 2 points were put on all remaining numbers in order to guarantee a win on the rare 0 or 1 someone else puts up."
227,0,6,7,11,12,21,3,31,4,5,A bit modified basic game from the data with optimalization
228,0,0,11,11,16,3,21,3,31,4,"assumed people would gravitate to even castles, and round numbers."
229,8,8,12,16,1,12,2,2,19,20,"This whole strategy is entirely centered around beating people who try to use the predominant strategy from last year, while also attempting to beat most other teams. Since middle road castles like 8, 7, (6ish), and 5 were heavily contested by these competitors, I'm only sending several troops to each of these so no one gets any points for just sending 1 there, except 5 which they can tie. I then send 11 to six to beat those who only send 10 or less while not sending too many there as well, while sending 18 to 10 and 9 to guarantee their capture. That leaves me 48 troops for castles 1, 2, 3, and 4. So that would be 12, evenly divided, but I'm taking some away from 1 and 2 to bolster 4, so 1 will be 8, 2 will have 8, 3 12, and 4 20. Since I don't like sending the most troops to 4, I'm gonna make it 16 and send those extra 4 to 10, 9, and 6. Yippee."
230,3,5,7,16,13,21,22,3,5,5,"Using the data from the first challenge (and my primitive Excel skills), I built a spreadsheet that helped me simulate battles against the original batch of responses. I used this to come up with several different deployments that were more successful than the first round's winner. I then identified, to the best of my ability, a deployment that allowed me the most wins against the original data while also  beating all of the ""optimized"" strategies I identified for the first round."
231,4,6,8,11,11,10,13,11,14,12,Brilliance.
232,1,3,4,12,4,13,2,2,27,32,"Overload on 10, 9, 6, and 4. Tried to pick numbers just above ranges of what people picked last time."
233,3,4,5,9,12,2,22,31,6,6,"I drew over the top of the old graphs how I predicted the distribution would change with people going after value points harder. Overall I think this is the biggest factor that will change the graphs, although I'm also betting on elevated levels of 4-castle YOLOers (10-9-8-1 or 9-8-7-4) to hard counter this trend.

The more I looked at it, the more I realized how brilliant the previous winner's strategy was. I ended up just adjusting that same strategy for people going after value points harder, while ensuring it will still beat those YOLO nerds."
234,1,3,4,8,12,13,16,25,6,12,I wanted to win.
235,0,3,5,6,18,23,2,32,6,5,"I started by looking at the last battles data My thought was that this time the data would to some extent converge to last years data as more people go with the strategies that appeared effective in the last battle. I used Excel VBA to simulate the last set of battles. I then weighted how well each plan did based on its win% in the last battle. I then reran the whole series of battles assigning weights to each strategy based on its winning percentage. 

After thinking for a while I decided to weight each plan using its win % squared. This mean that if a plan won 80% of its battles (the best plan were around that) it would count as .64 while decent plans (those with a win% of 60) would count as .36. In addition any plan that won less than 20% was considered to be a ""troll"" plan and I counted those all as if they had won 60% since I assume there will still be more people who troll this round as well.

I then ran each strategy again to find the best weighted winning strategy from last round. It turned out to be (0,3,4,7,16,24,4,34,4,4). 

Surprisingly the top strategies were still pretty much the same. I expected strategies that went for the 10 or other counter strategies to be more effective but even with much higher weights they were not.

After this I ran another macro that look at every combination of 1 increase and 1 decrease to pick the best strategy. This continued until I got t the point where the plan did not get a better weighted winning percentage with any possible change which is mf final answer.

Interestingly the same answer actually also won if I used winning percentage to the 1.5 power. This confirm my strategy."
236,2,2,12,21,21,21,3,6,6,6,"Disrupt strategies that rely on 3, 4, 5, 6."
237,4,5,7,8,10,5,23,25,6,7,I expected people to put slightly more troops where deployment was low and slightly fewer troops where deployment was high. I also expected people to try and account for that shift somewhat.
238,3,5,6,10,13,18,1,1,23,20,"Concede castles 7 and 8 which were most over-contested last time, then distribute troops in order to beat the average placement from last time at each other castle."
239,2,15,15,15,2,1,1,11,16,22,"Attempt to capture 10 and 9 for majority of points 8 and either 4,3,2 or 4 and 3 and 2, the rest to capture if 0 sent"
240,3,3,13,2,4,1,27,30,10,7,"This strategy was found after simulating tournaments with an agent-based model, where warlords who succeeded enough would eventually reproduce (with the possibility of a mutation in the offspring) and those who were not successful died. On Monday, May 29, 2017, there will appear a blog post describing my strategy on https://ntguardian.wordpress.com"
241,2,4,6,8,12,22,5,31,5,5,"Ran a genetic algorithm to determine the optimal solution to beat previous submissions, fitness was weighted toward submissions with a higher win percentage."
242,10,0,0,0,0,0,0,30,30,30,I don't need big wins. All I need is 28 points. I figured that I would be able to win the 1-point castle most of the time with 10 troops there and then hope that most people won't be sending more than 30 troops anywhere.
243,10,0,0,0,0,0,0,30,30,30,"With the caveat that deploying 30 troops for the biggest three is very unlikely, I should guarantee myself 27 points (which is just under half available). I only need to win just one more point to triumph hence deploy the remaining to castle 1 (although there may be some game theory that in the event of others deploying this strategy I should deploy to castle 2 or 3 to take the win over them also)."
244,4,6,1,18,20,23,1,2,2,23,I tried to dominate in areas that I don't think will be strongly contested.
245,0,1,5,2,5,16,28,30,6,7,"I ran a genetic algorithm against the previous submissions, which started to sub in its own creations to test against."
246,5,0,0,0,0,0,0,28,32,35,"I am trying to use the most efficient way to 28 points (minimum needed to win) assuming that most players will distribute their troops to more castles. The fastest way is to win castles 10, 9, 8, and 1. I've distributed my troops proportionally to their value."
247,8,8,9,9,10,10,11,11,12,12,I don't know.
248,0,2,3,3,4,22,26,3,31,6,"Chose to focus on 3 of the top 5 castles to score most of the winning points with smaller bands to the lower castles to score the remaining points needed to win. Small bands were also sent to castles 10 and 8 in case of easy victories. Exact numbers were chosen based on the distributions from the previous competition. Since more than half of submissions in the previous competition had no more than 2 soldiers at castle 10, I would expect many competitors to now send 4-5 soldiers to castle 10. I sent 6 soldiers to castle 10 in hopes of beating that strategy."
249,6,7,8,9,10,10,11,12,13,14,"I was lazy, and also noticing that divvying up the troops relatively evenly seemed not to have worked out, I assumed that people would be gearing up for the semi-spaced setup by putting a ton of troops in the bigger ones, so I split mine up evenly, with a bigger emphasis on the more valued castles, simply because I get more incidental points that way."
250,9,9,11,11,9,11,11,9,11,9,"This plan is designed to beat a plan that would slightly superior to the previous winner (ie a plan that was based on the the previous data set) in which soldiers are randomly assigned to dominate a few high scoring castles and make a ""college try"" at the smaller castles."
251,12,12,12,12,12,8,8,8,8,8,Not much thought - I just wanted to see how this somewhat regular distribution would fare against a system where a lot of people are placing between 1-5 people in a lot of the castles.
252,3,5,1,6,5,11,26,14,17,12,Gut instinct mostly + some game theory
253,1,1,1,3,4,7,32,37,7,7,"Low end - trying to win only if matchups are low as well, since they are low return. High (and 6) I put low to not waste soldiers on matchups where everyone clustered lots of soldiers. However I chose 7 for these because most people going for this strategy like lower numbers up to 5 based on the chart. 7 gives me 5&6 soldiersas a buffer. I put relatively high numbers on 8 and 7 because this alone is enough to secure a big chunk of points - those I do well against likely 'wasted' more soldiers on my matchups for 9 and 10, while those I do poorly against probably put fewer points than me in 9 and 10 which I will potentially take."
254,4,4,3,2,14,2,26,33,5,7,"Where the first dropoff of deployments in the last round took place down low and up higher going after 5, 7, 8 and hoping 9 or 10 or the lower castles will get it through there."
255,4,3,7,9,7,8,22,23,9,8,"With this strategy, I likely foolishly assumed that the general troop deployments used by others would remain generally constant with a few fluctuations in the initial and subsequent castles."
256,0,0,6,6,6,6,32,32,6,6,"My strategy is to capture one of castle 7 or 8 as well as all castles that my opponent is not focusing on.  This is based on two observations.  First, castles 7 and 8 are involved in most strategies (soldier distribution is weighted towards the right, with few sending 0-3 soldiers).  Second, 4 soldiers would have been sufficient to capture most castles in cases where your opponent didn't focus there (the left hand side drops off by 4).  I anticipate that many will send forces of 4-5 to castles they aren't focusing on and that their strategies will rely on capturing one of 7 or 8. If they are planning to win by less than 14, capturing 7 or 8 will swing the points in my favor, provided I've picked up all the points they are not focusing on."
257,4,6,4,11,4,16,4,21,4,26,"The strategies that worked last time worked, in part, because so many people had the same idea to leave castle 10 un- or under-guarded. I decided not to replicate that strategy, because its revelation as so common may make it obsolete. It's impossible to compete everywhere, so I chose to compete for the even castles, worth one point more than the odd ones. Last time, un- or under-guarded castles tended to have 0,1, or 2. This time, such castles will likely either replicate the strategy or maybe increase to 3. I chose to keep my under-guarded castles (the odd castles) guarded with 4. That way, I'm not giving away any of these castles, but am only devoting 20% of my resources to them. I may pick up some odd castles that way. I then allocated increasing resources to each of the even castles (6,11,16,21,26) in light of their increasing worth."
258,0,0,3,15,16,19,3,32,6,6,"Well, obviously Castle 9/10 are the most important, with 6 each I should get many wins. In order to get 28 points, Castle 8 is a safe call with Castle 6/5/4 as highly likely wins."
259,1,1,1,6,6,14,27,28,8,8,Seemed like a good idea at the time
260,0,0,0,1,12,21,3,32,27,4,best distribution based on last round's submissions (as far as i can tell). fingers crossed for lots of resubmissions
261,2,5,6,8,10,20,31,6,6,6,"I'm playing a spread, as had successfully won before. I anticipate a little more resistance for the top points...but not too much more."
262,12,7,10,10,10,6,11,8,13,13,"I randomly assigned each soldier to a castle. Each castle had an equal chance of acquiring each soldier, regardless of that castle's value. The reason for this is to confound and confuse any game theorists who might try to anticipate my strategy. An alternative strategy I considered, which may have been too predictable to work, was to assign each soldier randomly and uniformly to each victory point (i.e. weight the castles by their victory point values)."
263,0,5,7,12,12,21,3,32,3,5,Genetic algorithms against historic data and optimal strategies found in the previous loop
264,2,6,8,12,18,3,27,10,10,4,"Send at least 2 to every castle. I'm expecting people to send few troops to Castle 10 (since that strategy failed last time), so I'm trying to send slightly more than a ""few"". In general, assuming people will use the winning strategy from last time and aimed to beat that strategy."
265,12,0,0,0,0,0,0,30,29,29,Need 27 points to win. Target the fancy castles hoping people follow winners strategy from last time.
266,5,5,5,5,10,15,5,5,20,25,I tried to do the converse of the previous winner's strategy.
267,2,5,6,6,12,6,17,17,17,12,"I figured most people would either a) mostly copy the winner from round 1, b) try to beat group a, or c) try to beat group b.  I aimed to defeat a mix of those groups.  I also noted a bias in favor of round numbers (multiples of 5), and so biased myself towards bids that are one or two higher than a round number, in order to beat both people who fall prey to that bias, and people who try to exploit it themselves."
268,3,6,8,3,17,22,28,3,4,6,"To marginally beat strategies that are replicating the previous winning strategy. Further, this strategy aims replicate ideas of the previous strategy by placing high values on winning certain castles, while ensuring that weakly held castles with 0-2 troops are defeated in all cases."
269,10,10,10,10,10,10,5,5,15,15,It beats most people at most castles
270,6,8,11,11,14,22,0,0,22,6,Intuition
271,1,5,1,11,5,15,9,19,14,20,"Focus on 10, 8, 6, 4 without yielding any"
272,4,5,4,4,4,19,22,16,11,11,?
273,1,2,3,3,4,5,6,31,35,10,"I drew over the top of the old graphs how I predicted the distribution would change with people going after value points harder. Overall I think this is the biggest factor that will change the graphs, although I'm also betting on elevated levels of 4-castle YOLOers (10-9-8-1 or 9-8-7-4) to hard counter this trend.

The more I looked at it, the more I realized how brilliant the previous winner's strategy was. I ended up just adjusting that same strategy for people going after value points harder, while ensuring it will still beat those YOLO nerds."
274,7,9,11,13,13,15,17,5,5,5,Most troops are committed to castles 1-7 to hit 28 points. 5 troops should be enough to compete in castles 8-10 based on the prior results
275,3,0,0,0,0,0,0,32,32,33,"I need to win 28 points, and I'm anticipating heavier resistance at the higher numbered castles."
276,0,0,1,10,23,24,25,2,7,8,just winging it
277,7,12,11,13,11,0,13,8,12,13,Ran a quick simulation in R studio
278,0,0,0,0,16,16,2,31,4,31,"9,8,6,5 is the best deployment to get to only 4 castles but this swaps my 9 and 10 castle deployments because people seem to think ""everyone is going for castle 10, so no one goes for it. So I think it is worth a shot this way too.

Divisible by 5s seem to get a lot of play so I went one above them. Tolkens in 9 and 7 as backups for when one of my main 4 castle battles fail."
279,3,3,14,20,20,20,0,0,10,10,_™_àŠ—ŠÈä´Ù
280,3,4,6,4,4,4,7,31,31,6,Try to definitely win castle 8 and 9 while squeaking out whatever other castles people are ignoring.
281,0,1,1,11,13,13,1,1,27,32,"28 points wins the game. The focus here is to win 19 points for the big 2 castles a majority of the time. Then find 9 other points. The easiest way (I think) is to win 2 out of 3 of castles 4, 5, and 6. That will always get you 9 more points. I threw an army at castles 2, 3, 7, and 8 just to cover myself against similar strategies where those castles are completely un-attacked by my opponent."
282,12,0,0,0,0,0,0,29,29,30,The top 3 castle account for 49% of the points so I decided to hit them hard. The 12 troops to castle 1 should be an easy win and put the total beyond 50%.
283,2,5,8,3,6,15,15,14,17,15,"I figured people would react to the first graph, so people would try to edge out the distribution from the first graph, so I tried to anticipate that and edge out the edge-outers. Or some such."
284,2,2,3,3,15,15,15,15,15,15,Maximize higher Castles
285,2,2,3,3,15,15,15,15,15,15,"Didn't want to try to predict which castles others would go all-in on, so I went with a normal distribution with 90% of my soldiers among the top 6 castles to try to get to 28 points by winning what I can there from any under defended castle. I abandoned the bottom 4 castles as they such a small proportion of the points, just sending a token amount to avoid getting it completely stolen."
286,0,4,7,14,12,22,3,2,32,4,"In Excel, I started with last round's winner strategy and looked for ways to improve.  I ultimately found what I believe to be the best possible allocation vs. the 1387 entries submitted last round.  I then tweaked just slightly so that my entry beats that ideal entry in a head to head matchup, thinking many people will derive and submit that exact entry."
287,4,5,8,16,18,23,15,3,2,6,Combination of best responses to old answers as well as against a first iteration of best responses to the old answers.
288,1,5,10,9,12,22,2,3,32,4,"I found it after brute forcing then fine tuning. I randomly allocated 100 soldiers in 10^5 realizations, found the allocation that had maximum % wins against the armies listed on the github, and found the ""optimum"" around this set. This set won roughly 87.9% of the time. Probably not a global optimum, but heck, let's see how it does."
289,2,3,3,6,6,16,21,31,6,6,"Based on the previous models of deployment, it's clear that most people threw away the #9 and 10 castles, so using 6 soldiers on these would beat anyone using 5, which is a number that seems likely to be used. In addition, using 31, 21, and 16 on castles 8, 7, and 6 respectively was done to beat anyone using a round number. Castles 5 and down were mostly thrown away, with the idea that returns are great diminished. Winning castle #10 is worth as much as the bottom four combined, so more emphasis was placed there."
290,0,3,3,3,16,16,21,26,6,6,"Popular spikes at 0,1,2 across the board, and generally spikes on multiples of 5.  This makes 2, 3, 6, 16, 21, 26 appealing choices to win most at least cost. Strategy is to win 8765 and at least one of 432...OR to lose 1 of those but win 9 or 10."
291,1,2,5,7,10,1,27,35,6,6,"Started with last round's winning deployment.  Moved one troop from each of the low yield castles (1-5) each of the high yield castles (6-10). Then assumed that most contestants will continue the strategy of winning castles (1-7) over (7-10) and moved 2 soldiers from each of 1-6 and distributed evenly (8-10).  This left castles 1 and 6 unguarded, so i moved one soldier each from 9 and 10 to cover these."
292,3,3,3,8,13,14,18,26,6,6,"Be competitive across all castles, focus on moderate to high-value targets, and avoid deploying troops divisible by 5. Previous battle showed that troops tended to be deployed in groups of 5. However everyone else also has this knowledge, so some deployments have several additional troops assuming most forces are deploying multiples of 5 +1 or +2. May my troops show no mercy to my enemies."
293,2,5,8,11,3,17,3,21,25,5,"The winner last time gave away three castles (6, 9, 10) to higher bidders, while still betting a few soldiers on those castles to pick off opponents who abandon those posts entirely. I'm doing the same, with two modifications designed to defeat my fellow copycats. First, I'm choosing to give away different castles (5, 7, 10). Second, at castle 10, I'm going with a slightly higher threshold to defeat the majority of abandoners, who will likely skew to a slightly higher deployment there vs. what happened the first time. This doesn't feel like a perfect strategy, but it feels like a good use of my time to stop here rather than obsessing & second-guessing the whole thing. :)"
294,3,6,6,8,12,12,14,16,16,7,"In this second wave, people will over-emphasize or under-emphasize 10 and reduce their numbers on 9, 8, and 7. I chose my values to ""ride"" just above the curve and precisely tie last time's winner."
295,0,6,7,12,12,21,3,31,3,5,"Yet another submission.  I allowed the max solders at one castle to be a bit larger, even though no previous solutions were sticking at the boundary.  Oddly, I started getting better solutions.  This one has 1202 W, 4 T, and 107 L for a total score of 1204 out of 1313 (same 1313 as previous submissions)."
296,5,14,6,17,13,1,4,2,30,8,Random solution meant to help my initial submission.
297,0,6,7,12,12,21,3,31,3,5,"For the first game, this is the optimal strategy (one of the three, but against each other, this is the best)."
298,0,6,7,12,12,21,3,31,3,5,"This is the best deployment I could find for the first battle. I'm hoping not much will really change. I found ti using an evolutionary algorithm where I ""mutated"" my best guess repeatedly."
299,0,6,7,12,12,21,3,31,3,5,This is the best strategy I found against the submissions from the first one. Seems reasonable to assume that a lot of people will under value 9 and 10 again.
300,0,6,7,12,12,21,3,31,3,5,"Assuming nobody else changed their strategy, this is the best I could find."
301,0,6,7,12,12,21,3,31,3,5,I used an algorithm to optimize the deployment against the first round entries.
302,1,1,9,2,2,2,27,31,2,23,"Using the numbers from the previous version of this riddle, I calculated the average and then added two standard deviations to that. I focused on Castles 3, 7,8, and 10 as it's a relatively cheap way to get to the necessary 28 points. Giving those castles two standard devs above the average, I attempted to put 2 soldiers in the other 6 castles and then normalized and made some tweaks to account for rounding."
303,2,5,7,11,11,21,2,31,5,5,Spent too much time dorking around in Excel searching for enlightenment
304,5,6,7,9,12,23,27,1,5,5,"Strategy #2, trying to beat first 7 castles."
305,3,8,17,14,4,14,6,13,15,6,Good question.
306,4,6,8,10,10,10,15,10,10,17,"I'm treating the game theory as irrelevant cause it isn't predictive of future moves since the information remains the same. What I'm banking on it people overcompensating by changing the weighting of their troops so this deployment will forfeit certain castles but will outweigh them in enough others to hopefully stack up some points. I won't win every match up, but should win some."
307,0,0,0,0,16,16,2,31,31,4,"I focused on 9,8,6,5 as that is the fewest castles to get to 28 electoral college votes, umm... err, I mean victory points. I also wanted a few backup chances on anyone going zeros on castle 10 and 7 and there seemed to be a slight spike on troop allotments divisible by 5 so I went one above that to weed out the lazy commanders"
308,4,4,12,16,22,22,5,5,5,5,Going hard for castles 3-6
309,0,10,7,10,0,0,10,21,21,21,Get top 3 + 1 other for 28.
310,4,6,8,10,12,14,1,1,21,23,"Forfeit 7 & 8 which were winners last time.  Proportional for the rest, adding troops saved from 7 & 8 evenly."
311,0,0,0,0,0,10,30,35,10,15,Tried to beat last year's winner
312,4,6,7,8,9,10,11,13,15,17,"Bigger castles worth more points, so sent a few more there"
313,6,11,8,6,7,14,10,15,13,10,"I made sure each castle got a minimum, then rolled dice."
314,1,1,3,3,7,21,26,21,11,6,"Don't leave any without troops, fight hard for mid range (6-8), more than just 2/3 at 9 and 10 (I expect many followers from the last winners strategy)."
315,0,1,3,4,5,6,33,36,6,6,"I ran a crucible function in which strategies were selected based on their behaviour to beat strategies and convex mixtures of strategies. Rather than a genetic approach, this should ensure that the strategy chosen will beat a good chunk of the naive strategies as well as the (perhaps higher?) number of well-thought-out strategies. I hope that the number of crucible rounds chosen was chosen aptly, as it somehow encapsulates the number of metagames ahead my opponents think."
316,2,3,3,4,6,11,26,26,12,7,"My goal is to win castles 7,8 the majority of the time. I mainly ignored castles 1-4 and felt I could make up for it by a few extra troops in castles 9-10 to win those around a 50% clip. Overall I tried to stay away from multiples of 5 as those will be popular numbers and lead to less points."
317,1,1,1,1,14,14,1,31,31,5,"I made sure to put 1 in each castle in order to get free points from people who put 0, and at least a split from those who do this same strategy. I put 31 in both 8 and 9 because I wanted to make sure that I beat someone who puts a whole number (30). 5 should win me 10 most of the time, but if it doesn't, 9+8+6+5 is enough to take the game."
318,5,6,7,8,9,12,15,12,12,14,"This deployment directly counters distribution of soldiers based solely on the values of each castle, which I expected would be a commonly used strategy."
319,5,7,7,7,7,7,15,15,15,15,Tried to get a couple high value ones with uniform moderate troop deployment and then tried to get a few lower ones with a uniform low troop deployment.
320,1,2,10,3,4,10,14,17,19,20,I think that this is the most effective way to deploy my troops overall.
321,1,8,9,12,12,19,1,2,32,4,"Avoids the fight for 10, 8, 7 in order to have better chance on 2 through 6"
322,1,0,3,0,13,6,21,21,10,25,"I ran a simplified, randomized 2000 king tournament in Excel and the above strategy was the winner"
323,9,2,3,3,4,1,3,33,36,6,optimised against previous results
324,4,5,8,4,11,9,13,15,14,17,Divinity
325,3,3,3,3,3,10,30,33,6,6,"I hope to barely win castles 9 and 10, win the big battles at 7 and 8, and mop up the smaller ones if they are left undefended."
326,2,3,8,11,1,1,31,31,6,6,"Looking at the distributions from the previous attempt castle's 9 and 10 were either the most contested or most thrown so I'm sending only 6 to each to get easy victories if they're thrown, but not wasting too many troops if they're contested. Instead I'm sending more troops to 7 and 8 to secure what should be more guaranteed victories for the troops I'm expending. I'm essentially throwing 5 and 6 and instead putting the troops towards 3 and 4 where I feel I have more guaranteed points. 1 and 2 are low troop counts for the low points, but still putting points towards them to snag easy points if other people throw them. I also chose to use odd/not perfectly rounded numbers (e.g. 6 instead of 5, 31 instead of 30) in a bid to dodge anyone who had similar thoughts to me."
327,3,4,7,7,7,7,7,9,22,27,I want to be sure I at least have a chance of winning each castle by sending at least 2 soldiers into each castle. I figure a lot of people will see the numbers from last time and send at least 1 soldier to each so I'm trying to stay ahead of the game. I figure a lot of people will spread their troops out sending 5 or 6 to a few castles and my goal is to win each battle by as small a margin as possible to maximize my 100 troops hence the 7s are prevalent in my strategy.
328,0,0,0,0,17,22,23,0,0,38,Try to hit 28 by winning on 4 numbers.
329,2,2,2,6,16,26,5,6,31,4,"tried to prioritize 6s and ones, to beat people who gravitate towards 10s place and 5s place"
330,1,4,3,2,12,13,2,27,30,6,"I went with a similar strategy to the winner of the first battle, but concentrated on a different set of numbers (9,8,6,5).  If all of these castles are won it would total 28 points which is what is needed to win a particular battle.  Although using 2 or 3 soldiers on castle 10 would win a significant number of times based on the first battle, I think people will end up adding a few to that castle based on that data and therefore I added a few more than I thought others would add.  I am willing to concede the other castles for the most part, but will still win them a reasonable amount of time."
331,6,3,2,2,2,2,2,27,27,27,"10+9+8+1=28, which is a majority of the 55 points needed."
332,2,2,3,12,4,4,30,4,34,5,Hazy battle plan
333,0,0,0,0,18,21,25,0,0,36,Sounds good
334,6,7,11,12,0,23,28,0,7,6,"Two principles: never fight a land war in Asia, and never go in against a Sicilian when death is on the line.  Also, tried to anticipate that other players would adjust around the prior distribution, and then adjusted around their anticipated adjustment."
335,0,6,7,11,12,21,3,32,4,4,"This is my final submission.  My last two submissions were very similar, and optimized to score well vs. the Round 1 entries, minus the obvious ""losers"" (1313 remaining entries --- I removed plans with less than 100 soldiers, plans that couldn't win 28+ points vs. *any* strategy, etc.).  For this submission, I added 200 ""fake"" round 1 entries, 100 each of my last two submissions.  This submission was optimized against the 1513, instead of the 1313.  It scores a clean sweep against the ""fake"" entries (200-0), while only scoring 3 points less than my previous 2 submissions against the 1313 ""real"" entries (1201 out of 1313 instead of 1204 out of 1313).  So, it seems like a decent ""next level"" strategy (trying to think one move ahead of the ""field""). I'm anticipating more overall entries in Round 2, that will include several entries optimized against the Round 1 plans --- someone else will win this I'm sure (my submissions are all ""over-fitted to the data""), but I'm anxious to see what the winning submission looks like, and how far behind my plans are."
336,0,0,14,0,0,0,26,30,0,30,picked the easiest looking quartet worth a majority
337,1,2,2,2,12,22,26,3,3,27,"I have been torn between two extremes. On one side, one could assume a comparable distribution of deployment plans from BFRN Round 1. On the other side, everyone thoroughly looked at the data and came up with a strategy to have a high win percentage against BFRN Round 1's troop distribution. I am banking on the troop distributions being close to what they were in BFRN Round 1, and that most people aren't going to dive deeply into the data.

I know some people will do that, and they likely will have run simulations and determined an optimal strategy. I mostly just used trial and error and compared my strategies to the data set from last time. I'm confident that I'll have a winning record (above .500), but not really confident that I'll have a top 5 win percentage."
338,3,4,6,10,13,3,23,3,30,5,"Eyeballed the distributions from round 1 and kept it simple. Want to win castles 1-5,10 >50% of the time and nothing more. Concede 6+8 to all but the absolutely undefended and attack and win 7+9."
339,0,0,3,6,13,9,6,35,23,5,Random solution meant to help my initial submission.
340,5,6,7,8,10,12,20,1,15,16,"I might be meta-gaming a little too hard, but I figured I wanted to win 10, 9, and 7 against the majority of players. I figured having above-the-curve bets on 1, 2, and 3 would help me win at the margins on matchups that would otherwise skew to even. The winner last time tried his hardest at 8, so I decided not to fight that and let that help me accrue a soldier advantage at other castles.  This is more on feel than anything else -- no way to predict the meta except to use the past meta, but everyone else is doing that too and there's no way to predict how they'll do so."
341,10,10,10,10,10,10,10,10,10,10,This is just too simple.  It may just win
342,10,10,10,10,10,10,10,10,10,10,gut feeling :-)
343,1,1,1,1,16,20,25,10,2,23,"Looking at the previous dataset (game theory be damned), I picked a 4-castle combination of 10-7-6-5, and allocated enough troops to be in the 80th percentile for each. The remaining 16 troops I distributed to the other castles so that each was in at least the 20th percentile, but also so that they got at least 1 troop each."
344,10,10,10,10,10,10,10,10,10,10,Uniform distribution always wins!
345,10,10,10,10,10,10,10,10,10,10,"I notice a flaw in the game - I can submit as many answers as I want. If I know that my solution beats 10, 10, 10, 10... 10, and I know that 10, 10, 10, 10... 10 beats the winning solution from last time, I can just submit a bunch of 10, 10, 10, 10...10 solutions under my name to stack the box and try to pick up more wins where others might lose."
346,10,10,10,10,10,10,10,10,10,10,Why not?
347,4,5,15,2,1,27,10,10,5,21,Random solution meant to help my initial submission.
348,1,1,7,3,5,5,5,21,23,29,"Castles 3, 8, 9, and 10 equal 30 of the possible 55 points so I am hoping to win those castles in most battles. I left 5 men in castles 5-7 so if someone overloads on one of the castles I want I should be able to recoup my points there. I am expecting a shift after the last battle to make castles 9 and 10 more competitive, but probably not enough to totally abandon the mid-range castles, which I am willing to lose most of the time."
349,5,6,7,8,9,10,11,12,13,19,Just cause
350,1,3,6,0,2,3,26,31,22,6,"I got confused when making a previous entry, thought other people might have as well, so I doubled my data set from the one you provided and optimized for all previously submitted sets backwards and forwards using stochastic modeling."
351,0,4,6,9,12,0,27,32,5,5,Crush enemies.
352,5,7,5,8,10,11,13,13,14,14,I used a genetic algorithm to find a good solution.
353,3,6,8,7,16,16,2,33,4,5,"Wish I didn't see previous answers, tried to base mine of both them and what others would do based on them.  Recipe for a cluster"
354,1,2,3,1,19,21,23,1,23,6,"I'm a lawyer in training which is to say my math skills are less than stellar.  I figured the key was to try to choose a spot that had the largest incremental decline.  For instance, last time adding three troops to castle 10 if you had none would have been a lot more valuable then adding 5 troops to castle 9 if you were already at 3.  I then tried to compensate for the fact that other people would be doing this."
355,3,4,6,11,15,4,26,4,23,4,"Looked at the most successful setups from last time, create a setup that would beat those setups, since many will try them. Somewhat even distribution, with emphasis on Castles 4, 5, 7, 9. Going heavier on 9 as not many did last time, so will sacrifice 8 instead."
356,2,2,2,2,12,7,17,22,22,12,At least 2 per castle to win any that opponent abandons.  Then use mid level numbers to try to pick off as many high ones as possible or force opponent to spend significantly higher
357,0,7,8,6,13,9,6,20,26,5,Random solution meant to help my initial submission.
358,5,6,7,8,9,11,12,13,14,15,The best way to keep someone from out-thinking you is to not think.
359,3,3,3,6,3,16,26,26,8,6,Ran against previous results to optimize results. Changed up some to based on assumption that people would do that same.
360,7,9,10,2,4,7,11,22,10,18,Sam Holton
361,1,3,5,7,9,20,25,10,10,10,Seems like a good idea at the time.
362,1,6,9,13,16,21,0,0,31,3,"I saw that many strategies loaded up on boxes 7 and 8 (either focusing on the top 3 or the middle few), and that there was relatively less competition for 9 than for 10, so I allocated, roughly proportional to how much they contribute to getting me to 28, so I would win 9, 6, 5, 4, 3, 2. I saw that most people who put more than me on lower values left their higher values completely empty, thus my thinking that I can win castle 10 with just a few folks there on all those who totally ignore it."
363,7,10,12,13,14,14,0,0,15,15,"Previous winner's solution was to focus on the middle part, while leaving 9 & 10 undefended and focusing on a select few castles.   My assumption is that many others will try to copy this.  Intent is to therefore leave the middle undefended and have a blanket defense for the others."
364,1,2,4,6,15,2,28,32,5,5,Trial by error
365,0,7,8,6,13,9,6,26,20,5,Random solution meant to help my initial submission.
366,5,5,0,0,0,0,0,30,30,30,Banking on people neglecting the highest point castles
367,3,4,5,9,13,10,16,29,5,6,Think people will model similar to last round so tweaked a little off that
368,4,16,4,16,16,4,16,4,4,16,"Based on the previous results, it seems like there were a lot of instances where people placed a token 2-3 on castles that they did not see as decisive to their chances. So I decided to place a minimum of 4 on every castle hoping to be able to win against people who are taking a more concentrated approach. I donŠ—Èt think putting an even distribution of straight 10s is going to work because itŠ—Ès an easy strategy to counter. So I decided to arbitrarily select a pathway to 28 points (2+4+5+7+10) to be my concentration, trying to sidestep the relative popularity of 8 and 9, and evenly distributed the remaining soldiers to these five locations. I also made sure that my combination would at least beat the last winning combination, in case a bunch of people try to submit that strategy in particular. I doubt it will work, but it would be amusing if it did.
"
369,3,3,3,3,17,30,3,3,30,5,"My strategy is to stay one game theory step ahead.  This time, I think stategies are going to converge.  People will mimic the prior winner's and/or use the first dataset to develop and test strategies. I did exactly that, developed a set of strategies that did well against the first dataset; then I developed a strategy to beat those strategies."
370,3,5,8,1,1,15,2,2,30,33,I tried to emulate the opposite of the winning strategy from last time.
371,0,5,6,9,12,1,26,31,5,5,"I built a tool that could test any deployment against all the attempts from round 1, plus repeats of the previous top 5 and minor variations, as I guessed some people would just make very minor tweaks to these this time round.

The tool would also then test all 90 movements of a single soldier from the first deployment, take the highest scorer, and start again with that deployment until it reached a (local) maximum score.

For starting points, I took the previous top 5, plus some random deployments to see if I could improve on them by chance - I couldn't.

A couple of deployments stood out as the best, but I suspected other players might find them (who knows), so I fed them back into the test set and re-ran the process. This is where I ended up."
372,12,0,1,1,1,1,1,25,28,30,"Last time, nobody went for the highest castles, including the winner. If I do, I should beat many of them."
373,0,1,2,2,2,22,26,32,3,10,"I took the original data set. I made a table of how many strategies each number of soldiers would beat at each castle. ie 5 soldiers in castle 1 would beat 1175 strategies. this created the function w(x,y) where w is the number of wins, x is the castle and y is the number of soldiers.

I then used that to calculate how much each group of soldiers is worth x=number of the castle y= number of soldiers p=points. 1387 is the total number of strategies. 
p(x,y)=((x*w(x,y)+ (x/2)*(w(x,y)-w(x,y+1))/1387)

For this for formula there is a mytic 101st solider who beats everyone

I then calculated at each x,y the value of each solider by calculating
p(x,y)/y
and the incremental value of each solider 
p(x-y)-p(x,y-1)

I graphed the later to see any spikes where one more solider means a lot. Using the graph a created a cutoff of  .3 and whenever a new solider and using the latest point each solider was worth .3 I recorded those numbers. Then left me well over 100. I changed to cutoff to .35. The left me with 91 soldiers so I looked for places where the drop off wasn't great so I add the one to series 6 (incremental value .33) and  one to series 8 (additional value .15). The remaining 7 soldiers didn't have any real good places to go so I sent to all to Castle 10 guess that because it was under fought for last time it might get pushed outward.

using p(x,y) for my strategy i came up with a total expected point value of 33.60 well above the need 27.5 points to win 

With more time I might be able to find a more optimal strategy. looking just at the p(x,y)/y and taking the highest number of soldiers where each solider is worth .275 (total points needed/100) yield exactly 100 soldiers but gives only an expected value of 27.79 points. 
"
374,4,6,8,8,9,8,15,19,15,8,"Looking for a bell shaped distribution, with a little hump"
375,1,7,2,2,11,15,21,31,5,5,"Analyzing the top 5 finishers from the first event I found that the 5th placed army was actually positioned to be the most successful, with a few minor tweaks to add wins on 9/10 at the expense of 5/6.  Against the original data set, this deployment would have finished with a record of 1205-17-166."
376,3,6,1,12,15,22,1,2,3,35,"I started with some analysis of the previous top performers teams and their common traits. First, I looked at the number of soldiers that they deployed per point available for each castle, so that I could compare between castles. This showed that the tops teams put a minor number of troops (~0.2-0.3 soldiers/point) at three of the largest castles, attacked two of the largest of castles with a high ratio of soldiers (~3.5-4.0), and used the remaining soldiers on the lower castles with a lower but still fairly high ratio of soldiers (~2.5-3.0). For comparison, if you were to split soldiers evenly between all points the ratio would be ~1.8 soldiers/point. The top teams were targeting about 28-30 points, while still sending soldiers to each castle. After completing this analysis, I realized that the players did well, because their strategy was able to beat the average player. Being able to predict what most people will do and having a strategy that can beat it is an important factor in winning. Finally, I tested out some strategies, trying to use the trends I had found and settled on one of the better competitors."
377,6,0,0,0,0,0,0,51,24,19,Based exclusively off the results in the prior round.
378,0,0,8,0,23,26,31,0,6,6,Poor intelligence
379,4,5,5,1,10,15,20,25,7,8,2cd level counter to the winning deployment previous.
380,0,6,7,12,12,21,3,31,4,4,"I ran a genetic algorithm to identify the optimal strategy based on prior submissions. If people deploy troops in a similar way this time, this strategy should perform well."
381,3,6,9,10,16,18,25,5,3,5,"Troop deployment was broken down by a number of factors. The risk/reward of placing a high number of troops for a x amount of points, the percentage chance with respect to past data on winning a battle for a castle with a certain number of troops, and the distribution of troop placement in the previous event."
382,5,7,0,0,0,0,22,22,22,22,"Top 4 castle get all the troops, higher than 20 deployment of the higher points castles to beat anyone else using my system, and another one added to beat those following my system with only one iteration. No point wasting troops on lower point castles, leftovers given to them to maybe snag a few points"
383,4,3,2,16,3,21,21,6,3,21,Assumed most people would avoid the castles that were ignored in the previous riddler in fear of others thinking they would be the obvious option.
384,0,0,3,6,13,9,6,23,35,5,Random solution meant to help my initial submission.
385,2,3,0,4,0,19,21,0,25,26,"basically winged it, with some sacrificial 0s and some minor deployments to steal some weak castles."
386,2,4,4,9,7,13,9,18,12,22,"I wanted a distribution that would beat 3 principal options: a flat distribution, a linear distribution, and an exponential distribution -- calculated as linear increase * 1.26 for evens and *.74 for odds rounded"
387,0,0,0,0,17,20,2,27,31,3,"Targeting an exact win by 28 victory points, so chose a rather arbitrary set of four numbers which give this sum: 5,6,8,9. Decided not to use any troops on castles 1-4 since winning one of them won't make up for a loss of one of my core targets, but did dedicate a handful to 7 and 10 since they can save me if my opponent leaves them defenseless."
388,3,1,9,11,15,21,3,2,32,3,It seemed like a good compromise of hedged bets.
389,2,5,8,12,13,22,2,2,31,3,"Others' new strategies fall into three categories: similar to previous top strategies (1), similar to strategies that previous top strategies beat (2), and similar to strategies that previous strategies did not beat (2). I wanted a strategy which would do good against all three groups. First, I recognized that this round was a whole new game. The fact that everyone could see the previous strategies (especially winning strategies) would surely change how people thought and therefore influence their choice of strategy. I figured many (if not most) would not look too closely at the data and would simply choose a strategy similar to the winner strategies, so I had to beat these (1). With this in mind, I sifted through the data and made a google spreadsheet that would allow me to quickly test strategies against the previous game data. I looked at the 200 or so strategies that beat the top strategies, thinking these would beat the influx copycat strategies, and tested them. I found a few which beat all 5 top strategies and fairly high overall number of victories. Making small adjustments here and there, I created this strategy which in the previous round would have won 1211 games, making it the winner. I believe it will do well against strategies in group (1), (2), and will do okay against the (3). Unrelated, I would guess the game theoretic ""winning strategy"" is a mixed strategy where probabilities are related to the weight of each castle. Hope your vacation was nice!"
390,2,5,6,8,11,14,16,14,15,9,Castles 6-9 total 30 points. Need 28 to win.  Focused troops there while still sending at least 2 troops to every castle.
391,5,6,7,15,12,22,22,1,6,4,"This is an update to my previous strategy. Turns out a brute force algorithm showed a far better strategy. The same rules applied: I used the previous entries as a training set to test strategies against, and chose the strategy that won the most games."
392,4,4,5,8,10,14,4,21,18,12,"I based it on the data from the first war, specifically the median, mean, and mode for each castle. I didn't have enough soldiers to cover them all, so I chose to sacrifice relatively well defended castle 7."
393,1,3,1,1,11,1,31,21,24,6,"Ceding most 10 matches, but ideally beating a chunk of people who had same thought!"
394,0,0,0,0,18,18,1,31,31,1,"Giving up on Castle 10 but still trying to go for the win with only 4 castles I can win with castles 5, 6, 8 and 9.  Send more troops to 8 and 9 since those will be tougher battles.  Then divert 2 troops to castles 7 and 10 just in case my opponent sent no troops to those castles since those are the most valuable of the castles I ignored."
395,5,4,8,9,12,13,10,27,7,5,"Graphed all previous results. Determined wins per added soldier, deployed inflection point +1"
396,0,0,11,13,15,21,0,0,0,40,"Third variation.  Try to guarantee castle 10, get 18 more with 4 lower cost castles, ignore everywhere else"
397,0,0,0,0,17,19,26,0,0,38,"Win castle 10, and what appeared to me (after looking at last round stats) to be the least contested way to get 18 more points. Know that I lose to outliers who beat me at castle 10 (and realize an overcorrection from players who realize 10 was undercontested last round may be coming) and won't win many matches if I tie or lose in the middle, but think its okay to concede those rather than dilute strength with token opposition in castles I don't care about"
398,0,0,8,2,11,15,23,32,4,5,"Based on prior castle deployment created a ""winning strategy"" by trial and error in a spreadsheet. Then, to approximate more informed players in round two, took the top 100 strategies, and added them each five more times to the overall set. Finally, manually tweaked deployment from there to maximize wins against entire boosted set."
399,1,0,3,10,8,12,4,9,25,28,Evolutionary algorithm said so. github.com/TedSinger/blotto
400,0,6,7,12,12,21,3,32,3,4,"Yet another submission.  This one moves a single troop from Castle 10 to Castle 8, and achieves the same score as the previous submission (1202 W, 4 T, 107 L, 1204 out of 1313 possible, same 1313 plans as previous submissions)."
401,0,6,7,12,12,21,3,32,3,4,"I stole this pattern from Diarmuid Early. He and I were both searching for an optimal strategy after getting the results from the last battle.  I came up with a strategy that won 1248/1387, but Diarmuid's won 1274.  

I'm operating under the assumption that any attempt I make to guess how people's strategies will change upon seeing the data will probably be misguided."
402,2,2,9,2,2,2,17,18,23,23,"Avoid round numbers, have at least 2 soldiers everywhere"
403,0,6,7,12,12,21,3,32,3,4,"I ran a simulated annealing process to determine a troop allocation that would have won as many battles as possible in the previous game.

If this allocation was used in the previous tournament, it would have won 1272 battles - a staggering 91.7 win rate! Note that the previous winner only achieved an 83.5 win rate.

I am making a (faulty) assumption that this tournament's distribution of group allocations will be the same as the previous tournament's distribution. We'll see if that assumption is good enough or if what worked last time no longer works."
404,1,1,1,15,21,22,5,24,5,5,No real strategy. SAC
405,0,6,7,12,12,21,3,32,3,4,someone told me this was a good combination
406,5,7,9,2,2,13,27,2,28,5,"Get to 28 points, by not conceding any castles but take avantange of others willingness to do so. Predicting 1-3 and 10 as most likely to be conceeded. Predicting 4-9 to be the highest invested in, I placed troops in a way to get the most points out of the middle numbers. Hoping that when I get beat for the middle numbers, I'll get castle 10 and 1-3, and when I win 6,7, and 9, I can win 1-3 or 10 to get me over the top."
407,0,0,0,0,5,30,10,40,5,10,idk
408,8,2,2,2,2,2,2,22,26,32,"There are 55 points available, so the way to win is to get at least 28 points.  One way to get to 28 points is to get the three most valuable castles (8-10) and least valuable (1) castle.  I put 2 soldiers at the other six to ensure a lone soldier can't capture them."
409,3,4,5,4,4,4,32,34,4,6,"4 is more than most are willing to use as token forces, also other reasons"
410,2,0,3,0,0,0,0,33,31,31,"Go for broke. Win 8,9,10 and either 1 or 3."
411,1,1,2,3,20,3,3,3,31,33,Deploy to beat my best startegy.
412,1,3,4,6,6,12,12,30,13,13,Started out going with 13's because people are superstitious but then started overthinking things.
413,11,11,4,4,4,4,4,11,21,26,"Hit the high castles, as well as the low ones, get a winning sum, and lowball the rest."
414,0,5,7,9,12,1,26,31,4,5,"St. Louis, MO"
415,3,8,10,12,13,15,16,14,4,5,Needed ascending numbers for the values with at least some troops in the top castles.
416,0,0,0,0,15,16,2,31,33,3,"I'm going for 9+8+6+5, and hoping to pick off 7 and 10 from people who leave those empty or nearly empty.  I figure the bottom 4 castles are unlikely to be decisive, so I will abandon those."
417,1,1,1,1,12,15,17,20,22,10,To win
418,2,2,2,17,2,3,28,3,36,5,"As this is the second round, most people will probably congregate around the main strategies (power castles + poachers). By having fewer power castles, both my poachers and my power castles are stronger. I am counting on fewer people choosing an even distribution, which will easily destroy my strategy."
419,0,0,0,19,0,0,27,27,27,0,arad.mor@gmail.com
420,3,5,6,10,9,18,24,12,8,5,"It was somewhat random, but I tried to use a general's intuition as to where my troops would be most needed."
421,1,3,5,9,11,13,17,18,12,11,"I wanted to cover 10 on most of the top castles.  8&7 seem underguarded, so I want to capture these.  Hopefully I can win either 10 or 9, as well as 5 or 6 to win the game!  I think this is a good distribution, I started with the number of the castle for each, and then I added with my intuition, with trying to get just enough to carry.  If I do well though (like 60% or better) I'll be impressed."
422,6,6,6,6,6,6,6,46,6,6,Trying to steal a few other castles from most strategies that only send a few to 5-6 castles and loading up on the most popular choice
423,3,3,3,8,15,25,31,2,5,5,"Most of the focus is on 7 and below, with some reserve troops on the high numbers for easy points if my opponent gives up on those completely. I figure most people taking the easy point strategy are going to go with 3 or 4 troops, so I lose some strength on the 8 and low numbers to get 5 on the 9 and 10."
424,4,4,0,0,0,0,0,27,31,34,"Win 8, 9, and 10 outright and either 1 or 2.  This wins me 28 or 29 out of 55.  Hope that others put their troops in the middle."
425,0,0,2,2,11,21,3,31,26,4,Brute force computation finding a deployment that did better than all of the entries in the last contest. I've described this here: http://blog.rotovalue.com/fighting-the-last-war/
426,3,6,0,3,11,11,18,13,17,18,Because the prophet muhammad speaks through me
427,0,0,0,0,20,25,0,25,30,0,I wanted to consolidate my troops on the lowest possible combination to reach 28 pts.
428,2,2,2,2,2,13,26,2,24,25,"I considered the distribution of scores from the first time, and decided to give up on any major point getting on the first 5 castles.  Instead focusing on four of the top 5 castles.  I essentially randomly chose 8 to send a scouting party to (just in case) and leaned into castle 7, 9, and 10."
429,1,2,3,8,10,20,21,23,6,6,"I figure enough people will try to split to taking 10/9 that I can take 8/7/6 from them. While other people are going to try to do beat the ""2 in 9/10"" strategy with 3/4, so I'll send 6."
430,1,1,4,12,12,10,25,25,5,5,Math
431,7,13,0,15,20,20,0,0,0,25,"To win, you only need to get 28 points, so I focused on hitting that number exactly and put no additional troops on excess castles. I selected 9, 8, 7 and 3 as the castles I would intentionally forfeit, and sent troops to secure every other castle. After making that decision, every castle is equally important in order to win a battle, so I distributed my points with a number hopefully conservative enough to beat out a large number of opponents."
432,3,5,7,9,14,25,25,4,4,4,"I over committed to the middle, giving up the top end. I tried to make sure that I didn't lose the entire bottom though because I needed to make sure that I didn't lose to the 1,0,0,0,0,0,0,33,33,33 strategy."
433,3,8,8,2,12,20,17,20,4,6,"Last time, a lot of people put 0 for castle 10, and got taken advantage of by the people that put only 1 or 2. This time, I bet a lot of people will try to take advantage of THOSE people by putting 3 or 4. Well, I'm putting 6, so I can take advantage of all of THEM! Hah!

I put 4 on castle 9 because it was easier to count, having put 6 on castle 10.

I put 20 on castle 8 for a similar reason. It is easier to think in multiples of ten.

I figured castle 7 is worth about 3 less than castle 8, so I put down 17.

6 is my lucky number, so I gave it a lot.

As for the rest, I kind of just put down random numbers, except on castle 4, because castle 4 is unlucky."
434,1,6,8,11,5,5,27,27,5,5,Similar to what I did last time but with the many excess troops I placed on 9 and 10 redeployed to 7 and 8
435,3,4,5,10,9,12,15,20,11,11,Randomly by looking at previous distribution maps
436,2,4,7,12,16,22,0,2,32,3,With the earlier battle plans I maximized the win percentage taking into account that you need an integer amount of soldiers in each castle and that you have just 100 soldiers. This battle plan had an win % over 87% against battle plans that had 100 soldiers (I discarded the ones with a different amount of soldiers since it's not logical)
437,2,9,1,15,5,0,19,18,18,13,Quick simulation in Rstudio.
438,3,2,4,4,3,24,26,3,4,27,I used pure intuition. People here are going to be better at analytical strategies than I am.
439,3,6,3,3,11,4,28,32,5,5,Looking at previous results.
440,1,1,3,4,10,13,17,8,34,9,"Modified version of previous strategy - focus on securing 1 of 8/9/10 with >1/3 of troops, small but non-trivial support on other two to capture unguarded/poorly guarded high value castles. Wide support - at least one soldier on every castle, take advantage of those with small support. Significant support in middle castles as backup against opponent winning at least 2 of top 3."
441,0,0,2,7,14,11,27,19,15,5,Trained a simulation to determine the most successful deployment strategies and iterated against various results.
442,2,6,8,12,15,18,28,3,4,4,"My assumption is that many people will base their new strategy off of the winning strategy from last time or one of the contenders, or will implement similar strategies to that. Alternately, there are still the possibilities of people submitting the average number of troops (or similar, such as sending 0 or 1 to castle 10 and then the average * 1.2 to the remaining castles). So my strategy is focused on beating similar strategies as last time while not losing to the averages.

I'm assuming the way people will try to adapt the strategy of the winner is to do one of the following: apply similar metrics but with different castles contested (sending 2 to high value noncontested castles, about 2 x Value troops to high value must-win castles, and about 1.5 x Value troops to low value castles); OR implement a strategy that strictly dominates the winner of last time. And some will still send in things similar to the average.

My strategy is designed to win high value castles where neither of us are trying hard to win (sending 4 instead of 2 to castles 9 and 10, and 3 to castle 8). Where I contest must-win castles, I've added 2 to the winner from last time to beat out someone who adds 1 troop over the winner or applied a similar point multiple to the number of troops I'm sending (castles 4, 5, 6, 7). And castles 1 and 3 are contested with similar numbers of troops somewhere between the average and the winner from last time.

In head to head matchups, this ties with the average number of troops and strictly dominates the winner and any strategies similar to the winner, unless they do something similar by sending more than 2 troops to high-value castles that they aren't contesting."
443,4,8,16,20,6,6,4,17,4,15,"I focused on beating the previous winners' castles by small margins, and losing by large margins to castles people would think to invest highly in (i.e. 9, as the previous entries were quite low)"
444,3,0,3,4,0,22,27,31,5,5,"You only need to win 28 battles so all castles won should at least add up to 28.

Based upon previous data, 6, 7, 8 appear to be hotly contested while not having a strong plurality of ""1"" troops. Many people appear not to try for 10, perhaps because everyone assumes everyone else will try to win 10.
"
445,5,5,5,5,5,5,15,20,20,15,I think there will be some different strategies based off of the results of the first battle. I need to have slightly higher minimum soldier counts for the lower castles (I expect the mode for those castle to shift higher by 1-2 soldiers). I also decided to more evenly distribute my soldier counts rather than randomly selecting a few guaranteed winners.
446,3,3,3,3,16,16,16,15,20,5,Random strategy. Not a real thought
447,0,5,6,13,14,21,1,31,6,3,Used an algorithm to generate deployments that perform as well or better than the winner from round 1. This happens to be the best deployment I could find against round 1 submissions.
448,4,4,4,4,4,4,4,33,4,35,"Last time, the key was to focus on just enough castles to hit 28 and to basically abandon the rest. I'm hoping to trump that strategy by poaching either the 8 or the 10 castle (assuming most people will include one of these in their focused-upon castles) while still claiming every single castle that my opponent leaves abandoned."
449,2,3,2,10,2,11,17,3,22,28,"To capitalize on some of the bigger castles, I had to pretty much ""sacrifice"" some of the castles by sending in only 2 or 3 token troops (just in case the opponent only sent in 1)."
450,0,5,7,9,13,3,26,3,31,3,"Contesting 7 and 9 most strongly should work against a) people that copy the last winner's strategy and contest 7 and 8 since I'll win 9, they'll win 8 so I start a point up if the low-value castles are close and I put extra on 7 to win that as often as possible or b) people that try to contest 9 and 10 since I'll lose 10 but win 9 since those people probably will have more on 10 than 9 and then hopefully have more left for the lower castles than them. I also put 3 on the castles I wasn't contesting since a lot of people are likely to a) put 2 since that was successful last time or b) put 3 like I'm doing, so this way I beat and tie those people without wasting that many troops."
451,0,0,0,12,0,0,26,28,30,4,San Jose
452,1,2,4,7,11,15,22,21,11,6,"Castles 7 and 8 provide the median points of the 55 available. The farther away a castle was from 7 and 8, the fewer troops I assigned it."
453,4,5,6,7,8,7,17,19,11,16,"I looked at the charts and went above what a large portion put by one or two, while not betting on winning any one in particular, but instead to try to win at least 28 points (4, 7, 8, 9, 10).  As long as can win 3 or 4 of the above, I can win.  In addition, many people will see 9 as a path to victory and will go for it."
454,0,0,3,3,19,21,3,23,25,3,"Need 28 points to win - chose to invest troops in Castles 9+8+6+5 as the cheapest way to get to 28, with some opportunity troops sent to 10, 7, 4, and 3 to pick off any lightly contested by the  opposing strategy.  I favored trying to win 4 key high value castles over 5 or more ""cheaper"" ones because I figured a strategy with fewer troops at a larger number of castles just has more ways to get knocked out.  I modeled out several different strategies against random opponent troop deployments (not ideal, but I was in a hurry) and this seemed to be the best overall strategy.  (Note: I tried submitting a plan earlier but ran into a security warning from my office internet related to the google doc, so I'm assuming you didn't get that one.  Forgive me if this is a duplicate!)"
455,3,2,2,8,11,13,22,27,6,6,"Essentially the same deployment I used last time, but tweaked a little bit. I found it very difficult to come up with another deployment that would be effective against every one (or even most) of the handful of strategies I expect to see. My guess is that there will be a lot more highly distributional setups that aim to win with a very specific set of castles (I strongly considered a 10-7-6-5 or 10-9-4-3-2 strategy.) I'm excited to see how this turns out!

"
456,4,4,5,5,5,31,31,5,5,5,GG
457,0,6,7,12,12,21,4,31,3,4,This was the most optimal solution for the last time I found via brute force search.
458,3,4,6,7,10,15,18,19,11,7,An attempt to mimic but also beat the winners last time.
459,1,7,10,12,2,17,2,22,23,4,"You need 28 points to win. Castles 1-7 are worth 28 points, and Castles 8-10 are worth 27 points. I want to get 14 points in each group against most armies. I assume most people are going to optimize to copy/beat both the previous median & the previous winners. 

Based on these two principles, I think the best opportunities for points are Castles 2, 3, 4, 6, 8 and 9. Except 8, these were all undervalued. And I believe the group will shy away from 8 because it was the most hotly contested last time. I expect to lose 1, 5, 7 and 10 most of the time. I put token forces in 1, 5, 7 and 10, and pump soldiers into the other 6 Castles."
460,7,8,0,0,0,0,0,25,30,30,28 points wins
461,1,1,4,8,15,5,26,30,5,5,I looked at the previous winner (which many will choose) and I tried to beat that by one or two for the high point castles.
462,3,5,6,8,4,18,17,28,4,7,I did the math
463,0,22,11,11,11,0,11,11,12,11,"Putting 10 across the board beats the current champ. Sacrifice the first castle to beat the other people who think of this. sacrifice 6 to double up on 2 because 8,9,10 needs one other castle to win."
464,1,1,1,1,17,20,1,27,30,1,Tried to find the fewest number of castles to attack to equal 28 pts (a majority) and deploy # of soldiers proportional to their value and then put 1 on each of the remaining castles in order to snag extra points from anyone who puts 0 on them
465,2,6,8,8,16,17,13,21,2,7,"I put several on each castle to beat anyone who chooses to put none. Then, I selected some of the middle ground castles to get a good number of points up on."
466,2,4,4,12,17,23,27,3,4,4,"This is my don't overthink it too much battle plan.  I figured out how many points each entry would score, and then took the top 699 entries (total points, not Winning percentage).  I eliminated entries that used less than 100 soldiers and had 690 entries.  Then, through a bit of trial and error, I think that I successfully maximised the amount of points a battle plan could earn against those soldiers.  On to round 2."
467,4,4,4,5,12,12,23,25,6,5,"I considered the distribution results of the last war, assuming the distribution would remain pretty consistent.  I chose a number that would beat most opponents no matter the point value of the castle."
468,2,2,0,8,5,19,14,20,14,16,It seemed robust against a variety of counter strategies.
469,2,3,4,5,11,11,20,31,8,5,I wanted to win.
470,4,1,6,4,1,1,19,30,19,15,I just want to win... and be victorious... and have my name live in GLORY ON THE 538 WEBSITE!! ARE YOU WITH ME?!?!!... AHHHHHHHHHHHH!!!! ~|--------------->
471,2,2,2,6,11,16,16,16,21,8,"Tried to maximize the odds of greater than 5 point castles, while conceding the 10 pointer"
472,1,1,2,3,3,3,3,35,11,38,"Get 10 and 8, and then coast to victory."
473,2,2,4,6,11,16,21,26,6,6,With castles 5-8 I can get most of the way 26 of the 28 points needed to win. Core winning strategy will be to win those and put enough on 2-4 to pick up the other 2 points I need. There is also lots of value putting 6 on castles 9 and 10 to cover incase I lose one of my core castles I will likely steal one of those to make up for it.
474,2,4,5,11,3,14,21,4,4,32,Trying to gerrymander my way to 28 points
475,3,3,11,3,3,3,21,23,3,27,i just looked at it
476,5,7,9,11,13,18,25,4,4,4,"Based upon knowledge of the previous winning plans, I planned accordingly.  I liked the strategy used by the third place in the Battle for Riddler Nation (Round 1), and attempted to win Castles 1 through 7 (for half +1 points), and only send a small number of troops to Castles 8, 9, and 10.  However, as some of the best strategies from Round 1 sent only 2 or 3 troops to Castles 9 and 10, I wanted to send 4 troops to those castles to slightly outnumber any smaller scouting parties also sent to those castles."
477,2,3,5,5,10,10,15,30,10,10,Sorta strategy... but not really
478,0,0,5,5,5,5,30,40,5,5,"From the last battle, capturing castles 8 and 7 were the key.   Sending bigger scouts up and down hopefully enough to secure enough points to win."
479,2,2,2,2,2,26,5,27,27,5,Just by looking at the distribution and trying to see what I would do and then how to beat that.
480,1,7,10,12,13,19,5,26,5,2,"This distribution wins against a large number of the entries from the previous version, as well as the winner and similar strategies. It is easy to enter and I'm counting on there being a large number of submissions made in reference to the winner or ignoring the other information."
481,0,0,0,6,4,4,25,25,11,25,Maximizing opportunities to get 28 points
482,1,8,7,9,13,0,23,30,3,6,"This randomly generated strategy had the best win rate I could find against the previous dataset (of the previous 1387 strategies, this wins 1192 of the matches)... I think."
483,2,7,10,12,15,3,28,15,4,4,for glory
484,6,1,7,13,13,22,1,1,33,3,"Random strategies generated and tested against previous dataset (I think it wins 1212 of the 1387 matches, a 87.4% winrate)"
485,2,5,6,7,7,9,15,19,23,7,The vibe.
486,1,3,3,8,5,13,1,18,24,24,"I distributed my first 55 soldiers according to each castle's numerical value (10 to 10, 9 soldier to 9, etc.). Then I made another distribution that way, but only to castles 8, 9, and 10. I distributed the remainder to the top castles and the even numbered castles, hoping to strengthen my plays for the most valuable castles, and in hopes that people might cue into the last winner's placement and devalue top castles and 6's in this go-round. Finally, I decided that I would realistically pretty much never win castle 7 with 7 soldiers. So I decided to simply send a single soldier (to beat anyone not contesting it at all) and redistribute the other 6."
487,3,2,6,10,3,16,22,3,31,4,"I figured many people would try to set up like the previous winner, or in a manner to beat the previous winner, so I wanted to set up in a manner to bear both of those types of players (2 orders removed)"
488,2,1,7,1,8,1,1,26,26,27,Shut up don't talk to me I won.
489,3,5,7,9,12,3,25,27,4,5,"Took inspiration from the last winner. Increased the number soldiers on castles 10, 9, and 6 as those may not be won as easily the second time around. To balance things out, removed some soldiers from the castles with heavy deployments."
490,2,2,2,13,13,23,3,34,4,4,"I agreed with Ken in the last round -- what's the use in narrowly matching your opponent's troop populations when you can focus your attacks more clearly?  I knew that plenty of people would be basing their deployments based on the same data I saw, so I tried to mix it up a bit.  I put 4 on the last two castles because I assumed that most people would try to best the leaders' troops from last round by only one point."
491,0,5,7,9,12,1,26,31,5,4,"This is my 2nd submission.  My 1st submission scored 1176 out of 1313, this one does slightly better, with 1181 out of 1313 (1178 W, 6 T, 129 L).  The 1313 are the GitHub plans from battle #1, minus some ""clear losers"" (i.e. couldn't get to 28 points, used <100 soldiers, etc.).  As before, this may not be the global best vs. those 1313.  If I find improvements, I'll submit them.  I'm sure I'm ""over fitting the data"", but oh well. :)"
492,0,5,7,9,12,1,26,31,5,4,trial and error modification on previous winner
493,0,5,7,9,12,1,26,31,5,4,"Use simulated annealing to try to find the optimal deployment given the list of deployments from the last competition. Then append that deployment to the list (simulating someone who did the same thing that I did) and repeat for a while. This assumes that people will take the last battle's results into account.

(Simulated annealing: take a deployment, make a random switch, and test the results against all other deployments. If it's better, continue from the new deployment. Occasionally continue from the new deployment if it's worse Š—– don't want to get stuck in local minima. )

I also made sure it beats last time's winner, in case many people play that.

This is not the optimal deployment for the last battle's results (> 91% is possible, though it still would have won) but it's the best one I found that has good performance for both the original list and the list containing good players."
494,0,5,7,9,12,1,26,31,5,4,Optimal under previous deployment distributions
495,0,5,7,9,12,1,26,31,5,4,Took previous winner's spread and tweaked it to get ~90% win rate using the data provided.  Hoping that history repeats itself.
496,0,5,7,9,12,1,26,31,5,4,My boyfriend said to.
497,4,2,4,3,5,8,17,18,29,10,No particular reason :)
498,1,1,2,3,5,8,13,21,34,12,Fibonacci.
499,0,0,0,14,2,0,26,26,31,1,"I already submitted one entry based on ""gut"".  I thought I should do something more method-oriented.
This time, I wrote a genetic algorithm as follows:
I chose 1000 ""random"" configurations, each constructed by placing troops 1-by-1, with the chance that a troop goes to a castle proportional to 1+n with n the number already chosen to go to that castle (""Bose stimulation"" so the occupancies behave as in a bosonic system of 100 particles in 10 wells).

Then I repeatedly held a tournament between my 1000 configurations, recording the best one and keeping the top half.  Each of the top half was kept once exactly and once ""mutated"" by randomly removing 1 soldier and putting him back in with the same (1+n) method, 100 times.  These were then the configurations used in the next round of the algorithm.
After 1000 tournaments, I had 1000 tournament winners.  I played a final tournament between these winning strategies, and submit the one which won that tournament.
The winners of ""normal"" tournaments are mostly of the form, with a few castles heavily fortified and several with less fortification.  But the winner of the ""tournament of champions"" is always of the form, with 28 points worth of castles heavily attacked and a few stray troops sent to other castles.  So this seems to be a strategy to use when the other strategies have been ""battle tested"" to at least some extent.
"
500,3,3,9,3,3,3,22,23,3,28,"Need 28 points to win, 10+8+7+3=28.  After distributing 3 soldiers to each castle, I was left with 70. I distributed the remaining 70 troops between my 4 vital castles by determining their importance. 10/28=35.7%. 35.7% of 70 is 25, so I added 25 troops to castle 10."
501,2,2,2,4,20,20,20,20,5,5,"went for the middle high ones in hopes of winning more of those over people who went for the high values, but still wanted a chance at winning other castles"
502,4,4,13,17,23,23,4,4,4,4,Follow your heart to the very end
503,2,5,6,6,6,10,18,19,17,11,I asked my cat
504,1,2,2,8,2,11,21,21,21,11,"I based my answers mostly on intuition.  Assuming most people would use round numbers (we'll see if that is true), I went with 21 and 11 for the top 4 value castles.  The rest I allocated fairly randomly."
505,0,0,0,20,2,2,23,25,26,2,"The goal is to just get to 28 points. The shortest route there involves 4 castles (even 10, 9, 8 falls short), and the easiest way to get there is by snagging the 4 while taking 7, 8, and 9 (avoids taking the 10 where there are many troops from last competition's data). Thus, the majority of the troops (94) will go to winning those four, while the remaining ones will be split evenly among the 5, 6, and 10 castles just in case we lose one of the big ones and the opponent leaves these castles open. The split among the four I need to win should have the most troops in the most competitive castles. Since I need to win all of them to win, I'll put 20 in 4 because that number is big enough to stop any strategy that involves stacking on the bottom value castles. Then, I'll gradually increase troops as competitiveness increases."
506,0,0,0,0,15,15,0,35,35,0,"Go big or go home!! I need those four castles to win, so I'm maximizing my soldiers there."
507,2,2,5,7,8,12,13,7,18,26,Educated guess on how the crowd will play the data with castle 8 forfeited
508,4,4,6,6,11,16,21,21,6,5,Edjemacated guesses based on the previous distribution of the contest.
509,6,15,20,2,20,15,6,2,7,7,Trying to steal castles 10 and 9 then deploy troops to take castles that add up to 8. (I wonder what would happen though if I copied last winner's strategy)
510,2,4,6,8,10,9,12,10,18,21,I Randomize it-Like a Boss
511,1,5,4,5,5,12,10,15,16,27,"I am predicting others will try to emulate the previous winner's allocation, or try to -beat- the previous winner's allocation. I am trying to beat both of those pools of players at once."
512,2,2,6,6,11,11,16,16,21,9,"Roughly scaling with number of points (except for the last castle, which I figure people will either go for or not, so I just dumped the extra there). Hopefully people like round numbers (i.e. multiples of five) so I mostly made mine multiples of 5 plus 1 to try to edge people out. To glory!"
513,0,0,3,3,4,22,27,32,5,4,"I'm trying to one-up the last Riddler Nation Battle, then one-up that one."
514,4,6,9,11,15,21,26,1,3,4,i just want to win i have no plan to rule
515,0,0,0,1,7,20,3,13,28,28,"I chose this deployment because it gives me a high chance of winning. It is a lovely solution mathematically. Also, because I plan on getting a shout out, I would like to say ""I love you"" to my mother, Debbie Firestone in Tulsa, Oklahoma. Hi Mom!"
516,0,0,0,0,25,25,0,25,25,0,Maximise each soldiers worth so I have no wasted soliders in any battle that the match does not depend on.  Maximise my force where it is needed.
517,2,2,2,2,15,10,27,30,5,5,"Sun Tzu once said ""If you've got 100 soldiers to defend 10 castles, pick the nicest looking castles."""
518,0,0,0,0,25,25,0,25,25,0,Putting all my eggs in one basket (winning all 4)--ceding the rest.
519,1,2,2,3,4,16,21,24,21,6,Assigned enough troops to 6-10 in order to beat 60% of the previous Battle Royale for each castle.  Assigned enough troops to 1-5 to vulture some of those.
520,4,6,6,6,6,6,26,4,32,4,fighting the last war - tested against the precedent war data with a touch of randomness to allow for the fact that others are doing the same
521,0,0,0,0,25,25,0,25,25,0,"I decided to go simple this time. If you win castle 9, 8, 6 and 5 you win so I am going all out for just those castles"
522,0,0,0,0,25,25,0,25,25,0,Somewhat-randomized castle selection in the butter zone (adding to 28)
523,0,4,1,0,2,4,11,22,26,30,"My strategy was selected so that if I get the shout out on 538, then I would like to say ""Hi Mom!"" to Debbie Firestone in Tulsa. I would also like to thank the 538 for the awesome Friday puzzles! I really like this one."
524,0,0,4,12,15,20,24,1,1,23,10 was underutilized
525,0,4,2,0,2,2,11,22,26,31,"This is a sub-optimal human solution, but a close to optimal optimized solution. I would think this makes it into the top 10 to 20 finishers. Used stochastic methods."
526,0,6,1,11,1,14,28,2,34,3,Nate Blair
527,5,5,5,5,5,10,15,15,15,20,Felt like i over-thought it last round.
528,1,2,11,13,16,1,20,20,1,15,I designed several strategies that seemed good to me and then designed this one specifically to beat all of them.
529,6,7,7,25,25,10,5,5,5,5,I focused on strategies that would win a majority of wars against strategies that would be customized to win against the specific strategy of the past winner. Would you also accept a probabilistic distribution of armies?
530,4,6,9,11,14,3,27,18,4,4,"Add 1 to the winning troops from last time, except for Castle 8 gets whatever is left over."
531,3,4,4,5,6,7,9,11,17,34,"I weighted castle N by approximately (1/N)/(1/1 + 1/2 + ... + 1/10), which could be thought of as an inverse harmonic distribution - a name I just made up. There is no deep theory about why I expect this to work, I just have a hunch."
532,0,4,8,10,13,1,26,30,3,5,Computer Program on the last data set
533,2,4,6,8,10,12,14,17,15,12,"I did a progression of increasing troops up to Castle 8, then lessened it for 9 & 10, assuming many people will put more troops on those castles.  Against those people, I should win the majority of the other castles.  But I put enough on 9 & 10 that I should win those against people that mostly ignored them.  Who knows?"
534,3,3,4,4,5,13,21,21,5,21,God bless America
535,2,2,3,5,5,5,5,11,26,36,Seat of my pants
536,5,5,5,5,8,12,15,16,15,14,Looking to beat majority of previous players
537,2,3,4,8,8,12,12,12,22,17,Birthdays and lucky numbers!
538,0,0,0,15,0,0,20,32,33,0,Forces marshaled on castles in hopes of winning 28 points
539,4,4,4,4,4,4,34,4,34,4,Looks like 4 troops will winna castle most of the time. Put the remaining 60 troops randomly around in batch of 30.
540,3,4,6,2,22,23,28,4,4,4,Win or bust
541,4,6,8,10,15,22,27,2,3,3,"This is an adaptation of last tournament's bronze medalist (Brett Seymour's) strategy of punting the last three castles in favor of winning the first 7. I've slightly adjusted for the metagame, so to speak, by including 3 soldiers at the 9th and 10th castles, to anticipate many people placing 2 at each of these based on last tournament's results."
542,3,5,7,9,2,13,26,3,28,4,Another variation on the last winning strategy.
543,4,4,4,4,7,23,23,4,23,4,no
544,2,4,4,4,4,4,4,4,35,35,"Win 9 and 10 almost all the time, and hope to get the remaining needed points from putting 4s in the rest."
545,0,4,5,9,10,4,28,32,4,4,A few more than the prior winner on the more valuable castles and a few less at the less valuable castles.
546,2,4,4,4,15,3,28,32,4,4,"I wanted to counter anyone who added a single troop to each of the big castles from the prior winning strategy. So, I added 2 troops to castles 5-10, and removed some from the lower castles."
547,8,9,10,11,12,15,3,15,0,17,eh
548,5,5,5,10,10,15,10,20,15,5,First I set a minimum of 5 to every castle. Next I placed extra groups at 5 where I felt there would be a higher opportunity to win castles.
549,4,4,4,4,4,14,26,30,5,5,"Focused on the mid-range with the intent of picking off forgotten castles, Castles 9 & 10 will require too many troops to capture."
550,1,3,5,3,17,3,28,32,4,4,Tried to beat the winner from last time and added a couple troops to certain numbers
551,2,2,3,3,5,20,20,20,20,5,I Have a secret plan to defeat ISIS and I will build a wall
552,5,15,5,15,5,5,15,15,15,5,I consulted the Necronomicon
553,0,0,0,0,12,14,16,18,19,21,It's so obvious it may beat the subtle ones.
554,0,0,0,11,0,0,31,32,26,0,"There are 55 possible points, so you only need 28 to win.  I put a bunch of soldiers at 7, 8, and 9 to total 24 points.  I put the remaining 11 soldiers at 4, because I think my opponent won't put many soldiers there.  I also made sure to put 1 or 2 more than a round number everywhere I put a soldier."
555,0,5,7,10,12,1,26,31,4,4,"Alteration of the best solution from the 1st time that would have performed better and won.  Additionally, it beats most of the other top solutions."
556,2,3,3,15,17,22,27,3,4,4,"I used a genetic algorithm in which randomly distributed troops were shuffled one at a time to different castles and compared to the Git Hub data and 30 of the distributions. (The major problem is that the best distribution depends on what it is being compared to, so there is no guarantee it will work, especially if other contributors do something similar. Ugh. But let's see how it goes.) This was the best distribution."
557,2,4,6,8,14,20,28,10,5,3,"There are two competing factors. Some castles are more valuable, but they engender higher competition. My goal is to commit enough resources to the medium-value castles to win them, thus outcompeting those who commit higher resources to the high-value castles, while maintaining a sufficient attack on the high-value castles to win them over other people who choose my medium-castle strategy."
558,0,0,0,0,16,16,17,17,3,31,"I'd like to pretend that there is some really sound reasoning behind this strategy but there honestly isn't. Mostly, the strategy hinges on if I can win Castle 10, as well as at least 3 of the 5 remaining castles that I've deployed soldiers to, that puts me at at least 28 points."
559,12,11,11,11,11,11,11,11,6,5,"Have assumed many people will divide evenly, 10 soldiers per castle. Hence 11 will beat them and then for Castle 8 & 9 a lower number should score sufficient wins! Fingers are also crossed..."
560,0,4,8,9,12,2,26,30,5,4,"If you could make my crown a size 7-3/8 that'd be great.  I started with the previous winner as my initial base strategy.  I pitted this against all other submissions in the previous challenge.  Then I simply experimented with the distribution until I seemed to get a maximum number of wins.  Knowing the previous winner distribution is a new piece of information I didn't have before.  I went with an assumption that even with this new info, game theory would still point me back to highly weighted Castles 7 & 8 as a winning strategy."
561,0,0,6,3,12,17,27,27,3,5,"I looked at the values that others were placing from Round 1. When It made sense, I placed slightly more than where a mass of others where placing. I also did a bunch of math."
562,1,3,3,2,7,14,10,17,22,21,"I wrote a script to continuously generate random troop deployments and semi-random troop deployments based on the most successful existing deployments. As new deployments were generated, I evaluated them against all previous deployments and (if they were the best) use them as the template to generate new deployments. The answer I had was the best of the 21,400 deployments that were semi-randomly generated."
563,5,9,12,8,9,15,17,15,4,6,High chance of 6-7-8 points.
564,5,9,12,8,9,15,17,15,4,6,High chance of 6-7-8 points.
565,0,4,8,12,12,2,26,28,4,4,In antiquity those that excelled in warfare first made themselves unconquerable in order to await the moment when the enemy could be conquered. - Sun Tzu
566,2,2,3,10,22,22,27,4,4,4,
567,2,4,4,5,5,10,10,10,15,35,More troops on the bigger numbers
568,4,4,4,4,4,22,4,24,26,4,I had a hunch
569,2,3,4,4,4,14,14,16,17,22,Focus on higher half of numbers.
570,1,1,1,4,4,22,27,31,5,4,Win probability maximization.
571,3,4,4,12,11,1,26,30,3,6,Randomly selected
572,2,4,8,10,12,2,27,27,4,4,"Slight alteration of the last winning strategy, based on the last game's histogram and how I expect others to react to it."
573,2,4,6,8,10,10,12,14,16,18,It is a sound dispersion of troops.
574,0,1,1,15,3,2,21,29,25,3,Cause my daughter told me so
575,1,1,10,12,5,3,28,32,4,4,Basically the winners picks from last time plus 2.  and then I account for that by dropping 5 to 5 and 1 and 2 to 1 each.  I'm trying to next level all the people who attempt to next level the last winner.
576,1,2,3,3,6,11,16,26,26,6,"A quasi-exponential formula peaking on castle's 8/9 and using n+1 troops in most castles to win against people who pick ""round"" numbers."
577,4,4,4,6,10,12,14,16,14,16,To be contrary to how it played out last time
578,3,3,3,3,17,3,28,32,4,4,"I just took a quick look at the distributions from the last round. 3 troops would have won castles 9 and 10 a surprising amount of the time, but I figured other players would have the same idea this time around, so I iterated one more time and put 4 on each. I decided further iterations (5, 6 troops...) weren't worthwhile, as they would begin to limit my ability to target other castles. I tried to deploy just enough troops to castles 5, 7, and 8 to put me safely on the right side of the bell curve. Not fighting hard for castle 6, as the last round's winner did, seemed like smart resource allocation. Finally, I assigned a token force to castles 1-4 to try to steal whichever of them was lightly defended. This strategy is similar to all of the last round's top five submissions, but would have beaten all of them - I'm not sure if that's a good or a bad sign. The only other improvement I could see to their strategies was not fighting hard for castle 4 either."
579,0,0,8,4,13,16,17,22,2,18,"I randomly generated ~200,000 deployments and picked the one that come out on top."
580,0,5,6,12,12,1,25,31,4,4,###OPTIMAL SOLUTION FROM ORIGINAL DATA SET### (1255 wins)
581,0,0,4,8,11,11,14,13,14,25,This is my guess based on a simple GA i wrote to fight against a random armies.
582,2,2,6,9,11,3,27,32,4,4,"I chose something very similar to the previous round's winning strategies, but tweaked a bit to win against a straight copy of those strategies. The counters to this type of plan all seem to have serious disadvantages of their own, so I'm hoping that few people will try to use them."
583,5,10,15,3,3,3,3,3,22,33,"With so much conflict in the center group of castles, I thought it best to work at the edges.  If I can guarantee getting castles 9 and 10 with large deployments, getting to a winning total of 23 points (4 more) should not be difficult with higher deployments at 1, 2, and 3 as well as a lucky break at any of the other castles."
584,6,12,12,16,21,17,4,4,4,4,"It's easy to snag a few of the top castles with a handful of troops. I guessed that many people would send 3 troops to these this time, so I sent 4. I then tried to pick near the top of the prior range for the lowest castles. I put the leftover troops in castle 6, hoping to snag many from the bottom 5, some from 6, and some from 7-10."
585,0,0,6,11,18,2,2,26,32,3,Avoid battles at 10 7 6 and low value castles while still beating a large percentage of the previous field.
586,3,4,4,6,19,8,23,2,27,4,Need 28 points to win. Pick some minimum for each castle based on charts and hope I get 1/4 of the points I need. Then place leftover soldiers on castles that add up to 21 points.
587,5,1,10,15,17,1,23,1,26,1,trying to get number 9
588,0,0,0,0,3,8,18,28,31,12,We chose the number of troops randomly starting with castle 10.
589,2,3,6,9,9,3,28,32,4,4,"slightly overweight castles with greater value versus previous winning strategy, slightly underweight castles with lower value versus previous strategy. Something to do with the number of winning combinations in which castle appears!"
590,3,3,9,12,3,16,17,29,4,4,Random
591,0,3,2,11,14,2,28,32,4,4,Try to win a few key castles without losing to many troops
592,1,2,3,4,10,15,15,15,20,15,"Going for a balanced attack, yo."
593,2,2,2,2,22,23,2,21,22,2,Yeah Boiz.
594,1,5,6,9,12,2,26,31,4,4,Andrew Simmons
595,0,5,7,10,12,2,26,31,3,4,Plan: sum(2:5)+sum(7:8)=29
596,1,1,2,3,8,18,22,18,22,5,"By analyzing the first dataset, primarily using the median number of troops sent to each location."
597,0,0,2,12,15,3,28,32,4,4,"Two above all winning deployments from last time, to get the troops I reduced the low value castles"
598,0,0,0,0,0,0,25,25,25,25,"In round 1, the higher castles were taken by much lower #s of troops. I'm going for the big ones."
599,1,1,1,1,1,19,22,24,27,3,"I want to win castles 6-9 because that adds up to 30 points, which wins automatically"
600,2,2,3,3,4,4,20,20,21,21,Big Points!
601,1,1,7,10,12,15,2,25,2,25,Gut feeling
602,0,1,0,1,7,12,12,6,26,35,"I first created a randomized 2000 king tournament. I submitted the winner of that tournament but then realized an error in my ways, the randomized version created some deployments that would not be used by anyone. So I culled 50% of the deployments and re-ran the tournament, then culled 50% again etc. Until there was one clear champion."
603,1,5,1,11,2,19,2,25,2,32,"I chose to compete at all castles in case my opponent left one unguarded, but I chose to prioritize the even numbered castles based on their point value.  Then, anticipating a similiar 1-soldier strategy among my opponents, I rebalanced the higher value odd castles with two soldiers, borrowed from the lower value castles."
604,6,14,10,8,10,7,17,11,4,13,"I created two random number generators (RNG) for each castle, each for integers between 1 and 10. Then I ran the RNGs until the sum of all 20 generators equaled exactly 100. I added the two numbers for each castle and recorded them above."
605,2,2,2,19,2,2,22,23,24,2,I picked four castles to focus on that total 28 (the magic number).  Put two armies on each of the remaining as insurance.
606,5,4,5,4,14,14,16,29,3,6,"In the data from the previous iteration, I looked for the biggest decrease between consecutive bars, and added 3 to that."
607,0,0,6,3,12,17,27,27,4,4,I analyze the previous round's data and used the number of players who won by taking a castle with a certain number of troops. I then weighted it to also look at the point value expected per troop deployed.
608,1,2,5,5,5,6,15,18,20,23,"Wanted to distribute based off of proportional weighting, but where's the fun in that? Hoping that people distribute more troops on ALL the higher value targets this time around, and that my troop deployment is enough to beat the distribution."
609,20,8,19,0,0,2,28,8,8,7,Random solution meant to help my initial submission.
610,1,7,1,12,1,19,1,26,1,31,"I divided the 10 castles into 5 adjacent pairs, allocated troops based on the relative value of each pair, and then placed 1 troop in the odd-numbered (and lower-valued) castle to leave no castle uncontested with the rest of the troops in the even-numbered castle."
611,6,0,5,5,5,10,21,2,21,25,Game theory
612,0,0,0,0,0,25,25,25,25,0,"To win I just need the majority of points so if I 9, 8, 7, 6 castles win the battle."
613,4,5,8,11,4,17,20,23,4,4,"8/7/6 is greater than 10/9 as well as 8/7/5 from last time.  Pick up any ""punted"" castles from others who did 3 or under."
614,0,1,8,9,2,16,26,31,3,4,"3rd submission. 1181.5 out of 1313 (same 1313 cases as first two submissions).  1179 W,  129 L, 5 T.  This solution is light at Castle 5 and heavy at Castle 6 compared to the 1st two submissions."
615,0,0,0,11,0,0,25,31,32,1,"Figure #10 is overvalued and #7 is undervalued, enough in #4 to beat even distributions, and 1 in #10 to beat those that abandon it."
616,2,1,8,8,9,0,0,22,20,30,Fight for the weak points compared to last time
617,1,1,3,4,20,3,31,3,31,3,Never leave a castle behind!. Going for the in between wins.
618,3,4,5,6,9,11,13,15,17,17,"Ehh, more troops for the bigger points but more of a general strategy to take as many castles as possible."
619,2,2,2,7,8,17,2,23,33,4,"Who knows, man? Who really knows."
620,5,9,4,6,3,32,0,15,5,21,Random solution meant to help my initial submission.
621,2,6,2,4,15,5,27,31,4,4,"I want to be competitive in almost all castles so I will made sure to have more than 1 in each. On top of that I want to win 8,7,6,5, and 2 to get to 28. My distribution is then done to best the previous winner at each of those castles."
622,3,4,5,8,11,15,18,4,28,4,I wanted to beat the median from the previous round.  I beat it by 2 in case anyone else thought to beat it by 1.  I also focused on Castle 9 as I thought there would be people going back to castle 10 after it was underdefended previously.  Go Jets!
623,0,1,0,1,13,18,27,3,33,4,"Assuming that most people won't learn much from the prior submission data, wrote a genetic search trained by total wins against those submissions. This one won 1285 out of 1387."
624,3,3,3,18,3,3,20,21,23,3,"I run a Physics weekly announcement list for the undergraduates and faculty in our department.  On a lark, I set up this puzzle for the participants on the list the first time around.  Of the ~50 strategies put forth, this was the winning strategy by a pretty good margin.  (The second place strategy was along similar lines)."
625,6,7,10,13,16,20,28,0,0,0,I need 28 points.  I'm going to take a high risk strategy of only trying win the 7 least valuable castles.  And I'm going to make sure I have more troops at everyone of those than our last genius military strategist.
626,2,2,2,7,7,13,16,16,17,18,Because I'm the best there is. Plain and Simple. I wake up every morning and I piss excellence.
627,9,21,10,3,1,10,13,16,8,9,Random Number Generator
628,4,6,8,8,7,9,24,25,4,5,1/3 of my soldiers for Castles 1-5 and 2/3 of my soldiers for Castles 6-10
629,1,1,3,3,3,21,25,4,4,35,To get the castles 10/7/6 and maybe pick up a random other castle to round things out. And to defeat Cyrus. Down with tyranny
630,0,1,11,12,2,17,23,28,3,3,Win 5 castles worth 28 vp and make token bids for un-contested castles. Seems to be a local maximum against published strategies.
631,1,3,4,7,9,11,13,15,17,20,"Roughly the percentage of total points which each castle was worth, with some fudging to make the numbers round."
632,0,0,0,0,10,20,15,15,20,20,No attempt at low numbers
633,1,1,1,1,1,19,22,25,28,1,"Castles 6-9 have the same total point value as 1-5 and 10. I split my troops between those four based on their relative point value. I sent 1 to each of the others just in case my opponent chooses to send no troops to those castles. This way, I always tie or win if my opponent neglects one of the lower point castles."
634,0,5,7,12,12,1,25,31,3,4,I believe it was one of the best possible combinations for previous battle; it may not work if others change their tactics substantially.
635,0,5,7,12,12,1,25,31,3,4,This seems to maximize the number of wins with data from Round 1
636,2,4,5,7,9,11,12,15,17,18,"I based my deployment off of the percentage that each castle made up the total number of points. For example, the first castle is worth 1 point, out of a total of 55 points. 1/55 = .018 -> 1.8% This rounds to 2 troops, so I found the percentages for all castles, rounded, made sure they added to 100, and submitted them."
637,1,7,2,11,2,21,21,2,31,2,"If I win 9-7-6-4-2 and opponent wins 10-8-5-3-1, I win, but I could also be in trouble if I rely just on those because if I lose one I lose everything, so I will put two soldiers in each other castle just in case someone has a similar strategy as me."
638,1,3,4,6,10,12,14,16,16,18,"n*(100/55) is the most efficient pointer per soldier, and you can see there's number of people last game who played those values.  Since I expect more unusual strategies this time, I think overall efficiency is going to beat trying to out guess everyone with something crazy.
But I didn't go exactly the efficient route.  I slightly overweigthed 2,5-8 because winning those 5 castles beats winning the other 5.  This means I beat anyone playing exactly the efficient strategy, without being substantially inefficient myself."
639,4,7,11,6,8,4,20,32,4,4,"I looked at the distribution from the previous match-up and tried to make small adjustments over the winning strategy. I assumed that people will be influenced by those winning strategies, but won't copy them exactly. I also assumed that some people won't be influenced at all."
640,0,0,0,11,0,0,31,31,26,1,"There are 55 available points, so you only need 28 to win.  I loaded up 7, 8, and 9 to get 24 then put the rest on 4 to total 28 (as well as 1 on 10 just in case I lose 7, 8, or 9).  I also made sure to put 1 above a round number to beat anyone who put said round number.  For example, I put 31 on 7 and 8 so I beat anyone that puts 30 on either."
641,2,4,5,7,9,11,13,15,16,18,Value of points
642,23,15,14,9,8,6,6,7,6,6,Tried to pick sweet spots from previous distribution without overspending
643,2,4,5,7,9,11,13,15,16,18,It's Math Magic!
644,2,3,3,3,2,2,2,25,28,30,"I focused on the top 3 castles, expecting most of the opponents to battle it out for the middle. And then tried to make a small land-grab for the smallest castles. Basically, a Barbell approach."
645,2,2,3,7,16,3,28,32,3,4,Placed a minimum of two soldiers at each castle.  Allocated balance to maximize score against entries from round 1 data.
646,2,2,6,5,11,22,23,21,3,5,Based on the frequency of soldiers deployed for each castle in the past round. Simply wanted to beat more than 600 players for each castle.
647,25,0,0,0,0,0,0,30,25,20,"Last time I put a TON of thougth into it. But so did everyone, leading a lot of people to come up with clever strategies and many people not bothering to fight very hard for the highest value castles.

So this time I flipped that on it's head. Nice and simple. Go for the highest value castles (and castle 1) so that my point total, if I win them all, is 28, the minimum necessary to win."
648,1,1,2,5,6,6,4,20,25,30,because theres more pts in 7-10
649,1,4,5,9,15,15,20,20,1,10,Focusing in the middle
650,0,0,0,10,0,0,0,30,30,30,"Have to win 28 VP, so go all in on the top 3 and then go for #4 as a random guess."
651,0,3,3,1,4,6,19,17,21,26,The strategy is to be correct.. and to be correct more than your enemies... and for 538 to give me a shout out as having won more than 95% of the matchups. BOOM BABY!
652,1,1,1,1,1,15,20,15,25,20,Looking at the previous year's deployments I realized that people did not go all in on the higher level one. My plan is to hopefully win 3 out of the top 5 and then hope that i get a few points from the bottom 5.
653,2,3,6,3,15,15,25,23,4,4,"I looked at the data graph and aimed for the second local maxima for 5,6,7, and 8. All others were min-maxed to offer the highest return for troops spent."
654,2,2,2,3,3,3,17,20,23,25,Random but contesting all castles with more at the higher castles
655,0,0,12,13,0,23,25,27,0,0,maximizing points
656,1,4,5,7,9,11,13,16,16,18,Estimated Pts per Soldier ratio
657,1,3,5,7,9,11,13,15,17,19,"Military secrets, that information is classified"
658,1,3,5,7,9,11,13,15,17,19,Tom Hazlett
659,1,3,5,7,9,11,13,15,17,19,Linear
660,1,3,5,7,9,11,13,15,17,19,"Roughly, troop percentage per castle ~= castle value as percentage of total points."
661,1,3,5,7,9,11,13,15,17,19,Proportional to possible points.
662,1,3,5,7,9,11,13,15,17,19,(2* number of points the castle is worth) - 1
663,0,0,0,7,11,21,22,31,4,4,tested configurations against previous submissions data set
664,0,0,4,4,4,4,4,36,40,4,Targeted two wins and picked the rest to counter other targeted strategies.
665,2,3,4,7,11,11,18,21,18,5,"Looking at the averages, medians of the original dataset, I figured this would beat those who looked at the data set and try to beat the averages and medians. I think studies have shown most people don't go more than 2 steps out? So this is my two step out answer."
666,0,17,11,17,8,28,3,7,5,4,Random solution meant to help my initial submission.
667,0,0,2,8,10,12,14,16,18,20,The most troops going to the largest point value castles without wasting so many that there wouldn't be troops for the mid-point value castles
668,2,3,4,2,2,4,25,26,27,5,"Out of 55 total points, I figured that fortifying castles 7, 8, and 9, which would (hopefully) be less defended than castle 10, I would start off with a solid 24 points. Then, needing only 4 more points to win, I placed the remaining 22 soldiers hoping to get those points through either splits, or wins on castles that weren't heavily fortified by the enemy. I also didn't place a single soldier at any one castle because I figured that people would place only one at some, and i would get a narrow win in those locations."
669,1,3,5,7,9,10,12,14,19,20,analysis
670,0,4,7,9,10,0,0,0,30,40,High risk- high reward. Gotta lock in those big points then have enough of a chance to win the smaller castles to move past the 50% of available points needed to win.
671,4,4,4,1,16,11,21,2,2,35,Beats virtually any strategy? Maybe no.
672,0,5,6,9,15,1,26,31,4,3,"Downloaded GitHub data from battle #1, ignored plans that were ""clear losers"" (couldn't score 28 points, didn't use all 100 troops, etc.), and optimized over the remaining 1313 plans.  This deployment scored 1176 out of 1313 (1169 Wins, 14 Ties, 130 Losses).  Can't say this is the best vs. those 1313, could be a local maximum rather than a global, just the best I could come up with."
673,4,6,9,11,14,17,30,5,2,2,"Focusing on winning the bottom 7, with a few troops on the top 3 to beat people with a similar strategy"
674,7,0,0,5,0,15,24,19,14,16,"Took starting point of old, using simulation against those answers to create some possible responses, then created a response to those"
675,1,1,3,3,3,3,22,2,31,31,"Not too much thinking involved, but you fail to concur 100% of the kingdoms to you don't try to invade."
676,3,2,5,12,15,11,7,23,19,3,"I looked at the winning strategy from before, a strategy designed to perform optimally against that strategy, a typical strategy based on previous data, and a random/point-weighted strategy.  I then tweaked the last strategy to perform optimally against the other 3 ( most cumulative points).  I went against my better judgement which said to just stick with the random/point-weighted approach"
677,3,5,2,2,15,18,22,25,4,4,"Most people are going after 28 points and leaving other castles under defended, by concentrating on a few in the high-mid tier I can snatch away a few of their key castles and then nab all the remaining under defended ones."
678,1,23,1,1,1,1,1,23,23,25,"I liked the idea of the 23 distribution that I saw on the Git Hub page, but since everyone was concentrating on Castle 1 as the castle that would push them up to 28, I thought since most of the plans put no emphasis on Castle 2, I would go for Castle 2!"
679,1,2,2,7,10,12,14,16,17,19,Tweak of Ceiling[100*n/55]
680,1,2,3,4,10,12,14,16,18,20,I doubled the number of points of castles 5-10 and sent that number of troops. For castles 1-4 I sent the corresponding number of troops.
681,3,3,3,13,18,3,23,3,28,3,"This strategy did well against a sampling of the last tournament's entries.  Usually gets to 25 via 4+5+7+9, and usually wins a sufficient combination of 1, 2, and 3 to get to 28.  If the strategy fails to do that, there's a good chance the opponent is under-represented in slots 6, 8, or 10, and can then be beaten there to compensate for surprise losses."
682,1,2,1,1,1,17,21,27,28,1,"I decided to just give up in 10, figuring everyone else would send a tin of resources there. I allocated to the next highest ones in descending order. I popped a few into 2 just to try to steal those."
683,1,4,7,10,13,2,26,30,3,4,"Basically the winner of the last game, a bit modified"
684,0,0,0,6,8,11,16,16,16,27,"I was able to distribute most troops to the castle that carry the highest percentages of the total points. By sacrificing the bottom three castles, I am trying to give myself a greater chance at winning the top castle, which I consider a swing ""castle"". As well, I still contribute points above the average amount for castles 4, 5, and 6 because they are worth 27% of the total points, and might swing battles for those who put all the soldiers in the top 4 castles. If I am able to split the top castle then I would be able to tie those matches."
685,5,5,8,7,10,3,23,30,5,4,"Similar to the winning strategy from last time, but a bit more effort on the highest two castles."
686,2,7,9,11,2,2,27,32,4,4,"I aimed to dominate the previous winning strategies from Round 1.  Minimum of 2 troops to any castle.  4 troops to castles 9 & 10 to defeat anyone sending 3 or less.  Focus on castles 7 & 8.  Minimal (2 troops) to castles 5 & 6.  Decreasing troops to castles 4, 3, 2, and 1.  Downside to this strategy is that it will lose if I lose castles 5, 6, 9, and 10."
687,0,1,1,2,2,2,20,23,24,25,"So I figured a lot of people won't do any analysis and will just play this as if it was the first time. Some people will do analysis and just try to beat the previous winning strategy. Others will take the full set of data and try to come up with something that will win the most matches given the previous round. Yet others might do an even deeper analysis going from there and try to reach some sort of Nash equilibrium based on everyone making the best decisions. But I feel like all of that might be overthinking it. Sort of as if we played rock-paper-scissors: if in the first round it turned out most people threw rock, then analysts might say ""you should throw paper to beat the typical throw!"" or ""you should throw scissors to beat the supposed winning strategy!"" But in reality it will just end up being random anyway. So I just went with a reasonable general strategy of focusing most armies on the higher-value castles, and leaving enough troops for tie-breakers on the lower ones."
688,1,0,5,7,9,11,13,15,20,19,"Proportional, except forfeit 2 and go for 9."
689,1,5,7,10,12,2,26,30,3,4,Optimized based off all intelligence at my disposal. #DFTBA
690,1,2,3,5,8,13,21,21,21,5,"Assuming a Castle 0 my first 7 Castles employ the Fibonacci defense. Castles 7,8 and 9 use the standard Blackjack defense and the remaining 5 troops hope the distribution curve has moved high enough to make them useless."
691,2,3,6,9,13,6,24,29,4,4,Beat the noobs.
692,0,0,0,12,3,0,19,33,33,0,Need 28 points- overwhelm 4 castles to achieve 28 points
693,0,0,0,0,0,20,20,20,20,20,"Try to grab the first 6 castles, I will loose to the ones who will try to get the first four, but take a lot of other armies."
694,2,7,10,12,12,25,1,25,3,3,"I wanted to build a coalition of castles that would give me a win versus the averages. I chose 8, 6, 5, 4, 3 & 2 which would give me a winning 28 points versus an average deployment. Then I chose to put a small but tangible number of troops at the other castles so that I could pick off wins against people who sent 0-2 troops to the remaining castles. Hopefully if someone stacked a castle and beat one in my firewall they had a 1 in there that I can pick off."
695,2,2,2,2,2,2,2,26,28,32,I thought I would win
696,0,0,2,2,2,17,15,18,22,22,"I am attempting to place a balanced attack against the high castles, but sacrificing the low castles with increased weight to the two highest castles"
697,1,3,3,1,1,1,0,30,30,30,I figured I'd set myself up with a pretty good chance to win the top three castles. That puts me one point away from victory. If I'm lucky my opponent will have left some other castle undefended.
698,0,0,0,0,0,20,20,25,35,0,so I can win
699,11,11,19,19,20,5,4,1,5,5,We'll see?
700,1,2,6,6,12,13,31,21,4,4,Looking for dropoff points: https://github.com/nabraham/538-riddler/tree/master/2017.05.19_classic_battle
701,1,1,1,1,1,5,15,25,25,25,Best Placement
702,0,0,0,0,0,0,20,23,27,30,because no-one did it last time and I am curious if people will repeat that
703,1,1,1,1,1,18,19,19,19,20,"Last time, a ridiculous number of people split their troops evenly among the ten castles. Beating that strategy should earn a bunch of points in the head-to-head matchups."
704,5,7,9,11,15,21,25,2,2,3,"I analyzed the previous submissions and looked for patterns, then built a tool that let me try different combinations. I noticed that you usually needed to be able to 'pick' one or two castles from other leading submissions. This variant, 'pick'ing castles 6 and 7, had the best win total against the previous generation. While it loses to the ""classic"" solutions of 10s across the board and maxing 1/8/9/10, because of how obvious those solutions are, nobody actually ever chooses them."
705,0,1,2,3,4,13,14,15,16,32,Focus Heavily on Bigger Point Values. Less on 1-4
706,2,4,7,11,14,16,19,1,25,1,"Looking at the winning strategy, it appears that ignoring castles 9 and 10 largely paid off with a strong indication that 7 and 8 were good bets. Taking this a a level one strategy, I move to level 2 assuming that good players notice this. From there, I do some math and realize that dividing my forces reasonably among 8 castles is likely to beat both players who spread evenly and some players who bulk up on the higher value castles. An evenly spread player loses to me on all but castles 8 and 10, and a player who aims for the top loses even if they beat me in castles 8, 9, and 10. Aiming for castle 9 instead of 8 in this way makes the split with the 8-9-10 player 28/27 and also seems like the kind of twist needed to take this strategy to at least level 2, which may be as high as this rationally goes before it gets silly."
707,3,21,17,10,10,10,8,8,8,5,Whatevs
708,0,5,8,10,13,1,26,31,3,3,A: It beats the previous winning strategy (which a lot of people are bound to try). B: It beats all possible 1 move changes from the previous winning strategy (which naively I suspect may be the most common strategy?) C: It beats all possible 2 move changes from the previous winning strategy (which I'm sure a good chunk of people are also bound to try) D: The previous winning strategy was obviously a good starting point for beating strategies created without prior information (which for sure a whole bunch of people are bound to try) E: Anything more complicated than this would require actual thought and/or effort.
709,2,4,6,9,13,2,27,31,3,3,"Ran a simulation against first round results and randomly generated plans, tweaking the allocation by hand."
710,0,3,5,5,11,14,2,26,32,2,"Using the basic strategy of the winners from last time, but shifting towards higher value castles, hoping that people will compete for them less once they see the data."
711,1,2,3,4,5,20,25,32,5,3,"Tried to beat the previous winner, hoping to luck out otherwise."
712,2,3,2,2,3,22,27,31,4,4,It would have won last time!
713,3,17,3,17,3,17,3,17,3,17,"Always have at least one in a castle, but then try to win at least half the battles."
714,0,0,0,0,0,18,19,20,21,22,My brain is like a big bowl of soup: there's no real structure or purpose anywhere.
715,1,6,8,10,12,1,26,30,2,4,"I used Excel solver to find the winningest combination over the last battle's data, with last round's winner as the initial guess. Improved the winning percentage by about 4%. Figured it couldn't be too awful in the second round."
716,0,0,1,4,10,13,15,17,19,21,"Like evenish (2n-1) deployment, but heavier on top"
717,2,4,7,9,12,2,27,31,3,3,Selected for arrangement that would win the most total points (not necessarily wins) against the 1300 strategies from the first round (assuming people will not change too much)
718,2,4,7,9,12,2,27,31,3,3,"Looking at round 1 winner, just increased 1 troop to castles 6-10 and reduced 1 troop to castles 1-5.  I hope the small trade off may pay out significantly."
719,2,2,6,2,10,18,26,26,4,4,"Last time I got really close to winning, so I'm going to switch it up a little bit and stick with the same strategy. Trying to win all the ones people throw away and then if people spread out too much trey and beat them too."
720,1,3,7,11,16,16,16,11,18,1,"Modified my previous submission, which would have fared quite well against the top-performers. But because I think a lot of people will change their strategy to compete against the last version's winners, I have zigged to their zag."
721,0,3,5,17,17,17,17,17,5,2,Almost random ;-)
722,0,0,1,16,20,20,18,19,3,3,Used a genetic algorithm to optimized based on previous reader responses (http://htmlpreview.github.io/?https://github.com/kloppen/riddler-castles/blob/master/solution.nb.html)
723,1,1,1,2,2,14,23,23,30,3,"To start off, it appears that for every castle, 30% of people did not send any troops there, so it makes sense to send a single troop to every castle. 

Secondly, if we win castles 9, 8, 7, and 6, then that's a total of 30 of the 55 points, so if I send a disproportionate amount of troops to those places and win those, there isn't enough points to overcome that. So after sending a base one to each, I divided the 90/4 and determined that I should send 22 more troops to each of the four castles.

Then I reasoned that Castle 6 was likely not going to as contested as the other three, so I took nine away from there and gave 7 to Castle 9 to make an even thirty. That gave me four more troops (two from the 6-9 distribution and two from the fact that 4 doesn't go into 90 cleanly). I figured I might as well give two of those to Castle 10 since almost half of everybody sent either 0, 1, or 2 troops and that's ten free points. The other troops I gave to castles 4 and 5 since if I somehow lose Castle 6 I can make up the points by winning either 4 or 5 if they employed the same basic strategy as I did and dished out one troop to each location"
724,0,1,1,2,11,13,15,17,19,21,copied sharon
725,2,2,2,2,13,13,27,31,4,4,Try to work well against previous battle plans and beat previous winning plan.
726,2,6,1,2,13,17,22,30,4,3,"In needing to get to 28 points, I figured I could largely ignore the top two targets, and focus heavily on 8,7,6,5 and 2, which gets to 28, and deploy some remaining troops to hedge on other targets in case they are ignored by players more heavily invested with the same strategy."
727,0,0,0,10,0,0,30,30,30,0,Get 28
728,2,2,2,5,12,21,22,26,4,4,Increase the 9 and 10 to capture the higher percentage and increase castle 6 at the expense of lower numbers
729,4,2,6,11,12,2,26,31,2,4,Attempted a numeric approximation of a linear optimization based on the historic cumulative frequency distribution. Then performed a Monte Carlo simulation by changing the cumulative frequency distribution to see if there were any improvements.
730,2,3,3,3,3,21,21,21,21,2,"I figure for castles one to five, some people might put just one on to cover those who have none, but other than that don't care. So two beats them. But then people might think that and put two so I put three. Some people might also put 20 each on 6 to 10 to maximize points. So I put 21 on to beat them for 6-9 and one on 10, conceding it. I figure more people will concede one of the lower ones than 10 if they're doing the same thing.  So I should win a lot of 6-9, some 1-5, and very few 10. But hopefully what I win is enough. 

And then I swapped one on 1 for one on 10 just so I could beat people who tried the same strategy but not much else. 

Disregard my previous submission, I added up wrong."
731,2,2,3,2,3,22,27,32,3,4,Optimal with the given opponents.
732,2,7,2,2,12,15,21,33,3,3,version 2
733,2,2,3,3,3,22,27,31,3,4,"Nothing fancy. This is the hypothetical troop placement with the highest margin of victory over the first round data (an average of 14.55 more points than my opponent). 

It's not the winningest hypothetical from last round, however. (That was 0,5,7,12,12,1,25,31,3,4, with a MOV of 11.83.)"
734,2,2,3,3,3,22,27,31,3,4,"I used integer programming to maximize points against last year's submissions. It's not exactly the same as maximizing individual wins but it is a good proxy for battling against everyone. I ignored the ties and counted them as losses, which is a pessimistic approach and ties will bring even more points than I accounted for, hopefully. Got a total of 47058 points. IP is submitted here: http://imgur.com/a/6tHHI"
735,1,3,6,8,16,2,27,31,3,3,"I just varied the strategy of last week's winner, raising the number of troops at the more valuable castles and lowering it at the less valuable ones."
736,0,1,9,1,16,20,21,27,3,2,"Mostly sacrifice 1, 2, 9, and 10 to focus on getting to at least 28 points using the middle numbers."
737,0,0,0,0,0,0,20,20,30,30,Big Baller Brand only goes for Big Points ( I know it's a terrible strategy... just work with me on this one...)
738,3,3,6,10,12,2,27,31,3,3,"Starting with the previous winner's deployment, I looked at the graph provided and would take a troop from a castle where the % for the next number down wasn't too much higher than the % for the current number, and moved it to a castle where the next number had a large % compared to the current number. ex: Moved one troop from Castel 5 to Castle 10. Then I continued until I found a number of these deployments, and ran these deployments against each other. I chose the deployment that won against most of the fights against the original submissions as well as the fights against the set of modified-winner deployments."
739,4,4,4,4,4,18,26,28,4,4,"Old answers seem to suggest people leave some gaps in the deployment, hopefully I'll pick those up and be competitive in the middle."
740,1,2,5,6,3,21,27,27,5,3,Similar to my original strategy but slightly refined based on data from first simulation. Trying to get a majority of the middle value castles and steal a few low and high value ones.
741,4,6,9,11,14,2,17,31,3,3,I tried to barely beat the prior winner in as many places as possible.
742,1,5,8,10,13,1,26,30,3,3,"I took last time's winner, and moved 2 troops out of Castle #1 and into Castles #9 & #10, thus ensuring I beat last time's winner. I figure most people will either just copy the previous winner, or replay their first, losing strategy."
743,3,4,5,7,10,15,3,25,25,3,First try. Will think a bit more over the weekend but I am curious whether my snap guess is better or my actual thinking.
744,1,1,9,14,1,19,24,29,1,1,"If I win 3,4,6,7,8, it would be 28 which is over half. I guessed it would be easier (solder deployed vs likelihood of winning) to win lower numbers. I added 1 per castle to ensure they sent troops in order to win points."
745,1,1,1,2,10,12,24,29,1,19,trying to win ....
746,1,2,3,4,10,12,17,31,17,3,Tried to find the point values with the most marginal value based on the previous results.
747,1,2,3,4,10,12,17,31,17,3,Tried to find the point values with the most marginal value based on the previous results.
748,1,2,3,4,10,12,17,31,17,3,Tried to find the point values with the most marginal value based on the previous results.
749,0,0,0,0,10,18,21,24,27,0,Forget the 10th and focus on 9 and below.
750,3,4,5,6,11,16,0,25,30,0,I tried to barely beat the prior winner in as many places as possible.
751,0,0,0,0,0,40,10,10,30,10,"6 = 3 + 2 + 1, so all shares go to that #. 9 = 5 +4, so same treatment for those. Then, the rest are just allocated as normal. Then as long as I win 2 of the 3 remaining battles of 7, 8, and 10, I would win. Bit of an oversimplification, but hey who knows..."
752,1,7,0,0,12,16,29,32,1,2,"You need 28 points.  I expect most people to load up on castles 10 and 9, and then try to make up the rest on the lower value castles.  The middle castles are likely to be the softest targets.  I sent some troops to 10 and 9 in case someone else uses a similar strategy and does not go after either of those."
753,0,0,0,0,15,15,15,25,30,0,"You need 23 points to win, and that means if we exclude ties, I need at least 3 castles. I assumed smaller castles would have fewer troops, and the smallest sequence that wins is 9-8-7. Because I would immediately lose if I were unable to secure any of the three, I elected to spread the troops over 5 and 6 too."
754,1,1,6,11,11,11,26,26,4,3,Just a small variation on the winning strategy from last time... lame I know.
755,1,1,10,10,9,18,6,16,27,2,Took random number multiplied by points for each castle to determine the distribution.  Randomness mixed with a little common sense (you have to win some of the big numbers to win).
756,2,3,3,7,10,14,18,21,18,4,One more than median of original data set
757,2,4,6,8,11,13,15,17,20,4,"Keeping it simple! I assumed others would either overload high numbers or weight with 10 castles accordingly. I weighted for 9 castles and rounded all numbers down, then gave the leftovers to castle #10."
758,6,8,11,14,17,20,24,0,0,0,Take all the low value castles and gain 28 VPs
759,1,1,1,2,2,3,5,10,35,40,I wanted castles 9 and 10 (:
760,7,7,15,15,15,16,16,3,3,3,Trying to win all the middle areas with everyone else going for the high value ones
761,3,4,5,11,19,25,26,1,3,3,Varying the best winning strategies of last time to find an optimal solution
762,5,7,10,2,16,23,2,2,30,3,I tried to come up with a distribution that would challenge for 28 points against both the average try and the winning strategies from the previous battle.
763,0,0,0,5,12,13,16,22,32,0,"Maximize points.  Assumes overload on Castle 10, but maximize down the ladder"
764,2,3,3,3,3,12,14,26,31,3,The idea here is two fold. Best strategy is to think one step ahead. Most people are going to look at how many 1's there were and put 2's at castles. This will beat them. The second is most people overload castle 10. In a more balanced strategy we will never beat them so we relinquish castle 10 while still giving it 3 soldiers to win against armies that completely relinquish 10. The exception is lowering castle 1 from 3 to 2 in order to give an additional soldier to 6. This defeats the 11 across strategy. Games won will either involve winning 8 and 9 or sweeping bottom castles.
765,3,5,7,9,11,2,26,31,3,3,Variation on the winning strategy from last time.
766,5,4,4,2,10,15,27,26,3,4,chenbesler@gmail.com
767,2,4,8,10,13,1,26,30,3,3,"Several ways to 28. Prey on unexposed extremes, make your money in the middle."
768,3,4,4,4,4,4,1,1,35,40,Ran an analysis on the data you provided through some rudimentary regression and decided this was the best strategy.
769,1,2,2,3,10,15,20,31,13,3,"Tried different strategies (even balance, top heavy, linear progression) against others w/ computer simulation that varied the losing side slightly each time until it won. Tested against some of the common strategies used in round 1 this time and this distribution was generally successful considering how people might adapt this round."
770,4,5,7,8,10,2,27,31,3,3,Just a small variation on the winning strategy from last time... lame I know.
771,2,3,3,8,18,20,20,20,3,3,"I am banking on other players placing 1 or 2 troops on Castles 1, 2, 3, 9, and 10. The low-value incremental castles will hopefully push me over the top."
772,0,1,10,10,14,18,20,16,10,1,I prioritized castles 3-9 distributing troops based on a combination of weighing values of each castle and the results of the previous round.
773,3,5,7,10,11,2,25,31,3,3,Only slightly changed from last times winner.  I did a simulation for a previous submission and it gave pretty crazy data so I want to see if a more intuitive response will do better.
774,5,4,25,20,3,15,10,9,5,4,Random
775,2,3,5,0,10,15,20,25,17,3,I wanted to win the game
776,0,0,1,15,15,15,25,25,2,2,"I have to win 28 points.  Token forces at 9 and 10 to defeat anyone leaving them undefended or with 1 troop.  Focused on winning 4 through 8, which gives me 30 points if I win them all."
777,3,4,8,9,12,2,26,31,2,3,Classic force concentration and penetration of the center as military tactics.
778,0,0,0,5,10,18,20,20,25,2,"Sacrificing castle ten, concentrating on castles 9 through 6. If I take them, I win."
779,7,8,10,15,15,20,25,0,0,0,"initially i had all bets placed on the top 4 to win 34-21 but then i realized more people will bet on the higher castles to rack up points but if i bet my points on the bottom i can win 28-27 which will gain me a victory. so thats exactly what i did, its a little riskier but it will gain the most points from the smallest castles"
780,2,6,2,2,15,16,20,33,2,2,"It seems to me that the point of this exercise is to maximize the number of strategies that you beat.  In looking through the data, many people leave a lot of 0s and 1s, so I have at least 2 in each.  I would like to reach 28 with a combination of 2, 5, 6, 7, 8.  But I am trying to maximize the number of ways that I can win.  I hope I submitted this on-time, I dont know when the cut off is.  Thanks!  P.S. Did the last winner really not say anything about their strategy?"
781,2,11,2,2,12,12,20,33,3,3,If only we had something like this in Fire Emblem.
782,0,0,1,11,11,16,26,31,2,2,"(2nd submission) This is identical to the strategy that got me fourth place last time. If it ain't broke, don't fix it? maybe?"
783,1,1,3,12,16,3,27,31,3,3,"Sacrificial lamb: intended to be very similar to my previous submission, but lose to it. Marginally increases the other strategy's winning percentage while decreasing others'. It would be awesome if this one somehow beat my previous submission."
784,2,2,11,13,2,25,2,37,2,4,"I observed through some Excel trial and error that winning five castles (3, 4, 6, 8, and 10) against last time's top 5 and median and tying castle 9 against the top 5 would have been enough to beat those six strategies.  More fundamentally I was trying to beat a proportional allocation on several castles while still beating a lone outpost on the remaining castles.  We'll see whether this is enough to beat this round's crop of entries!"
785,0,0,0,0,5,5,0,30,30,30,To win
786,1,2,2,7,10,20,20,30,7,1,Impulse
787,3,3,3,3,7,12,17,22,27,3,"Based on what I think the new nash equilibrium will be. I think a lot of 0-2 man castles will be out, so I want to pick those up, while fighting for the least contested ones in my opinion."
788,4,6,8,8,8,3,24,33,3,3,"Well, I had to choose something. Used 3 as a baseline for all bases, then strengthened based on point value, with the aim to take 8 and 7 for the most points and contest all lower point castles with a reasonably balanced distribution at the lower scale points."
789,1,11,13,14,15,16,1,27,1,1,Distributed to get 28 points
790,1,1,3,9,18,23,22,19,1,3,"Reviewed all previous historical data to produce a model that would win the highest % of times. From there, knowing that many would use the same approach, and likely the same (somewhat simple) tools - the excel solver, I tweaked my final answer to beat the solution I found in the first step."
791,1,3,6,2,3,21,26,31,3,4,"Always include at least one, when possible go over multiples of 5 (higher concentrations shown there), don't sweat 9 and 10."
792,4,6,9,14,18,21,25,1,1,1,Tried to win the bottom 7 castles.
793,2,5,8,10,13,1,26,31,2,2,Slightly adjusted plagiarism.
794,2,5,8,10,13,1,26,31,2,2,previous winner solution++
795,0,18,18,1,1,1,1,20,20,20,To get 28
796,4,7,11,14,18,21,25,0,0,0,"I realized that I only needed to have my troops collect 28 points in order to win.  I then just gave up on the high worth castles, and spread my points among the lower 7 weighted by the points each castle was worth.  This is a rather simple strategy, but I wanted to see how well it works."
797,4,4,5,7,10,12,21,31,3,3,"Determined proportional values, redistributed numbers from 9 and 10 and assumed a disproportionate amount would end up in castle 1 for people's strategies."
798,1,1,7,9,11,6,28,32,2,3,"Based on the winners of the last one, trying to beat them."
799,2,3,3,7,10,15,18,21,18,3,Beat the median for each castle
800,3,3,3,3,3,2,4,32,3,44,Guessed that more people would try for the 10-point castles
801,1,1,1,15,20,20,20,20,1,1,Focus on the middle of the range.  Not paying much attention to what people did last time.  Too much game theory going on.
802,0,0,0,0,18,18,20,20,24,0,Strategery
803,7,7,7,9,15,25,30,0,0,0,"The way to win is to get 28 victory points. Generally, the data from the last round suggest that higher point castles are more competitive. This strategy involves investing all my troops into the lowest summing castles that get 28, which end up being everything but 10, 9, and 8. I placed them in increasing order with castle value."
804,2,3,4,5,5,8,20,25,25,3,Pure seat of the pants strategy
805,2,5,5,8,12,12,25,26,2,3,Averaged the top 5 distributions from Round 1.  Strategically made these values integers by rounding deployment to castles 1-5 down and castles 6-10 up.
806,0,0,8,10,13,18,23,28,0,0,Trying to win only castles 8-3.
807,2,5,6,12,14,1,25,31,2,2,"Modified version of last winner, optimized against all previous entries"
808,3,4,4,7,10,13,25,28,3,3,At least 3 troops in each. Heavier near higher value.
809,2,5,8,11,14,17,20,23,0,0,"You need 28 points to win each engagement. I'm expecting most people will deploy their greatest number of soldiers to the highest-point castles. My intent is to concede those and instead deploy my soldiers to the lower-point castles, where each soldier should have greater incremental value. If one could consistently win castles 1 through 7, that would be just enough points to win the battle. I've decided to contest castles 1 through 8."
810,2,2,3,3,2,2,26,30,27,3,"Using prior competition data, largest area under the curve I could achieve without higher maths. (I used excel and simulated competitions)"
811,1,4,13,14,1,1,20,23,22,1,"Going for close wins and major losses. Hoping to win 7-9 and 3&4. Will lose to opponents who used more than placeholders anywhere, but hopefully get lots of wins in the two groups that can help reach 28."
812,1,2,2,3,11,21,22,32,3,3,Just take the points
813,2,2,6,9,14,17,21,24,3,2,"I wanted to make sure that I had at least 2 at each castle to ensure I capture situations where my opponent sends only 1 or 0. Then I focused on the upper middle castles, 5 6 7 & 8, to maximize points from those as well. If I can win 6 or more castles, even without winning 9 or 10 I feel that I can win overall."
814,2,3,3,7,10,14,18,22,18,3,"The Price Is Right a-hole method. The median deployment per castle +1 got me to 99, add one to castle 8 because it had the deepest deployment."
815,2,3,3,7,10,14,18,22,18,3,"For this one, I looked at the median data from the last round, and chose numbers that would put me above the median for each castle. The sum of the median numbers was 89, enabling me to put median+1 in all castles (with an extra +1 for castle #8, the most contested castle last time)."
816,0,1,2,10,12,15,17,19,21,3,Picking my battles on medium strength castles.
817,3,5,8,10,13,1,26,30,2,2,"I figured that people would try and come up with new strategy to counter what they imagine will be the counter to last year's winning strategy, or they would go even further and try to counter the counter of the counter (etc).  I decided to copy last year's winner and see if lightning would strike twice."
818,3,5,8,10,13,1,26,30,2,2,Last time's winning strategy. Maybe people don't change.
819,1,4,2,3,21,21,21,21,3,3,"trying to beat the average bets, placing small ones on everything to pick up any additional ones I can"
820,3,7,10,14,17,21,25,1,1,1,Fight where your enemy is weakest and take just enough to secure victory.
821,3,6,1,12,15,18,21,24,0,0,"It's necessary to win 28 castle points. I'm aiming for that with about an %18 cushion. 33 points. Only losing castles 6, 7, or 8,loses outright.  And losing 6 is survivable if I get lucky and pick up castle 3. I divided the troops up evenly with 3 per castle point for the castles I attacked. And had 1 left over so I took a flyer on castle 3."
822,3,3,3,5,5,5,35,35,3,3,Use few troops on all but two mid level...
823,1,1,8,10,13,2,28,33,2,2,Can't waste too much time to lose anyway... decided to just beat round 1's winner.
824,2,3,3,7,10,14,18,21,19,3,I took the median of last battle's data and added one to each castle. The remaining troop was sent to castle 9 because I wanted to. I realize that because others are also analyzing this data I am probably going to get creamed but worth a shot.
825,1,1,3,13,18,3,25,30,3,3,Mach 1 eyeball.
826,1,1,12,14,31,31,1,1,4,4,I'm essentially just trying to beat the winner of the original submission at the same time as I'm beating the person trying to beat the original winner.
827,0,0,10,5,20,20,20,25,0,0,to win
828,4,6,9,0,14,3,27,31,3,3,old winning strategy +1 at the expense of castle 4
829,8,12,6,7,13,14,22,10,5,3,"Combination of intuition, randomness, and trying to match the winning deployment of last time."
830,0,2,14,14,2,14,25,29,0,0,"Majority of strategies opted for 1-7, or 1,8-10 then some variant of uniform distribution.  High amounts on 7 and 8 defeat first two, 14 each on 3, 4 and 6 brings total to 28 and counters even distribution. Castle 1 is not worth the troop for any strategy. 9 and 10 are more expensive than they are worth vs most opponents. 2 troops on 2 and 5 to beat 1 troop distribution. Wouldn't beat a computer, but I want to beat Riddler Nation."
831,0,2,9,0,0,5,2,0,41,41,"beat previous winner; try best to win (#9 and #10), then win either (#6 and #3) or (#7 and #2)"
832,0,3,3,3,22,22,21,20,3,3,Intended to defeat those that relied on information from the first game.
833,3,5,7,9,11,13,15,17,20,0,Random guess
834,3,6,9,13,3,10,25,25,3,3,"Amazed at how many zeroes were played in the first game. Assumed that more 1's would be played and increased all low winning counts and reduced all high winning counts. Assumed that Castle 6 would be a priority seeing as how low a score won that castle last time. Ensured always 3 soldiers per castle as 1 and 2 are arbitrary low soldier counts that many people may enter. Also statistically 3 soldiers  would have won about 30% of the battles for each castle. Many people again may use castle 9 and 10 as their attempt to win, but for each soldier placed there, there return on investment is lower. Probably totally off base though ;)"
835,6,8,9,11,14,16,17,19,0,0,sacrifice the top 2 and try to win the rest
836,6,0,5,7,8,9,16,22,27,0,Random; I thought to distribute the most to 7-9 and hope to win the small victories for small points.
837,6,11,13,15,14,15,2,20,2,2,decided 9 and 10 weren't worth it. the last winner really put effort in to winning 8 and 7 and i expect competition to overcompensate but i can't let both go so i'm only trying to win 8. the winner also left 6 alone so im hoping i can sneak a win through. the rest was just eyeballing what i thought would work
838,8,17,8,12,13,7,8,19,6,2,Im strategic
839,10,10,12,14,16,18,20,0,0,0,To win you don't need an optimal strategy just one that allows your opponent to waste men. This may not be a good strategy but it scores well against a 'normal' attempt to win the big battles.
840,0,0,20,20,0,20,20,20,0,0,"I figure people will for the 10's and 9's. Also, the max number of points is 55, so all I need is 28 points to win. Therefore, I want to maximize my chances of winning every small skirmish that I need to get exactly 28."
841,0,0,0,3,3,3,23,41,24,3,Stuck with strategy of de-emphasizing castle 10.
842,2,2,11,2,2,2,2,34,2,41,"The most popular strategy will be picking numbers that sum to 28, the minimum to win, which can be most efficiently done by picking four distinct numbers. I noticed that either 10 or 8 was in all of these, so those had to be priority. I calculated the expected troop allocation to each of these ((castle #)*100/28) and added a few troops to ensure my victory at both. I sent 2 to each of the other castles to beat anyone that would only send 1, and the rest we dropped at 3, which could beat the expected troop allocation of 10.71."
843,5,5,31,30,4,1,2,10,7,5,I tried to beat the winning strategy from last time.
844,11,7,12,10,15,20,25,0,0,0,It could beat many of the lower troop submissions
845,2,6,1,6,12,13,26,30,2,2,Focusing on 7 and 8 while not sacrificing any with 0. I'm hoping I can beat the balanced people at 5 and 6 to and stealing where they put 0s or 1s. The ones who go heavy up top I hope to beat them at 8 and win most of the rest.
846,1,3,3,3,3,23,27,33,2,2,"Castles 9 and 10 are too high risk, high reward, and not necessarily needed.  6, 7, 8 and any combination of 3 castles (except for Castle 1) would grant you a win."
847,2,0,0,1,12,14,12,15,0,44,"I spent a while playing around with genetic algorithms, this one ended up as the winner in a big run."
848,1,3,1,1,14,21,24,31,3,1,"I want to get 28 points from castles 8,7,6,5,2.  Then I win."
849,24,3,3,24,14,2,11,9,6,4,"In general, I wanted to deploy more soldiers to higher value castles. I could see that the previous winner broke with this rule on three castles, so I adopted that part of his strategy, but with my sacrifices occurring at adjacent castles to his sacrifices. Basically, I started with the previous winner's strategy and then tried to anticipate how everyone else would react to the info provided."
850,0,2,11,6,3,30,2,12,34,0,"Ground it out with an evolutionary approach. There is no stable point, of course, but it was getting pretty goofy when I got to 19k entries (mostly by perturbing the most successful ones of each iteration), so I had to stop it at some point. I stopped it when it looked... kind of neat... and I needed my CPU for other things."
851,5,5,10,15,20,25,17,1,1,1,I  chose to go for the lower numbers because I thought most people would focus on the higher numbers
852,5,6,9,16,0,26,31,1,4,2,Total points in the game equals 55. You need 23 points to win. May be silly but I took a low combination of numbers to equal 23 in order to win. Contingent i win all the castle I want but I added an extra guy on 9 in order to hopefully win a couple by luck. I suspect this might be a popular strategy since the data has been released but oh well.
853,1,1,1,2,2,4,12,14,13,50,"tested 100 random distributions for best round robin result, then hand tuned a little."
854,1,1,1,2,3,4,5,11,21,51,I don't know
855,1,1,3,0,0,9,15,35,35,1,I sent them to ones that seemed like a good idea.
856,1,1,1,17,1,21,1,27,29,1,"Just need 28 points lads! Also, who goes for #10 anyway?"
857,1,10,10,10,10,10,13,14,21,1,"I gave up on castles 1 (low value) and 10 (high conflict).  I distributed the extra troops to castle 9-7, focusing on trying to win castle 9."
858,6,0,16,20,0,1,46,1,6,4,Random solution meant to help my initial submission.
859,12,11,2,2,11,15,17,26,2,2,Minor tweaks to the previous winning strategy
860,0,0,11,11,21,21,1,1,32,2,Mind taking baby!
861,35,25,5,5,5,5,5,5,5,5,"Generally, it looks like 5 will take many castles, but also the 10 and 9 castles are probably more efficient per soldier to win, so I massed there."
862,9,10,11,12,13,14,15,16,0,0,"8 + castle score for first 8. It only takes 28 points to win. The bottom 7 castles add up to 28. Add in the 8th castle for a buffer and go all in, with a slight weighting towards higher castles."
863,0,12,12,12,12,12,0,40,0,0,"Last time I tried to minimize the number of castles needed to get 28 while getting as close to 28 as possible with some soldiers in other castles to pick up stragglers. This time I went for more castles than the minimum needed and didn't go for any stragglers to try and maximize my chance at my win condition. If I only go for what I need and someone else goes for stragglers, then I have more soldiers to work with where they count. Maybe."
864,13,21,5,5,14,16,10,8,5,3,"It looks like people left castle 10 open last time, so I put troops there, however, as most people will likely see that, I focused my efforts on the also under-exploited castle 9, while still spreading troops in order to pick up other castles."
865,4,6,8,2,16,0,28,32,2,2,to win. rp
866,1,2,2,2,2,2,11,1,26,51,"This allows me to take advantage of those who completely ignore 1-6, and I believe the n+1 strategy will outfox likeminded competitors on castles 9 and 10. By essentially giving up competition at castle 8, I am making myself much more competitive for castle 7."
867,6,11,11,11,2,21,2,32,2,2,Blind Guess
868,2,1,5,4,48,5,19,5,2,9,I created a random plan generator that kept track of the best point expectation out of a small number of attempts. Then I ran it many times. The one that survived I tested against many random troop deployments.
869,1,2,2,2,17,19,21,36,0,0,Victory
870,4,2,24,28,2,12,14,6,5,3,Looked at deployment values from the inaugural battle & attempted to put myself above the 50th percentile for all castles.
871,1,1,1,1,17,21,26,30,1,1,"I figure that too many people will overdeploy to castles 10 and 9, so it's not worth overdeploying to those castles.  I also figure that Castles 1-4 just aren't worth enough to overdeploy there.  But, I also want to capture any castle that anybody doesn't even try to defend.  So, I'll put a single defender on the 6 castles that I don't want to overdeploy to in order to pick up some cheap wins or ties.

As far as Castles 5-8, I figure those are the most valuable ones.  I also figure that Castle 8 is worth the most.  And, given that the winner last time put 30 there, I figure 30 seems to be about correct for that.  Then I just divvied up the rest of my troops in a configuration that makes some type of sense.

I probably have no shot, but this is an interesting exercise, and I like seeing the data that comes out of this."
872,3,3,21,21,21,21,4,4,1,1,"I estimated where most people would distribute their troops, assumed they would plan what I would plan to combat that. Then I tried to maximise a way of beating my own plan against them."
873,18,16,15,13,11,9,7,5,4,2,"If there is an optimal strategy for this game, it is beyond my modest abilities to figure out.  Also, with 1000+ entrants, trying to pick what the other entrants will do seems like a shot in the dark even with the data from the first game.  So I kept it simple and assigned soldiers proportionally to each castle's percentage of the total available points.  Rounding standardly, this worked out to exactly 100 soldiers."
874,14,14,14,14,14,14,14,0,1,1,Getting 28 so that I can always have a majority amount of castle points.
875,0,1,1,1,1,2,21,31,41,1,Outwit the guys who max castle 10. And don't half any points for the small ones
876,12,12,7,7,23,23,13,1,1,1,"I looked at the last winner's strategy (1), found the strategy to beat the last winner by as many points as possible (2), and found the strategy to beat that strategy by as many points as possible (3). The goal is to get to 28 points as many times as possible, so I came up with an ideal strategy to do that, while also making sure that my troop deployment would beat 1, 2, and 3, as those would likely be popular picks."
877,4,4,31,25,3,9,9,8,5,2,Went a bit bigger than the winner's choice on the big castles and a bit smaller on the small castles.
878,2,2,2,30,30,20,5,5,2,2,middle castles will be underplayed
879,10,2,4,27,13,20,0,6,17,1,Random solution meant to help my initial submission.
880,0,0,35,0,6,0,33,3,2,21,Random solution meant to help my initial submission.
881,1,1,2,2,2,6,6,4,3,73,(see my other try)
882,2,0,2,4,2,5,1,3,11,70,"Mostly ignored the previous tournament, though probably not a good idea because there are many ""joker players"" (players aiming only to create noise, with no intention to win, which quite unfortunately makes this more of a guessing social experiment, than a mathematical one). A simulation suggests that optimal mixed strategy should be randomising a plan around having some 50-80 men on castle 10, 0-25 on 9, 0-20 on 8,  0-10 on 7, and so on down to 0-3 on castle 1. This is one such random plan."
883,19,17,15,13,11,11,8,6,0,0,"I took the amount of points available and divided that by the number of troops so you'd get even troops per point available, and I rounded up and took some points from the bottom to reinforce the higher point value castles"
884,7,8,1,13,32,30,7,1,1,0,Random solution meant to help my initial submission.
885,0,4,31,27,14,0,12,8,3,1,Trying to defeat the winner from last round
886,12,15,20,24,2,2,22,1,1,1,Wild Guessing
887,22,27,27,5,4,5,4,4,1,1,"I tried to hit as many high value castles while simultaneously giving myself a decent (>25%) chance of getting the smaller castles.  I looked at last time's data and tried to stay out of the ""no-man's land"" where additional troops wouldn't have made a difference against most opponents"
888,0,0,0,0,0,0,7,0,32,61,Game theory is hard.
889,0,0,1,1,3,1,3,3,1,87,This is based off a a genetic algorithm fighting itself. If I had time I think a Monte Carlo based integer program would be interesting.
890,10,15,20,30,20,1,1,1,2,0,by gut feeling.
891,0,1,1,2,1,1,1,2,1,90,I had no strategy I just wanted to participate
892,2,13,1,2,62,5,2,1,11,1,Random solution meant to help my initial submission.
893,1,1,1,1,1,1,1,1,1,91,Why not.
894,1,1,1,1,1,1,1,1,1,91,HOLD THAT L!!
895,31,26,23,11,2,2,0,2,3,0,Because I like being right... and I can see the future. Crown me the victor 583!
896,0,0,0,0,0,0,0,0,0,100,"Because I am hoping nobody else would send 100 troops to castle ten, because they want to have stake in everything, or something else. They also wouldn't be stpid enough to take this calculated risk, like me. It is also hard to amass 10 victory points by a combination."
897,0,0,0,0,0,0,0,0,0,100,Just to see what happens
898,34,30,30,0,0,0,0,0,0,6,The top 3 castles and any other castle will win it.  This strategy allows me to big bid on the high value castle.
899,32,26,23,0,19,0,0,0,0,0,"The deployment aims to get 3 out of four of castles 10,9,8,6, which always gives you over 23 points.  I believe most people will spread their troops more evenly."
900,35,30,30,0,0,0,0,0,0,5,"You only need to win the top 3 castles and the last castle to claim victory (~51% of total points) and since these castles were way underdeployed last time, a big shot in the arm should be enough to take each of them. Since I am completely abandoning the rest, I should be able to over deploy the rest and win the castles that matter."
901,0,0,0,0,0,0,0,0,100,0,"Someone will try going for 10, just sending all their troops there.  Heck, many people may try that.  I want to guarantee to get castle 9, and hopefully split it among fewer people."
902,100,0,0,0,0,0,0,0,0,0,i am guaranteed one point