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Riddler - Solutions to Castles Puzzle: castle-solutions.csv

This directory contains the data behind the submissions for castles puzzle.

Readers were asked to submit a strategy for the following “Colonel Blotto”-style game:

In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war.

Submit a plan distributing your 100 soldiers among the 10 castles. Once I receive all your battle plans, I’ll adjudicate all the possible one-on-one matchups. Whoever wins the most wars wins the battle royale and is crowned king or queen of Riddler Nation!

The data includes all valid submissions, with solvers’ identifying information removed. The 11 columns represent the soldiers deployed to each of the 10 castles, plus a column where the reader could describe his or her strategic approach.

Correction

Please see the following commit: https://github.com/fivethirtyeight/data/commit/c3f808fda5b67aa26ea6fa663ddd4d2eb7c6187f

Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub

1,387 rows sorted by Castle 6

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Suggested facets: Castle 1, Castle 2, Castle 3

Link 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?
1 100 0 0 0 0 0 0 0 0 0 because, I am number one!
5 25 0 0 0 0 0 0 25 25 25 The total points up for grabs is 55, and to win the war I need 28 points. I want to get 28 points by using the least number of castles, so I can put more soldiers in each castle and increase my odds of winning that castle. I can earn 28 points by winning castles 1, 8, 9, and 10. So I will put 25 soldiers each in castles 1, 8, 9, and 10 to maximize my odds of winning each of those castles simultaneously.
6 25 0 0 0 0 0 0 25 25 25 Submission #4. A variation of my third submission. Equally divided among just enough points to win. (Not convinced this will win either).
7 25 0 0 0 0 0 0 25 25 25 There are 55 points up for grabs, so 28 are needed to win. Winning castles 1,8,9,10 are the fewest number of castles needed reach 28 points. Castle 1 is as important as castle 10 for getting to 28 points.
8 25 0 0 0 0 0 0 25 25 25 Since there are 55 available points, I only need to win 27.5 or more points to win any given battle. By maximizing my soldiers in the four castles that are worth 28 points combined, I maximize my chances of beating more evenly distributed enemies.
11 21 0 0 0 0 0 0 26 26 27 If you were to win castles 10, 9, 8, and 1 each time, you would win every matchup. I put all of my soldiers on those castles, with a few extra on the more valuable castles to beat out anyone with the same strategy
13 20 0 0 0 0 0 0 25 25 30 it put high power making it easy to win the castles with troops.
27 15 0 0 0 0 0 0 17 26 42 Submission #5. I guess I have the second most confidence in this (of my 6 submissions). Defending just enough points/castles to win and dividing them unequally in (probably vain) hopes that I can win.
38 13 0 0 0 0 0 0 29 29 29 Seeing as there are only 55 total points available, you only need 28 victory points to win. The "easiest" way to do this (in terms of total number of castles won) is Castles 1, 8, 9 and 10. I then split the number of soldiers such that the ratio of soldiers at castles 8 to 9 to 10 is 1:1:1 and the number of soldiers at castle 1 is greater than 10. This strategy will beat anyone who splits evenly between the 10 castles, and (I'm hoping) will beat a decent number of people who go for the same four castles. An example strategy this would lose to is is someone split all 100 of their troops between e.g. Castles 9 & 10. I decided not to employ a similar strategy since I think more people will try something similar to mine rather than something somewhat counter-intuitive like betting all their troops on only two castles (although this isn't really based on any evidence).
39 13 0 0 0 0 0 0 29 29 29 Focus all troops on the fewest number of castles that would win the minimum 28 points necessary to win.
81 11 0 0 0 0 0 0 29 29 31  
99 10 0 0 0 0 0 0 30 30 30 If I win castles 1,8,9,10 I will receive 28 points and my opponent will only receive 27. This is the least number of castles that I need to win in order to beat my opponent. Assuming that I need to win all 4 to have a chance and that my opponent will put very little into winning a single point from castle 1, I will only deploy 10 soldiers. Winning castle 1 is a lynchpin though and I need to win it or my theory fails. All other castles are very important to me and I am able to put 30 soldiers in castles 8, 9, and 10 because castles 2-7 mean nothing to me. I can lose them all and still win if I win 1,8,9,10.
100 10 0 0 0 0 0 0 30 30 30 Load up the soldiers on the minimum castles needed to win
101 10 0 0 0 0 0 0 30 30 30 Tried to choose the fewest number of castles (and in the case of #1' the least likely to be attacked) to attack that would give me a majority of the points.
102 10 0 0 0 0 0 0 30 30 30 Deploying hopefully overwhelming force at castles 8 through 10, and a token force to capture 1. It doesn't allow any room for failure, but hopefully will be strong enough at the one point to ensure victory.
121 7 11 0 14 16 0 23 0 29 0 I want a winning coalition of 28.
131 7 0 0 0 0 0 0 31 31 31 28 or bust.
132 7 0 0 0 0 0 0 31 31 31 There are 55 points total to be won between the 2 warlords if all castles are fought for, so whoever gets 28 or more wins in that case. In that case there are 14 ways to get at least 28 points, by winning one of the following specific groups of castles: {10,9,8,7}, {10,9,8,6}, {10,9,8,5}, {10,9,8,4}, {10,9,8,3}, {10,9,8,2}, {10,9,8,1}, {9,8,7,6}, {9,8,7,5}, {9,8,7,4}, {8,7,6,5,4}, {8,7,6,5,3}, {8,7,6,5,2}, {7,6,5,4,3,2,1}. I would like to try to win the fewest number of castles yielding at least 28 points and including a castle that fewer warlords would desire if possible so I can win it with a light deployment and concentrate in the others. From the above, it appears that a 4-castle group of {10,9,8,1} satisfies that, so those are my targets and I have concentrated the soldiers in the higher values castles as desired.
133 7 0 0 0 0 0 0 31 31 31 Well i was in the armed forces for about 27 years soooooo i think i know what I'm talking about pfffff
134 7 0 0 0 0 0 0 23 30 40 There are a total of 55 victory points available, so 28 are needed to win each war. Winning is not necessarily about getting the most victory points -- it's about getting to 28 victory points as often as possible. Thus I dumped almost of my troops in the 8,9, and 10 victory point castles, since winning those three is a total of 27 victory points. Unfortunately, I needed one more victory point, so I put 7 in the 1 victory point castle, hoping that it would be virtually ignored by most people. If one were to distribute troops to castles proportional to their victory points, only (1*(100/55))= 1.818 (which rounds to 2) would be sent there, so I hoped 7 would be enough to take care of that.
135 6 12 9 15 15 0 0 21 21 1 Picked favorite numbers.
156 6 0 0 0 0 0 0 26 27 41  
201 5 5 0 0 0 0 0 30 30 30 You need a minimum of 4 castles. Want to try to ensure the top three and gives a good shot at lower.
208 5 0 11 14 16 0 22 32 0 0 Put all soldiers on acombination that adds to 28 and hope the opponent chooses a more even distribution
209 5 0 10 0 0 0 20 30 35 0 Hope to win majority of points available and no more.
211 5 0 0 0 0 0 0 27 31 37 The three most-valuable castles are worth 27 total, and the 7 least-valuable are worth 28. So making a strong claim to 27 points and a weak claim to the 28th point seems like a good distribution. The vulnerabilities can be exposed, though, by a distribution that weights castles 2-7 as moderately important, and emphasizes a strong attack on one castle in the 8-10 range. I just have to count on my 8-10 range being fortified enough and few enough other people being crazy enough to send 5 soldiers to a castle worth 1 point.
212 5 0 0 0 0 0 0 25 30 40 Only need 28 total pts to win the battle
256 4 0 12 0 19 0 30 0 35 0 Simulation, using mode castle placement, where probability of assigning a soldier to a castle is based on points but ignoring even-numbered castles.
259 4 0 0 0 0 0 0 32 32 32 Since I needed to win just over 50% of the possible 55 points I put all my men into the 4 castles that would earn 28 points and conceded the rest to my enemies. I figured this would allow me to concentrate my forces on castles that would guarantee me a victory if I was able to capture them. I know this is a risky (foolish?) strategy because I'm giving my enemies 27 points and failure to capture my 4 target castles would guarantee defeat. I'll be interested to see how my gamble/this game plays out. "Once more unto the breach"
260 4 0 0 0 0 0 0 32 32 32 All in, just like in Poker - I bet you can tell I lose a lot of money :(
261 4 0 0 0 0 0 0 32 32 32 I decided to go all in on a single strategy instead of hedging. You need to conquer a minimum on 4 four castles to win. I am putting all my soldiers into those four castles, so I want at least one of them to be uncontested to free up soldiers for other castles. There is only one such group of four that includes the least contested castle. That is (1, 8, 9, 10). I put the minimum force towards 1 that I thought could gain me victory relatively often.
262 4 0 0 0 0 0 0 29 32 35  
263 4 0 0 0 0 0 0 28 32 36 I want to maximize my victory points, that is, with the least number of soldiers. The higher the castle, the more troops needed to secure a victory point. To win, I need more than half of the total victory points, which is 55 (to win, I need 28). To achieve this, I selected the fewest castles that will allow me to get 28 victory points, that is: castles 10, 9, 8 and 1 (10+9+8+1=28). So I need to distribute 100 soldiers in these 4 castles and let opponent take all other castles. I weighted the victory points to win vs the amount of soldiers, ie castle 10= 10/28*100=35.7, or 36 , castle 9= 9/28*100=32.1 or 32, castle 8= 8/28*100=28.57, or 29-1. and castle 1 is 1/28*100= 3.57 =4. I assumed castle 1 would be uncontested, but ensured at least its value of 4.
264 4 0 0 0 0 0 0 28 32 36 To choose a strategy, I have thought about two axes. The first one is the tendency of players to use balanced strategies such as x y x yäó_ with x+y =20 as a response to the simplest strategy of 10 10 10 äó_ the second one is to concentrate troops on castles with 28 as value sum (the number needed to win a battle). Each castle i with a number of troops proportional to its value i.e. 100i/28. Using these two hypotheses, castles with highest values would have fewer troops than their values required (using the first axe). The best strategy would be then (using the second axe) to use a set a castle with sum values 28 and with the highest values possible. We end up then with using Castle 10,9,8 and 1 (sum is 28). Proportional allocation would be 36,32,28 and 4 (sum is 100).
268 3 7 11 14 0 0 0 29 0 36 I've no real knowledge of game theory so I'd imagine mine is extremely primitive but it was based on the idea of attempting to win exactly enough points to have a majority and not contest the other towers. Obviously there are a variety of combinations that come to the 28 points needed. I then calculated how many troops should go to each tower proportionally based on the value of the tower relative to the target value of 28. As for which of the many combinations adding up to 28 I selected? Well I stook my finger in the air and picked (10, 8, 4, 3, 2, 1), as I felt it had a nice balance of covering the Highest value tower, but also covering a decent spread of other towers.
305 3 4 8 0 20 0 30 35 0 0 to not deploy forces to the most valuable castles where there would likely be the most competition. Place strength on mid value and low value targets to reach goal of 26
309 3 4 4 5 6 0 0 24 26 28 Started with 10 on each castle (assuming average of random assignment), and then made a "k-1" deployment that would beat that deployment, and then a "k-2" that would beat the "k-1" deployment, etc., out until k-10, then made some minor adjustments.
311 3 4 0 0 1 0 2 0 7 83 I ran a few simulations in MatLab, starting with warlords who randomly assigned their soldiers and then using the most successful warlords of each previous generation to bias the assignments of the next. This is a rough average of some of the winning strategies after a few hundred rounds.
341 3 0 9 0 0 0 21 31 36 0 It doesnt waste troops on castles that I dont need to win
342 3 0 4 8 0 0 15 35 35 0 Abandon hopes of Castle 10 and put all the eggs in the basket of 7-9 + 4 or 3 and 1
343 3 0 0 11 0 0 26 27 30 0 I expected that it would allow me to win multiple battles without wasting troops on likely losses.
344 3 0 0 0 0 0 0 31 32 34 To win the most wars you need to get >=28 out of 55 points the most often. Giving 30+ troops to each of Castles 8, 9 and 10 will hopefully guarantee you 27 points. Then 3 troops on Castle 1 hopefully gets you that one last point you need.
345 3 0 0 0 0 0 0 29 32 36 There are 55 available points, so the winner needs 28. Castles 8, 9, and 10 provide 29%, 32%, and 36% (respectively) of the 28 points required. I allocated my troops according to their relative importance, and then put the last 3 on Castle 1 to grab my last needed point.
346 3 0 0 0 0 0 0 29 32 36  
347 3 0 0 0 0 0 0 29 32 36 28 wins, proportional to castle value
348 3 0 0 0 0 0 0 29 31 37 There are 55 points available on the board, so only 28 are needed to win, assuming no ties. I could incorporate ties in my strategy, but I'm an engineer, not a mathematician, it's late on a Friday afternoon, and I'm kind of tired. 28 points can be achieved through winning only four castles: 1, 8, 9, and 10. I concentrated all my forces on those four keeps. I split up my army to assail those keeps with a distribution of 3, 29, 31, and 37 warriors, respectively. I chose those numbers because like a good commander I know my troops. And I know my warriors fight best when arranged in groups of Prime Numbers.
366 2 5 8 13 20 0 25 27 0 0 get to 28 points
373 2 5 6 6 21 0 25 0 35 0 You have the chose if you going for castle 10 or not. The problem with going for it is that how hard you try to win it depends on how hard the other person does. My strategy is to fight harder than normal on castle 7 and 9 and try to win by winning most of the lower castles.
378 2 4 9 0 0 0 15 15 25 30 Assume low value castles may be lightly defended, so try to pick up 3 castles for a total of 15 soldiers. Send most resources to highest value castles, and basically hope the archfiend has wasted troops trying to overwhelm me at 4, 5 and 6,
452 2 3 8 2 2 0 17 26 38 2 I'm ceding ten because others will deploy a lot of troops there--hopefully many will be wasted. Trying to get the next three plus Castle 3 which would just barely be a win. Also hoping to sneak in on some places where the enemy might have put in 0 or 1.
600 2 0 0 0 0 0 0 32 33 33 I need to win the top 3 castles plus one so I tried to optimise for this result.
601 2 0 0 0 0 0 0 31 33 34  
942 1 1 1 1 1 0 11 17 26 41 Heavy on big castles
944 1 1 1 1 0 0 0 48 0 48 28pts wins. I hope my opponent won't play for castles 1, 2, 3, and 4, and so I put one soldier each there, splitting the remainder between castles 8 and 10 to make exactly 28. Cool idea, BTW!
945 1 1 1 1 0 0 0 32 32 32 Tell us denote a particular deployment by a 10-tuple, castle 1 first. So the above deployment is (1, 1, 1, 1, 0, 0, 0, 32, 32, 32). I have been considering 3 broad classes of strategy. (Obviously there are deployments which don't fit into this schema, but which may still be meritorious.) I call these classes Paper, Scissors and Stone. Paper strategies cover all the castles with forces approximately proportional to the value of the castle, for example (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). I also consider an equal distribution of forces, 10 to each castle, to be a Paper deployment. Scissors surgically target a winning subset of castles, for example (10, 0, 0, 0, 0, 0, 0, 30, 30,. 30). Clearly Scissors will defeat paper. Stone strategies target subset of castles insufficient to win on their own, but additionally hope to win or tie enough other castles to gain the extra points to win the war. (1, 1, 1, 1, 0, 0, 0, 32, 32, 32) is a stone strategy. It will win if it wins castles 8, 9, and 10 and either wins castle 1 or ties any other castle. Stone loses to paper (it wins its targeted castles but loses the rest). It mostly wins against scissors because both strategies are likely to contest at least one high-value castle, and stone's forces will be more concentrated. It's my expectation that the majority of depoyments submitted will be Scissors or paper-scissors hybrids. My original idea was the stone (1, 0, 0, 0, 0, 0, 0, 33, 33, 33) This is elegant in that it wins precisely when it wins castles 8, 9, and 10, and any other castle is uncontested by the opponent. The first condition is nearly certain against a scissor strategy since these must target at least four castles, and it will be very difficult to commit as many as 33 soldiers to any one of them. The second condition is much less certain. I cannot predict how many competitors will decide to contest every castle. I decided to tweak my original idea as I suspect that rather more scissor players will put at least one soldier into every…
951 1 0 0 0 0 0 0 33 33 33  
952 0 26 32 42 0 0 0 0 0 0 I thought people would fight it out for the high value targets and end up splitting a fair number of those castles. If I could take enough of the lower (less competitive castles) I would win more points. Also, stay away from clean looking numbers.
953 0 25 25 25 25 0 0 0 0 0 HUNGER!
954 0 21 0 0 0 0 25 0 27 27 I think I need to get my minimum 28 points by trying to take 4 castles, which is the minimum it would take. There are 27 combinations of 4 that generate at least 28 pts. All of them require some combo of castle 10, 9 or 8. I chose the one that has two castles well below 8 where I think there will be less competition and concentrated my troops on 9 and 10. Bit of a punt. Can't wait to see the results!
955 0 20 0 20 20 0 0 20 20 0 Guesswork
966 0 12 0 0 0 0 28 0 28 32 I wanted make sure I was always ~2-3 points above a multiple of 5, since I think a lot of people will use either a multiple of 5, or add 1 extra to a multiple of 5. This is a risky strategy since I only bet in 4 rounds, and I need to win every single one of them. However, I think many strategies will be vulnerable to this one.
976 0 10 30 60 0 0 0 0 0 0 swag
982 0 10 0 0 0 0 0 30 30 30 I'm "cheating" in that I am doing the opposite of my first battle plan.
983 0 10 0 0 0 0 0 30 30 30 My goal was to defeat the strategies I thought would be most commonly used, specifically, 10 at every castle, 25 in castles 10-7, 25 in castles 10-8 and 25 in 1. My strategy does lose to 10-8 34 33 33 however I don't think that strategy will be heavily employed as it loses to 10 at every castle.
1006 0 5 10 10 0 0 20 25 30 0 Need 28 of 55 to win a matchup.
1031 0 3 3 3 21 0 21 24 1 24 I wanted to win 5 regions
1044 0 2 0 2 22 0 26 0 12 36 Simple simulation among randomly generated strategies https://github.com/mattinbits/fivethirthyeight_riddler_war_game
1053 0 1 5 5 5 0 21 21 21 21  
1090 0 0 30 26 20 0 14 10 0 0 I tried to target 28 points in places that are not as likely to be contested, allocating more troops to the more contested locations.
1094 0 0 15 1 0 0 0 27 28 29 There are 55 points up for grabs. I need at least 28 of those points. 10+9+8+1=28. So I need to win 10,9,8, and some other number. 3 seems like a good other number to win. It's probably not too popular. But one in 4, just in case it gets left open and is the points I need to win, or someone puts only 1 in it and it's the points I need to tie. The 27/28/29 beats this exact strategy except with 28/28/28 instead. And it doesn't leave me too vulnerable to 27/27/27s because if they let their fourth number be something other than 4 and they do put 1 into their other numbers, I win. (I win the 3, then I win with the tie from 4). If they don't put 1 into their other numbers, their fourth number needs to be 3.
1101 0 0 12 16 11 0 14 0 47 0 I wanted a strategy that would defeat the following strategies: (1) Maximize points -- give castle N 100N/55 soldiers (2) Greedy "maximize chance of getting 28 points" -- putting 100N/28 soldiers in castles 10, 9, 8, and 1 (3) Basic implementation of my strategy -- 100N/28 soldiers in castles 9, 7, 5, 3, and 2 Versus a strategy that puts soldiers in every castle, like (1) above, my strategy can only get 28 points max. That means I need to have at least 1+ceil(100N/55) soldiers in every castle I try to claim. Against (2), I need to make sure I win at least 1 of the castles they contest. I decided to contest castle 9, so I'll put my spare troops there. Against (3), I'll need to win castles adding up to at least 15. I'll probably win 9 with all my spare troops there, so I need to pick more castles that add up to 6 or more and give them extra soldiers. I put 1+ceil(100N/28) troops in castles 3 and 4, leaving 1+ceil(100N/55) in castles 5 and 7. Final results: Castle 3: 1+ceil(100*3/28) = 12 soldiers Castle 4: 1+ceil(100*4/28) = 16 soldiers Castle 5: 1+ceil(100*5/55) = 11 soldiers Castle 7: 1+ceil(100*5/55) = 14 soldiers Castle 9: the other 47 soldiers Let's see how it goes!
1117 0 0 11 0 0 0 26 27 0 36 This approach goes all-in on winning just enough points to win. It is very vulnerable to "random" distributions, which only need to win one of the castles I actually allocate troops to, but puts enough troops in the "target" castles that I should be able to win them most of the time.
1123 0 0 10 0 20 0 30 0 40 0 Higher points are worth more, so have more troops.
1125 0 0 10 0 0 0 0 30 30 30 Going straight from either end, leads to Castle 7 being the swing castle. I am therefore avoiding Castle 7 altogether. Putting 25 on the last four seems strong, but you would only have to lose one castle to lose. Putting 40 on Castle 7 and 10 on the first six would be good unless someone won castle 8-10 and stole a single other castle as 8-10 gives 27 points and to win you need 28. To avoid these scenarios, you could take 5,6,8,9 with force, leave 7 alone and try to benefit from a possible 0 on 4+10. Putting 30 on 8-10 and 10 on 2 would win all. Except Castle 2 may not be that under the radar so instead I will go after Castle 3 if that means I win against similar strategies to mine that choose Castles 1 or 2. I am avoiding the middle because of those that will go for the averages, avoiding the high value targets and the worthless low ranking castles. Scenarios that lose would be 31-33 on 8-10, but those would also lose to other scenarios.
1126 0 0 10 0 0 0 0 27 30 33 A good strategy needs to achieve a number of goals: 1) It should deploy troops in proportion to the number of points to be won 2) It should concentrate on getting enough points to win, rather than trying to win all of the points 3) It should be robust against opponents who make small deviations from the same strategy 4) It should beat every obvious strategy There are 55 points available but only 28 points are required to win. Therefore, most of the troops are concentrated on winning castles 8, 9 and 10, for which 27 points are available. The remainder of the troops are concentrated on trying to win castle 3, rather than trying to win castle 7. This is because castle 7 will be more competitive than castle 3, and deploying a proportionate number of troops to win castle 7 will be a waste of resources which could be used to fight for the other castles. This strategy is robust against another strategy which leaves a lot of the smaller castles undefended. Even if it lost castle 9 or castle 10 to such an opponent, it would still win because of the split points at the castles ignored by both sides. It would lose to a strategy which attempted to win castle 1 rather than castle 3 but it has an advantage over the latter strategy in that it would beat the "obvious" strategy of putting 10 troops on each castle, while the latter strategy would not.
1132 0 0 8 11 15 0 27 0 39 0 Rock-paper-scissors logic: A "wide" strategy that contests all 10 castles (55 points, avg 1.81 men-per-point) will always lose to a "tall" strategy that contests barely enough castles to win (28 points, avg 3.57 men-per-point). With a nearly 2-to-1 advantage in men per point, the "tall" build has a lot of wiggle room for differences in castle distribution where it can still win. A "tall" strategy will lose to a "focused" strategy that sends an unusual # of men to one or two castles (not enough to win by themselves) and then small #s of men to all remaining castles... but only if the "focused" player picks exactly the right castles. For example, a "1-8-9-10" tall player will lose to a focused-wide player that sends 54 men to castle 9 and 1 man-per-point to all other castles. However, a "focused" build loses horribly to any "wide" build... and even to some "tall" builds. (for example, 9-focused versus 4-7-8-10 tall) Therefore, "tall" is the strongest overall strategy as it is only soft-countered by "focused". When considering "tall" vs. "tall" fights... you're going to overlap on at least a few points. By definition if you win all of the overlap points, you'll have at least 28 victory points and you will win. So it is more important to contest the points you've chosen than to send single lonely soldiers to win uncontested points - you should go all-in on the limited # of castles you have. Tall builds will be more likely to involve the higher numbers (8,9,10) than the lower numbers (you need all of castles 1-7 to win) so you should send greater-than-average men-per-point to the high numbers.
1178 0 0 0 25 0 0 25 25 25 0 4+9+7+8=28 which is the least amount needed to win the war.
1179 0 0 0 25 0 0 24 25 25 0 10*11/2 = 55 points in the game, score of 28 wins, need at least 4 castles, so 4 castles it is, avoid the bing guns (e.g the 10+9+8+1 combo) since vegas addicted people will front-load the 10, the only other 4 castles combo without repeat is 9+8+7+4, even spread of ressources between castles since they are all equally important in this strategy.
1180 0 0 0 24 0 0 25 25 26 0 I tried to ensure victory at the minimum number of castles that would give me the minimum number of points to win.
1181 0 0 0 21 0 0 26 26 27 0 There are 55 victory points, so we need to win 28 to win the war. No three castles provide enough victory points by themselves, so my strategy is to concentrate on four castles that are cumulatively just enough to win the war, avoiding the most attractive castle #10, and concentrate all my troops there to maximize odds of winning these castles. Castles 4, 7, 8, and 9 work. (Another similar choice would have been castles 5, 6, 8, and 9.) I distributed the 100 armies across these castles with slightly more on the more valuable castles rather than evenly.
1188 0 0 0 17 0 0 17 33 33 0 Minimize castles. 9 & 8 are most important. 10 will probably be overvalued.
1192 0 0 0 15 18 0 0 0 32 35 Used the minimum number of castles to get to 28 points, and then allocated for the highest average win probability.
1194 0 0 0 15 15 0 0 0 35 35 There are 55 points up for grab, so any strategy should aim to win at least 23 victory points. Castle 10, 9 and 8 contain over half of the victory points in the war, so to get a majority of the points any strategy must attempt to win at least one of these. Also the minimum number of castles you need to get 23 points is 3 so you shouldn't waste troops fighting over a large amount of castles but focus on winning a few key ones. After getting that far in my thought process I couldn't decide what I should do, so I wrote a simple simulation to find interesting strategies for me. It randomly generates several thousands strategies and makes them fight in the same way you will be judging the contest. After that they are ranked by how many victories they achieved and then the losing half is removed and replaced by new strategies generated by randomly modifying ones in the winning half. This causes strategies to evolve over time. Strategies would rise up and start dominating the simulation then eventually be bested and move down to the losing half and disappear. The strategy I chose was one that I hadn't though of but my simulation did, so I'm hoping not many other people will have thought of it. It dominated the simulation for a decent amount of time when I didn't expect it to. It focuses on winning castles 9 and 10 and hedges its bets between 4 and 5. As long as I win 9 and 10 I only need 4 more points to get to 23, which lets me focus on castles that might not be very hotly contested.
1195 0 0 0 15 0 0 26 28 31 0 I need 28 points to win, so I'm trying to win castles 4, 7, 8, 9. Each of those I placed roughly n/28 * 100 troops. I'm hoping anyone using a strategy other than this would not place so many troops on any of those four castles.
1196 0 0 0 15 0 0 25 30 30 0 I know I have to win 28 value points to win the war. I think many people will overvalue Castle 10, so I'm punting. I then have to load up in the hopes I can blow away Castles 7-9 with the bonus troops I saved... that puts me at 28 pts. I then need only 4 more... I was split between trying to win both 2 & 3, or just going for 4, but I'm consolidating everything & seeing how it pans out. #trusttheprocess
1197 0 0 0 15 0 0 25 28 32 0 I considered a handful of common strategies and counter-strategies, and then picked castles that added up to 28 points (4,7,8,9). I assigned soldiers to each castle so that the ratio of soldiers to points was about constant- close to 100/28, noting that people who go for castles 1-7 might assign 14 to 4.
1198 0 0 0 15 0 0 25 25 35 0 Concentration of force on the lest amount of numbers needed to win greater than 50% of the victory points while avoiding the highest value numbers if possible.
1199 0 0 0 15 0 0 23 31 31 0 Only need 28 points. Fewest number of castles is 4. Wanted to avoid castle 10, which is often going to cost the most to win, so I'm going for castles 4,7,8,9. Few people will contest 4 with more than 14. Few people going for the 1, 8, 9, 10 win will put more than 31 on 8 and 9. I'm vulnerable to people who put 33 on 8, 9, 10 and only 1 on castle 1, but they're going to be vulnerable to all randomly chosen strategies and strategies that go for Castles 1-7 (strategies I'm robust to).
1200 0 0 0 15 0 0 20 30 35 0 I decided to consolidate my troops. As long as I win each of the castles I have sent troops to, I will have a majority of the victory points. I think I will rarely meet an opponent more invested in my castles than I am.
1201 0 0 0 14 18 0 0 0 33 35 55 total points divided by 100 soldiers gives each soldier an avg. point-to-soldier value of .55, and vice versa 100 soldiers divided by 55 points gives an avg. solider-to-point value of 1.81. 28 points is the minimum point to win, so any soldiers expended to guard castles beyond that point total are non-optimized. Multiplying each castle's value by 1.81 yields the average soldiers required to garrison that castle (ie, Castle 1~ 1.81, Castle 2~ 3.62, Castle 3~ 5.43, etc.). When rounding to the nearest whole number, Castles 4, 5, 9, and 10 are the least expensive to garrison (have the smallest soldier-to-points ratios), and they also happen to add up to 28 points. I sent double the minimum soldiers to each of those four castle in the hopes that, on average, this strategy will optimize on the best points-to-soldier ratio (ie, a point-to-soldier ratio of approx. 3.6).
1202 0 0 0 14 18 0 0 0 32 36 Select castles [4,5,9,10] and send troops there in proportion to the victory points in each.
1205 0 0 0 14 0 0 25 29 32 0 With 55 total points available, I only need 28 points to win. The least amount of castles I need to get 28 points is 4. There are 9 ways to get 28 points exactly with 4 castles. i chose one of the ways that doesn't use castle ten.
1206 0 0 0 14 0 0 25 29 32 0 minimum number of castles to win(4) and minimum values of castles (9+8+7+4=28) then allocate troops proportionally. Avoiding 10 because ppl will be tempted to take it.
1207 0 0 0 14 0 0 25 29 32 0 One only needs 28 points to win the war. The fewest castles one needs to win is four. There are only two configurations of four castles that add up 28 points, 10, 9, 8, 1 and 9, 8, 7, 4. I chose the second group because I can lose the 10 point castle and still win. I weighted the armies to the castle by what percent the points earned are out of 28.
1208 0 0 0 14 0 0 25 28 32 1 With 55 total points, 28 are needed to win. The 10 point castle will likely be highly contested so I ignored it. The 1-5 point castles aren't enough points for me to focus on. But if I can seize the 6, 7, 8, and 9 points castles I'll have 30 and the win. I need to get all of them in order for this to work though. Just in case anyone else adopts my strategy, I am dumping the 6 castle and pursuing the 4 castle partially because I am a pirate and like math/ship puns but mostly to throw anyone else off my trail. This puts me at 28 points. I weighted each castle based on the percent of points gained (4/28, 7/28, 8/28, and 9/28) to get a percent of my 100 soldiers/pirates to deploy. Rounding down, I have 14 pursuing castle 4, 25 pursuing castle 7, 28 pursuing castle 8, and 32 pursuing castle 9, with 1 left over from rounding. I put the extra one toward castle 10 in case my opponent also left it alone.
1209 0 0 0 14 0 0 18 29 39 0 Fewest # castles, estimated e^0.5x population distribution.
1215 0 0 0 13 0 0 24 29 34 0 Concentrate all of your forces in the minimum set of numbers required to get to 28 points (aka electoral college strategy!).
1216 0 0 0 12 19 0 21 4 21 23 A genetic algorithm told me to.
1219 0 0 0 12 0 0 25 30 33 0 Need 28 points to win so just focusing on putting troops at least amount of castles to get to 28, so 4 castles. Avoided 10 because may be most heavily guarded at other castles so only other combo is 9,8,7,4. Weighted 9 and 8 higher, 7 slightly lower, 4 lower than that.
1220 0 0 0 12 0 0 24 29 34 1 Trying to win 28 points exactly. One troop reallocated to castle 10 in case I get unlucky and lose castle 4 then maybe I can pick up 5 or 10 from winning or splitting castle 10.

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CREATE TABLE "riddler-castles/castle-solutions" (
"Castle 1" INTEGER,
  "Castle 2" INTEGER,
  "Castle 3" INTEGER,
  "Castle 4" INTEGER,
  "Castle 5" INTEGER,
  "Castle 6" INTEGER,
  "Castle 7" INTEGER,
  "Castle 8" INTEGER,
  "Castle 9" INTEGER,
  "Castle 10" INTEGER,
  "Why did you choose your troop deployment?" TEXT
)
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