Riddler - Solutions to Castles Puzzle: castle-solutions-3.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

1,466 rows

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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 2 2 2 2 6 18.0 2.0 28.0 36.0 2.0 DONT KNOW
2 1 1 1 11 19 27.0 37.0 1.0 1.0 1.0 I'm going for the crumbs, hoping that most opponents bet on the valuable castles. And by betting at least 1 soldier on each I'm winning the ones that the opponent doesn't send any soldier to.
3 2 3 4 5 6 22.0 6.0 22.0 22.0 8.0 Based on previous results, I focussed on castles 6, 8 and 9 and left myself a healthy backup in each of the others
4 2 2 4 6 6 10.0 11.0 14.0 17.0 28.0 Fairly evenly spread out, with an emphasis on the point-heavy castles.
5 1 1 2 3 16 22.0 1.0 1.0 33.0 20.0 Sheer whimsy.
6 2 2 11 12 12 16.0 16.0 17.0 6.0 6.0 I focused on getting the extreme castles (1,2,3,4,9,10) while hoping to steal one of the middle castles (5,6,7,8)
7 1 1 1 9 3 1.0 24.0 28.0 31.0 1.0 Need 28 to win. Don’t focus on 10 as others will. Hedge with a maybe getting 5
8 1 4 5 8 9 11.0 12.0 15.0 16.0 19.0 Simple weighting according to expected value
9 4 4 14 13 13 2.0 15.0 15.0 10.0 10.0 I mostly trusted my gut, but did a back over the envelop best response iteration.
10 2 1 5 20 4 20.0 4.0 20.0 4.0 20.0  
11 1 4 12 14 7 16.0 18.0 20.0 3.0 5.0 I focused on a combination that would get me to 28 points, but still tried to have above average on the castles that others might try to put 1-3 troops at.
12 1 2 1 3 5 20.0 21.0 33.0 7.0 7.0  
13 3 6 11 13 5 18.0 22.0 11.0 6.0 4.0  
14 4 0 0 0 0 0.0 0.0 32.0 32.0 32.0 You only need 28 to win
15 1 1 6 10 14 15.0 23.0 24.0 3.0 3.0 I'm reverting to something closer to the winning strategy of this question's first instance. I'm sending few troops to the highest and lowest valued castles, instead focusing my parties on the middle-values.
16 1 1 1 2 1 15.0 21.0 26.0 31.0 1.0 Goal is to maximize odds of winning 28 or more, and winning 6 through 9 seemed to have the easiest path of getting there. Skipping 5 and leaving 2 at 4 is because 4+6+7+8+9 is enough to win, happy to leave 5 behind to win 6-9.
17 1 1 1 21 1 1.0 21.0 21.0 31.0 1.0 In order to win a war I need to get 28 points, anything more doesn't matter and anything less may as well be zero. So I chose to strongly contest 4 spots which would allow me to get that score if I only one those (9, 8, 7, and 4). For each of the remaining spots I chose to place a single troop in case someone also heavily contests one of these numbers but leaves another spot entirely uncontested. Finally I chose numbers ending in 1 because I assumed that many people would choose round numbers and therefore I would have some chance of barely beating them.
18 1 0 0 0 1 14.0 34.0 34.0 14.0 2.0 It’s basically a bell curve, but with one soldier in Castle 1 because I had to.
19 1 1 1 1 1 19.0 19.0 19.0 19.0 19.0 I only need 4 of the 5 largest castles to win, so I just put all my troops equally in those 5 so there is no chance someone beats me in all 5!
20 3 5 7 9 11 2.0 16.0 18.0 15.0 14.0 I have optimised this strategy to beat the average deployment from the last iteration of the game, by sacrificing castle 6,which was not well contested last time, so I expect it to be hotly contested this time round.
21 1 1 1 1 23 23.0 24.0 24.0 1.0 1.0 Trying to capture the mid-high castles and sacrifice the others
22 3 3 3 3 3 10.0 15.0 20.0 30.0 10.0 Just guessing based on the previous two events. 678 heavy vs 459,10 heavy, sort of a mix.
23 2 2 2 2 12 20.0 20.0 20.0 20.0 20.0 I spread my troops on the five highest value castles, hoping that I can beat out some of them, and sent two to the lower value ones so I can beat someone who sends the minimum.
24 1 2 2 8 10 15.0 17.0 19.0 23.0 3.0 I tried to look for a mix between the successful armies in 1 and 2. I targeted 4-9 because they total more than half the points, and dropping 1-2 of these castles wouldn't stop my victory.
25 4 6 7 4 4 4.0 30.0 32.0 4.0 4.0 mostly random TBH, just gut feeling
26 2 2 3 14 2 16.0 2.0 4.0 32.0 23.0 Intuition.
27 2 3 4 5 7 9.0 26.0 33.0 6.0 5.0 It just felt *right*
28 4 4 4 4 16 4.0 16.0 28.0 16.0 4.0 To mess with the averages
29 6 6 7 0 0 0.0 21.0 25.0 0.0 35.0 Castles 1-3 and 6-8 were the most ignored by the top 5 warlords in the last round. 4-5 and 9-10 were most popular. I figured if I can almost guarantee getting 10 by placing 35 soldiers, ignore 9 where most others will send a significant amount, capture 7-8 which look to be ignored by most, and capture 1-3 which will be ignored for low point value, I could total 31 points which is more than enough to win a majority of the battles. Maybe a simpleminded strategy but this is based purely off the results of the last round and it could be an obvious one.
30 3 5 6 10 13 18.0 28.0 7.0 6.0 5.0 1 thru 7 are worth 28 points while 8-10 are worth 27. So sacrifice those for volume ;)
31 2 6 9 9 12 2.0 28.0 27.0 2.0 3.0 Just did a pretty similar strategy to Cyrus.
32 1 1 1 1 1 5.0 5.0 10.0 25.0 50.0 I figured if I can guarantee a split or victory of high level castles, that can override the lower level ones--this is not very scientific. Also, the form doesn't allow us to send 0 soldiers to a given castle.
33 2 4 5 8 10 11.0 12.0 14.0 16.0 18.0 Impossible to say.
34 1 3 6 8 10 12.0 14.0 16.0 18.0 20.0 Linear
35 1 1 1 1 1 1.0 91.0 1.0 1.0 1.0 Banking on winning ALL the battles at Castle 7
36 1 1 1 2 14 15.0 2.0 28.0 32.0 4.0 Winning 5, 6, 8, and 9 gives me just over half of the available points, so I went hard for those four.
37 4 5 7 9 11 13.0 14.0 16.0 13.0 11.0 Used the last answer and increased deployment for the first 5 by 1 and decreased the last 5 by 1 to account for evolution.
38 1 3 5 7 9 11.0 13.0 15.0 17.0 19.0 Linear
39 4 4 4 5 5 16.0 5.0 5.0 21.0 31.0  
40 1 6 6 11 11 16.0 16.0 16.0 11.0 6.0 Figure 5x would be a popular number to distribute, so 5x+1 along a skewed curve based on intuition.
41 2 4 6 12 12 2.0 21.0 3.0 30.0 8.0  
42 1 1 3 5 10 18.0 24.0 30.0 4.0 4.0 A few at top to steal from old strategy, then strength in higher numbers, gave up bottom completely
43 1 10 1 1 1 1.0 28.0 28.0 28.0 1.0 28 is the number needed to win so targeted to scrape a win. Did not contend the highest scoring castle as some will likely go very heavy there
44 3 4 4 4 6 8.0 11.0 11.0 23.0 26.0 A gradual top down deployment, going for numbers that would beat rounded off choices like 25 or 10 on some of the larger castles.
45 6 8 10 12 14 0.0 0.0 0.0 24.0 26.0 I think people will adjust back to the top half numbers after the success of the winning answers from last round but will still be scared to drop too much into the highest value targets.
46 2 3 4 6 8 9.0 18.0 20.0 12.0 18.0 I am uncertain as to how people will adjust to two contests worth of results, so I've taken a slightly more balanced approach that targets higher value castles more proportionately to their values, while still leaving enough troops to pick up the low and mid value castles that others may defend lightly.
47 1 5 10 0 0 0.0 0.0 28.0 28.0 28.0 Because I'm trying my best.
48 1 2 9 4 6 14.0 9.0 8.0 21.0 26.0 Send the troops where the most points are.
49 2 3 3 12 15 7.0 14.0 14.0 17.0 13.0 I looked at the historical success strategies of the first and second FiveThirtyEight crusades. It looked like people in the second war adjusted their strategy away from what won in the first war. So I took the top 5 from each war and took the average number of troops per castle. I picked numbers close to the average to deploy my troops for the Third FiveThirtyEight crusade. And once I take over the world, I'll change the name of your website to FiveThirtyNine.
50 1 2 2 2 2 2.0 29.0 29.0 29.0 2.0 Becuase I'm smart, in my head.
51 1 3 5 5 5 5.0 5.0 32.0 5.0 34.0 The most prominent strategies that have been winning have been strategies that have had the "four castle" strategy which would win the slight majority of the points (28). Assuming this is the strategy most people seek to optimize on I wanted to build a strategy that would beat these strategies. Every four base must win either castle 10 or castle 8 to reach this 28 point threshold (which is the primary way they win). After that the number of troops sent to the other castles should be greater than with a four castle strategy that you win the rest of the needed points on the castles that others gave over for free. I would like to test it with 30 in bases 8,10 and 5 troops in 1 and 3 as well but I think you need to make sure you juice your troop count in the bases you are going for because if you don't win at least one of those you are going to be in trouble. You will also lose to a split evenly strategy but I don't think that will be popular as most people will look at the data and realize you probably want to have a win condition.
52 1 1 4 4 22 22.0 17.0 17.0 6.0 6.0 I started with attempting to punish those who didn't send enough troops to the 'Extremes' (Castles 1-4 & Castle 9-10). Sending less than 5 will result in a loss at 9 & 10, and sending 0 or 1 to the first 4 will result in a loss. Next, I want to win at least 2 (hopefully 3) of Castles 5-8 so I went with 22 at 5 & 6 since previous winners from the first 2 iterations sent a max of 21. Finally, I distributed my last troops evenly to Castle 7 & 8.
53 1 6 6 6 11 11.0 6.0 26.0 21.0 6.0 Tried to use just above multiples of 5 because that is a human habit when splitting things.
54 4 2 5 10 10 17.0 16.0 16.0 4.0 16.0 I foresee a lot of fighting over Castle 9. Thus, I focused on 7,8, and 10 to hopefully get a fair number of victories there.
55 3 4 4 14 20 3.0 21.0 3.0 25.0 3.0  
56 4 4 4 4 4 24.0 24.0 24.0 4.0 4.0 I figured at least 4 in each would pick off the people who sent out tiny forces, but still let me sink in a few in more strategic spots.
57 1 5 8 12 13 1.0 26.0 30.0 2.0 2.0 I copied the first winner one minor arbitrary change.
58 2 4 6 7 9 11.0 13.0 14.0 16.0 18.0 Weighted distribuation
59 1 1 1 1 1 17.0 17.0 20.0 40.0 2.0 My line of thinking is that most other warlords would work to capture Castle 10 with the majority of their troops, so I avoid it completely and work with my forces to conquer the second-strongest castles. If however, my opponent ignores castle 10 as I did, and goes after the lesser castles, I'd designate two soldier in the off chance they could conquer the castle alone. If I conquer Castles 6-9, I'd win the war even if I lose all the others.
60 3 6 9 14 18 22.0 28.0 0.0 0.0 0.0 Ignore the top ones, focus on minimum needed for majority of points
61 1 1 1 1 2 7.0 10.0 20.0 35.0 22.0 I went top heavy and ignored the low point castles due to their inefficiency as the are 1.8 digits Soldiers per point.
62 1 2 0 0 0 0.0 0.0 32.0 32.0 33.0 The top 3 castles score 27 points in total, almost 50% of the point total. Assuming I can win all 3 and pick up a single unguarded low point castle, i will prevail.
63 1 1 5 10 1 15.0 16.0 17.0 1.0 26.0  
64 2 4 5 7 9 11.0 13.0 15.0 16.0 18.0 I took the ratio of the points for each castle against the total points possible (10/55) and multiplied it by 100 to determine the number of soldiers for each castle.
65 1 4 9 10 1 13.0 16.0 17.0 14.0 15.0 I assumed the number of soldiers necessary based a trend from the previous two events. I then added one soldier to castles 6 through 10 and subtracted one soldier from castles 1-5. I then decided to sacrifice castles 1 and 5 and minimize their defenses and put their soldiers on the other 8 castles.
66 4 0 1 1 1 0.0 0.0 31.0 31.0 31.0 My goal is to acquire 28 points. This is on permutations of castle attacks that makes it likely
67 15 1 1 1 1 1.0 30.0 30.0 25.0 24.0 First, we have to find the minimum number of points to needed to win (28). Then we have look at the minimum amount of castles needed to secure that, which is 4. Holding the top 3 pts Castles will only get to 27 pts; however, holding point 7 will get 34 pts, but that an extra six points not needed. So, having strong defenders on the top 3 castles, of which in previous games few went above 30 to hold, and then holding castle 1 strongly, will give the best opportunity to hold the least castles with the least wasted points to win. But if one is lost, all is lost. :)
68 4 0 0 0 0 0.0 0.0 32.0 32.0 32.0 I do have to win all 4 of my engagements, which doesn't leave any margin for error. I'm confident in castle 1, and 2/3 for 8-10. So I just have to get a little lucky that opponents spread their forces out too much.
69 2 2 9 11 16 10.0 30.0 5.0 8.0 7.0 Based on last year's deployments I observed that very few soldiers were deployed to the 9 and 10 castles so I send a force to that could take both of those. I sent a token force to the 1 and 2 castle as they are not worth that much. For the remainder I tried to get above last year's average except for castle 8 which I can afford to lose if I take either 9 or 10. However I may just be fighting the last war and be destroyed.
70 3 3 1 1 1 1.0 10.0 35.0 44.0 1.0 focus on castle 8 and 9 with the assumption that castle 10 is likely going to be taken and castle 1 and 2 will have 1 soldier brought to them
71 3 8 10 11 16 22.0 2.0 23.0 2.0 3.0 Designed to lose 10, 9, 7 which would counteract the strategy of only winning the bottom 7 (since I'll steal 8, in exchange for their 7), and the strategy of winning the top numbers (I'm sacrificing 9, 10, while investing a lot in 8, 6, and lower, which adds up to more points than 7, 9, 10).
72 1 1 1 2 7 18.0 20.0 22.0 23.0 5.0 Seemed pretty good I guess
73 1 0 0 20 20 0.0 0.0 0.0 35.0 24.0 Magic
74 4 8 8 8 12 32.0 17.0 4.0 3.0 4.0 Get 7 through 5 and then either 10 or 4 through 1.
75 1 0 0 18 18 3.0 3.0 3.0 32.0 22.0 Beats most of previous 2 games
76 2 2 4 0 22 10.0 12.0 13.0 0.0 35.0 Because this is what my future self told me to pick.
77 1 1 1 1 1 4.0 30.0 30.0 30.0 1.0 Folks are likely to put a concerted effort to a few castles to secure their victories there. I'm hoping to win the less contested, but higher value castles.
78 3 3 3 3 13 18.0 21.0 32.0 2.0 2.0 I put at least two people in each castle so I could beat the 0s and 1s in each castle. And then I tried to mimic the winners from the first time, thinking that the winning strategy would revert back to the first game.
79 1 2 5 11 15 3.0 3.0 27.0 31.0 2.0 First round won by 7/8 strategy. Second round won by 9/10 strategy. Went with 8/9 strategy.
80 3 4 5 5 8 21.0 6.0 23.0 4.0 21.0 get em
81 1 1 2 3 4 21.0 27.0 28.0 6.0 7.0  
82 1 5 9 13 17 19.0 15.0 11.0 7.0 3.0 Seemed like a good idea at the time.
83 1 1 6 7 9 11.0 13.0 15.0 16.0 21.0 100 points/55 weighted castles' value = 1.8181; multiplied that times each castles' value to determine proportioned weight; made a few gut adjustments
84 3 4 6 9 9 10.0 19.0 15.0 11.0 14.0 looked at prior results and then sort of winged it
85 1 2 3 16 20 3.0 3.0 3.0 31.0 18.0 Random!
86 1 1 1 15 1 20.0 1.0 28.0 2.0 30.0 Win 10 and 8 while giving up 9 to those who heavily go for it but winning it from those who send very few troops with the objective of winning 4 castles to get to 28 points.
87 2 2 2 18 18 18.0 18.0 18.0 2.0 2.0 I felt that it would be useless to deploy them evenly. Putting at least 2 in every spot meant that if some else puts 1 or 0, i'll win. I figured others are most likely to go after 9 and 10, so i didn't really bother with them. The remainder were split evenly.
88 3 3 4 6 7 9.0 15.0 25.0 27.0 1.0 I've never actually participated in something like this before. I assumed most people would attempt to capture the castle worth the most points (10). I felt if I essentially sacrificed that castle and then stuck to a rather linear distribution of soldiers increasing from 1-9 I stood a greater chance of capturing those castles and thus winning the Game. I guess we'll see.
89 1 2 3 6 9 14.0 16.0 17.0 16.0 16.0 It slightly beat something that slightly beat May's average.
90 4 4 4 5 11 17.0 23.0 26.0 3.0 3.0  
91 17 17 17 17 17 5.0 0.0 0.0 0.0 0.0 overcome 6
92 1 1 4 8 10 13.0 16.0 19.0 16.0 12.0 seems plausible
93 3 6 6 11 11 1.0 27.0 30.0 2.0 3.0 cluster forces around valuable castles most likely to be fought over (7 and 8), choose one middle but less valuable castle (6) to offer almost no defense of, give 11% of forces to next level valuable castles (4 and 5) assuming most will give 10% to those castles. Also assumes most will attempt to cluster forces proportionately to win larger castles in some ratio of all forces in the 10, 9, 8, 7 castles, keeping more than 25% in castles 8 and 7.
94 1 1 7 1 18 20.0 2.0 23.0 25.0 2.0 Go big on some, steal the rest with some 1>0s and hope for some luck!
95 2 2 5 5 10 15.0 20.0 25.0 5.0 6.0  
96 2 4 5 7 9 11.0 12.0 15.0 16.0 19.0 Direct mapping. Soldiers per castle = (points per castle / total points) * total soldiers, with rounding, and leftover soldier goes to castle 10. Trying to win by playing simpler than people expect. :)
97 1 3 5 7 9 11.0 13.0 15.0 17.0 19.0 Trying to be competitive at every single castle, without wasting too many soldiers.
98 1 1 1 1 14 20.0 30.0 30.0 2.0 2.0  
99 2 7 2 2 13 18.0 23.0 29.0 2.0 2.0 I wanted to get 28/55 points by committing to castles 8,7,6,5 and 2. I deployed these troops to help obtain 8 most frequently and 2 the least. I deployed 2 troops on each other castle to not allow for my enemies to get an easy 1-0 victory on any castle. If I can win one or two of those, that would be great
100 15 15 7 2 26 2.0 2.0 3.0 10.0 18.0 Last time winners focused on the middle. I'm focusing on the edges

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