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 sorted by Castle 2

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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?
14 4 0 0 0 0 0.0 0.0 32.0 32.0 32.0 You only need 28 to win
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.
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
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.
73 1 0 0 20 20 0.0 0.0 0.0 35.0 24.0 Magic
75 1 0 0 18 18 3.0 3.0 3.0 32.0 22.0 Beats most of previous 2 games
106 1 0 0 2 1 0.0 17.0 21.0 27.0 31.0 Securing the high castles is paramount to our victory, with a few sneaky +1 to counteract those who wish to tie us in mortal combat.
116 1 0 9 0 0 10.0 10.0 20.0 40.0 0.0 Adjustments to previous contest
126 1 0 0 0 0 13.0 17.0 20.0 23.0 27.0 Win big (I only want 0 troops at castle 1 but it won't let me. Hoping I dont get disqualified.)
131 1 0 0 0 0 0.0 0.0 0.0 99.0 0.0 Just Cause
134 1 0 0 14 20 2.0 2.0 2.0 29.0 30.0 I'm dumb
141 1 0 0 0 0 0.0 0.0 99.0 0.0 0.0 You need to get points, and probably the only way to do that is to win a house outright. I am guessing that someone will do 100 for 10 and 9, so guessing 8 will be the one where people don't apply 100.
147 1 0 9 15 0 20.0 25.0 30.0 0.0 0.0  
148 1 0 0 4 11 14.0 21.0 26.0 24.0 0.0 I started with zero at Castle 10, and a large chunk (25) at 8 and 9. I then gave 5 fewer troops to each Castle going down until I ran out. Then I went back and added in a bit of noise. Then I noticed it required >0 for Castle 1, so I put that in.
151 1 0 1 6 22 12.0 8.0 14.0 6.0 30.0 I chose a strategy that could beat each of the top 5 from the last two times, could beat an even distribution, could beat a focused attack at the top, and could beat a (10,0,0,0,0,0,0,30,30,30) strategy. The first strategy I found was (1,2,2,18,1,6,2,33,11,24). Then, I used random sampling to see if I could find strategies that would beat my strategy. Out of a sample of 200, I found 84. I compared these 84 against the original 13 strategies, and found 1 that beat all of them. This strategy was (0,1,1,6,22,12,8,14,6,30). However, your entry form won't let me put 0 for castle 1, so I switched castle 1 and 2. This seems to work just fine as well.
181 1 0 1 2 2 2.0 23.0 23.0 23.0 23.0 People seem to try to get clever by guessing which castles others will give up on or go all-in for. Maybe being not-clever and just going for the high-value ones counters that?
199 1 0 0 2 21 22.0 3.0 24.0 27.0 0.0 Key is to get to 28. Wanted to stack as few castles as possible to increase probability of winning those. Left 7, 4, and 3 as contingency plans in case someone was doing the same.
222 1 0 1 17 20 1.0 2.0 23.0 32.0 3.0 saw the best ones from the last 1 and combinated.
231 1 0 0 14 22 2.0 2.0 24.0 33.0 2.0 Why did you force at least 1 unit to go to castle 1?
236 1 0 0 0 0 9.0 10.0 10.0 35.0 35.0 For the goal of winning 28 points, I plan to take castle 9 and 10. Then win any two among castle 7-9. I'm avoiding castle 4 - - 5 as they seemed to be hotly contested in prior matches
237 0.00001 0 0 0 5 5.0 5.0 15.0 30.0 40.0 the previous winners clearly picked a lane, some highs and mids, or some mids only, my lane is to go top heavy. As long as I can claim two top tier and two lower tier, I can win.
239 1 0 1 1 19 5.0 5.0 6.0 35.0 28.0 :)
241 1 0 0 0 0 0.0 0.0 22.0 37.0 40.0  
243 1 0 0 12 14 13.0 0.0 0.0 31.0 29.0 I expect eight and seven to be hotly contested, so I left them open along with three and two giving the opponent 20 points out of the gate. One required a value greater than zero, so I gave it one. With an average of three, I will likely lose one and the opponent will have 21 points. I plan to take four and five which were hotly contested in the last round and may be less so in this round. Six will be a toss-up. Nine and ten must be taken. If I can take four, five, nine, and ten, I will have 28 points and the opponent would have 27.
246 1 0 14 0 0 18.0 0.0 0.0 33.0 34.0 Going big on castles 10, 9, 6, 3. It is designed to "just barely" win against what I figure is an average deployment. It matches up well with the top castles of Round Two but struggles against some of the top castles from Round One. As you might be able to guess, I don't expect people to go back to the Round One strategy.
249 1 0 0 12 0 12.0 25.0 25.0 25.0 0.0 In order to assign the maximum number of soldiers to selected castles, from all castle combinations that sum up to 28 with just 4 castles, I choose to ignore castle 10 and concentrate forces to 9,8,7 (25 on each) then I just need one of 4,5 or 6 so I had to share the rest 25 soldiers to those 3 castles. To increase chances I placed 12 soldiers to 4 and 6 and the last remaining to castle 1( that was unintentional, since I had to place at least on soldier to castle 1)
269 1 0 0 16 18 1.0 1.0 20.0 21.0 22.0  
272 1 0 1 1 25 1.0 1.0 1.0 35.0 34.0 Copy the same strategy as last time, but more extreme (thinking people are going to go back to strategy 1)
280 1 0 1 2 12 21.0 27.0 32.0 2.0 2.0 never gonna win 9 & 10, don't want 1-4, split the rest leaning higher for higher values
283 1 0 9 0 0 20.0 20.0 20.0 0.0 30.0 You must win at least 28 points. Since the given strategy seems to be to avoid large commitments on 10, and attack 4,5, and 9, I chose to deploy my troops to 10, 8, 7, and 6 in large numbers, concentrating the rest on 3 to offset losing 1 and two. Its a high risk strategy, because losing just one of the higher values will result in a loss.
288 1 0 0 0 0 0.0 24.0 25.0 25.0 25.0 Control the four top castles that add up to more than the rest.
294 1 0 0 3 3 21.0 22.0 23.0 24.0 3.0 Captain Chaos
295 1 0 0 6 17 17.0 6.0 4.0 23.0 26.0 War
315 1 0 0 9 0 15.0 0.0 35.0 40.0 0.0 Cheapest way to 28 total points. It did make me place one troop in castle one for some reason. Would rather have put that soldier at 4.
341 3 0 7 10 20 0.0 30.0 30.0 0.0 0.0 I targeted 6 castles that would get me 28 points. If I go 6/6 on those ones that I bet big on then I win (doesn’t really feel like a good strategy, but I wanted to see how it would play out)
343 1 0 1 7 1 20.0 3.0 27.0 14.0 26.0  
346 8 0 0 0 0 0.0 0.0 31.0 31.0 30.0 I am just trying to get to the minimum amount of points to win: 28. I found the combination with the least amount of castles I possibly need to win and dumped all my points into these 4, forgoing the rest completely as they are not important in my winning strategy. Also, based on the previous 2 games, I decided to put the least in castle 1 in order to stack 8, 9, and 10 to the fullest possible.
347 1 0 0 2 23 4.0 4.0 28.0 32.0 6.0 Picked some castles to go for, crossed my fingers no one else goes for them
366 0 0 0 14 17 20.0 23.0 26.0 0.0 0.0 Ignored 9&10 and chose the fewest castles past that to give me more than 28 points and weighed troops by value
369 0 0 0 13 15 18.0 26.0 28.0 0.0 0.0 Distributed my troops evenly through 4-8 which will give me 30 points each time banking on that I have more troop in those stations giving the other opponent 10-9-3-2-.
379 0 0 0 0 5 20.0 20.0 20.0 20.0 15.0  
383 0 0 1 3 1 1.0 22.0 23.0 24.0 25.0 This is my second entry. I created it as the counterpoint to my strategy (sort of) in the first. Here, I must win 3 of the 4 largest and then pick up 4 more points.
385 0 0 0 0 20 23.0 0.0 30.0 27.0 0.0 There's no way to win without at least four castles, so I focused on winning four and tried to optimize versus earlier distributions.
391 2 0 0 0 0 17.0 18.0 18.0 20.0 25.0  
393 0 0 4 0 11 0.0 30.0 31.0 0.0 24.0 I came up with about a dozen different strategies. Strategy A was an even distribution (10 per castle), B was weighted (2 for Castle 1 up to 18 for Castle 10); C was weighted to beat A-B, D could beat A-C, all the way until strategy O. After Strategy O, I couldn't make another distribution that could beat N plus the other ones I had already made. It's banking on chaos and people not wanting to overpay for Castle 10, thinking they can take Castles 6-9 for a little more points
395 0 0 1 2 20 22.0 3.0 24.0 28.0 0.0 Resubmission of my last entry, which required me to put at least one on castle 1. Want to concentrate my efforts on reaching 28, the required score for winning the battle. The others are slight contingencies, in case someone else does the same thing.
396 0 0 10 0 0 20.0 28.0 32.0 5.0 5.0 Because I'm the Grandmaster.
397 5 0 0 0 0 0.0 0.0 24.0 36.0 35.0 limit losing troops, look for highest return on investment
400 2 0 11 12 15 22.0 8.0 1.0 28.0 1.0 Focusing on a few moderate-to-large castles. Expected to lose 2 every time, 8, 10 almost every time. About half of 1 and 7. Most 4, 5, 6, and 9.
405 0 0 11 12 17 0.0 25.0 0.0 35.0 0.0 I need 28 points to win, castle 1 and 2 have little value, I feel like people will value 10 and or 8 highly. 10 seems like a median number and something someone would throw at 3 or 4 so I went with 11 and 12. It's really a win all or lose scenario for me. Hopefully people spend resources out instead of concentrating. 10,9,8,1 seems like the most common strategy for people to really go after, I think I can overwhelm the 9 slot and forfeit the others while getting what I want
408 0 0 0 0 0 0.0 0.0 0.0 100.0 0.0 Nash Equilibrium
413 0 0 1 17 22 2.0 1.0 1.0 33.0 23.0 I slightly modified Vince Vatter's distribution from Round 2. I'm very original.
414 0 0 0 7 10 0.0 0.0 24.0 28.0 31.0 Subscribe to the "Barely Win or Lose by a Lot" theory.
416 0 0 0 2 21 21.0 21.0 2.0 2.0 31.0 Try and get the 10 and then the 5-7 which weren't as heavily contested
418 0 0 0 4 1 16.0 1.0 16.0 31.0 31.0 To win.
432 1 0 19 1 1 21.0 0.0 23.0 0.0 34.0  
435 0 0 8 19 17 12.0 4.0 4.0 4.0 32.0 Trying to win 10, 6, 5, 4, 3. Probably not a strategy to win the whole thing but should be good enough to be in top 50%.
436 1 0 19 1 1 21.0 0.0 23.0 0.0 34.0  
437 0 0 1 19 0 19.0 1.0 25.0 1.0 34.0  
444 0 0 11 13 2 21.0 21.0 21.0 0.0 11.0 Gut feeling, picking the less selected castles by either of the previous two rounds.
454 0 0 0 16 1 1.0 25.0 28.0 28.0 1.0  
455 0 0 6 7 23 24.0 25.0 7.0 7.0 4.0 go for the middling castles while not totally abandoning the higher ups, hopefully will win a number of battles while just winning 4 castles, but hopefully will get 5 & hopes it be the right 5. willing to concede 3 points...
479 0 0 0 20 20 0.0 0.0 8.0 26.0 27.0 I tried to defend the minimum amount of castles needed to hold a majority of the hit points (assuming I understood the directions which, you know, 50/50), while another castle was defended with a small amount of troops to diminish attacking forces.
482 0 0 7 5 6 17.0 16.0 17.0 16.0 16.0  
491 0 0 15 2 2 2.0 23.0 25.0 2.0 29.0 This strategy should beat proportional strategies and rotations of proportional strategies, and I think that these will be the most common type. This will probably lose to some similar strategies (very concentrated on a few highest numbers and some low numbers), but by betting 2 on some of the middle numbers we'll hopefully beat more similar strategies than we lose to. We'll get crushed by strategies that beat us on 10 and 9 and also win a lot of low numbers, but I think these strategies will be least common.
500 0 0 0 11 0 0.0 26.0 31.0 32.0 0.0 I went for the less "psychologically significant" castles which would still give me a significant advantage. I sent 11 troops to 4 as an additional bonus in case someone is close to me in the upper ranges, or sweeps all the castles I didn't send any troops to - and since 11 just barely beats the simple strategy of sending 10 troops to each castle. I sent 26 to 7 because 26 is one more than 25 (another round number I expect people to use a lot), and similarly I sent 31 (rather than 30) to #8. Hope this works!
501 0 0 3 3 3 18.0 18.0 3.0 26.0 26.0 Focus on castles 5-6 and 9-10
502 6 0 0 0 0 0.0 0.0 32.0 31.0 31.0 If I win the 10, 9, 8 and 1, I have 28 which is just enough to win.
510 0 0 4 13 16 8.0 14.0 14.0 17.0 14.0 Took the average of the previous two winners and made a team that could beat that.
511 0 0 0 0 20 50.0 30.0 0.0 0.0 0.0 6 seems like a good number. And I didn't want to send any lone soldiers off to die. I expect to win Castle 6 around 1/3 of the time, so hey, that's like 2 points. I'm feeling positive about it.
514 0 0 0 1 18 21.0 0.0 22.0 36.0 2.0  
516 0 0 1 2 3 6.0 8.0 15.0 25.0 40.0 More troops at higher point total castles. Abandon the smallest castles as they aren't worth winning.
520 0 0 10 0 0 16.0 0.0 0.0 35.0 39.0 I started with the averages and the winners from the last 2 rounds. Then I tried to craft a few strategies: a few random ones, some crafted to specifically beat the winners, some crafted to take advantage of historically undervalued spaces between winners and averages, - with some variations on how little/much to put on some of the lighter weighted castles. Then I sat down and went for a hyper aggressive strategy that had a single path to 28 points and would defeat all of the above hahaha. And so we end up here, with a warlord who styles him/herself also as an edgelord, and possibly did not do enough to account for beating strategies that were previously losing.
521 5 0 0 0 0 0.0 0.0 30.0 30.0 35.0 I only need 28 points to win, so I'm only investing my soldiers in 4 attacks to get me the 28 - the three highest totals plus one point.
522 0 0 0 15 17 2.0 3.0 4.0 21.0 38.0 predictive to the human adjustment from round #2, I assumed flipped value on #9 and #10, otherwise assumed the meta deployment would be similar to before
524 3 0 0 0 0 0.0 0.0 32.0 33.0 32.0 I need 28 points to win, so I'm fighting hard for those 28 points.
525 0 0 0 0 11 11.0 11.0 21.0 21.0 25.0 Guarantee 10 and then assume no one else would expend more than 20 on any particular castle. Guarantee 9 and 8 on this rule and then spread the rest out descending.
526 0 0 12 0 0 22.0 0.0 0.0 34.0 32.0 4-castle all-in no scouts. Relative value. My min allocation has to be > 10 to beat naive even split. My overpayment vs avg cost... I must win castle 9. The other castles I will overpay relative to my overpayment on castle 9. Castle 3 +7, castle 6 +11, castle 9 +18, castle 10 +14. You really have to beat my contested castles. Weakness is castle 3, but I’m at +7 and castle 6, +11. Beats all past winners.
534 0 0 0 5 10 10.0 15.0 20.0 22.0 18.0 Maximize points from ties
538 0 0 0 16 20 20.0 21.0 21.0 1.0 1.0  
540 0 0 0 0 11 4.0 0.0 15.0 35.0 35.0 Compared the strategy against a uniform deployment (10 / castle) and against the winner from second round. Tried to get at least 28 points against both strategies.
541 0 0 0 7 8 0.0 0.0 35.0 35.0 15.0  
543 0 0 0 0 0 25.0 0.0 34.0 41.0 0.0 The minimum number of castles needed is 3 which have to add up to 23. 6 is app. 25% of 23 so 25 soldiers 8 is app. 33% of 23 so 34 soldiers and the rest go to 9.
548 0 0 0 13 0 12.0 0.0 0.0 37.0 38.0 23 points are needed to ensure a win - Overwhelming top two castles can get to 19 and then I just need to pick up one more of the other castles to win. Splitting between two helps cover bases if I lose one of the 9/10 and also increases odds i get the one castle to push me over 23 if I win the top two.
550 0 0 0 0 3 16.0 16.0 27.0 27.0 11.0 Sacrifice the low scoring to just barely overload the mid-to-high tier castles
562 0 0 9 22 22 6.0 27.0 2.0 6.0 6.0 I chose to give up 1 and 2 completely, focus on 4,5, 7 while putting enough points into the rest to hopefully stall non advances.
569 0 0 10 15 15 15.0 15.0 15.0 15.0 0.0 rather take the sum of the middle numbers over the first and last
575 0 0 0 0 16 19.0 5.0 26.0 29.0 5.0  
580 0 0 0 15 15 15.0 25.0 30.0 0.0 0.0 Play for the middle and push for the top but don’t over commit
582 0 0 0 0 16 19.0 0.0 30.0 35.0 0.0 I'm going all-in for getting the bare minimum points of 28 or more. The fewest castles I need is 4. 10-9-8-7 is an option but lots of people will go after castle 10, so I'm going after 5-6-8-9. Same number of castles, but I'm playing off the beaten path. Also, 5-6-8-9 are all castles that are in fewer winning combinations, so they're more likely to be won by me. The actual troop placements are based on the relative difficults I computed for winning those particular castles.
599 7 0 0 0 0 0.0 0.0 35.0 32.0 26.0 The bare minimum to win 28 victory points, assuming I win all of my chosen battles. This allows me to maximize my troop deployment to a minimum number of castles.
600 10 0 0 0 0 0.0 0.0 30.0 30.0 30.0 People are going to overthink it. 1/8/9/10 is enough to win.
602 0 0 0 0 18 22.0 26.0 0.0 0.0 34.0 Stakeout the middle and get the top one. Didn’t waste on other castles.
604 0 0 0 20 0 0.0 0.0 0.0 40.0 40.0 23 points to win. Overload the highest rated castles and sacrifice everything else
608 0 0 0 0 0 15.0 17.0 0.0 33.0 35.0  
609 0 0 0 0 15 20.0 2.0 2.0 27.0 34.0 Focusing resources where they could be useful, deliberately avoiding a couple of high-value targets to win the war
610 5 0 0 0 0 0.0 0.0 32.0 31.0 32.0 The goal is to get 28 points. Concentrated troops at the least amount of castles to achieve that.
614 0 0 25 0 25 0.0 25.0 25.0 0.0 0.0 Sacrifices must be made! Castles 1, 2, 4, 6, 9, and 10 are dead to me! Going hyper-aggressive (but not the most aggressive strategy). Best Case: I win! Worst Case: I am a troll!
615 0 0 0 0 0 10.0 15.0 20.0 25.0 30.0 Win four of the top five castles, and you win. This particular troop distribution fights harder for the bigger prizes; would win against four of the five top strategies devised last time; and should be able to compete against anyone putting significant effort in winning lower tier castles, as people have been doing.
623 0 0 0 0 17 21.0 0.0 26.0 36.0 0.0 I think a lot of people will be fighting for #10 and #1 because 10 is worth the most points and #1 is the tiebreaker if you went 10,9,8,1 or 7,6,5,4,3,2,1. I considered going for 10,9,8, 2 to avoid fighting over the #1 and because I could win even with a tie on #2, and then realized I could avoid #10 as well. In summary, I'm avoiding fighting over what I expect to be hotly contested #10 and #1 in favor of #6 and #5 while maintaining the concentration of my troops by only needing to capture 4 castles to win. As far as specific troop distribution goes, I made sure I had at least three times the castle number and dumped a bunch extra on #9, which I think will receive a heavy designation from anyone pursuing a variant of the 10,9,8,1 strategy. I did not assign any troop numbers that end in 0 or 5, they are too popular.

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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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