Riddler - Solutions to Castles Puzzle: castle-solutions-2.csv
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
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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 | 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 | 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 | 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 |
5 | 5 | 0 | 0 | 0 | 16 | 21 | 0 | 0 | 0 | 36 | 27 | Near optimal integer program vs previous round: beats 1068 of them. |
7 | 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 | 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. |
12 | 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 |
14 | 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. |
18 | 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 | 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. |
21 | 21 | 0 | 0 | 0 | 0 | 22 | 23 | 28 | 0 | 0 | 27 | This setup beat 1071 of the 1387 past strategies (found by integer programming) |
27 | 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 | 28 | 0 | 1 | 8 | 14 | 16 | 1 | 22 | 3 | 25 | 10 | https://pastebin.com/LSXrjJJV |
29 | 29 | 0 | 0 | 0 | 15 | 18 | 1 | 1 | 1 | 26 | 38 | Mostly random |
33 | 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 |
38 | 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 | 39 | 0 | 1 | 1 | 12 | 21 | 2 | 1 | 1 | 29 | 32 | I specified my deployment based on previous strategy but more concentrated. |
41 | 41 | 0 | 0 | 3 | 3 | 20 | 16 | 3 | 20 | 24 | 11 | not sure. |
44 | 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 | 45 | 0 | 2 | 2 | 15 | 5 | 25 | 3 | 31 | 5 | 12 | Scarborough, ME |
54 | 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. |
56 | 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. |
58 | 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). |
60 | 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. |
71 | 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. |
75 | 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 | 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 | 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. |
83 | 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. |
85 | 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 | 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... |
88 | 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. |
92 | 92 | 0 | 5 | 7 | 9 | 12 | 22 | 2 | 31 | 5 | 7 | Modified basic data; optimalization. |
94 | 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). |
107 | 107 | 0 | 5 | 9 | 14 | 5 | 15 | 8 | 3 | 9 | 32 | not enough time to submit too. |
114 | 114 | 0 | 4 | 12 | 19 | 25 | 4 | 5 | 6 | 8 | 17 | https://github.com/norvig/pytudes/blob/master/Riddler%20Battle%20Royale.ipynb |
119 | 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 | 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 | 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. |
124 | 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. |
130 | 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. |
138 | 138 | 0 | 0 | 0 | 6 | 6 | 8 | 32 | 8 | 32 | 8 | Modify from one of the best sample |
147 | 147 | 0 | 5 | 7 | 9 | 18 | 16 | 3 | 31 | 6 | 5 | Simulated annealing using total wins against prior entries as objective function |
151 | 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! |
167 | 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 | 168 | 0 | 7 | 7 | 9 | 16 | 15 | 3 | 33 | 5 | 5 | My boyfriend said to. |
173 | 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. |
175 | 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. |
180 | 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). |
189 | 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 | 190 | 0 | 5 | 7 | 12 | 11 | 22 | 2 | 32 | 2 | 7 | This beats 1250 of the previous 1387 matches :) |
194 | 194 | 0 | 5 | 6 | 8 | 13 | 23 | 3 | 32 | 5 | 5 | Historical performance^2 * Performance against those who optimized against that. |
195 | 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. |
204 | 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. |
210 | 210 | 0 | 4 | 3 | 15 | 3 | 16 | 3 | 31 | 3 | 22 | Best result of an alternate genetic algorithm including the given data set. |
212 | 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. |
215 | 215 | 0 | 7 | 8 | 6 | 13 | 9 | 6 | 35 | 11 | 5 | Random solution meant to help my initial submission. |
217 | 217 | 0 | 0 | 0 | 11 | 11 | 17 | 21 | 18 | 11 | 11 | Fight for the big points. |
219 | 219 | 0 | 1 | 4 | 6 | 8 | 12 | 24 | 32 | 6 | 7 | Arbitrary and malicious |
224 | 224 | 0 | 2 | 2 | 14 | 3 | 2 | 22 | 31 | 19 | 5 | Always leave the most number of doors open. |
227 | 227 | 0 | 6 | 7 | 11 | 12 | 21 | 3 | 31 | 4 | 5 | A bit modified basic game from the data with optimalization |
228 | 228 | 0 | 0 | 11 | 11 | 16 | 3 | 21 | 3 | 31 | 4 | assumed people would gravitate to even castles, and round numbers. |
235 | 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. |
245 | 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. |
248 | 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. |
256 | 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. |
258 | 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. |
260 | 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 |
263 | 263 | 0 | 5 | 7 | 12 | 12 | 21 | 3 | 32 | 3 | 5 | Genetic algorithms against historic data and optimal strategies found in the previous loop |
276 | 276 | 0 | 0 | 1 | 10 | 23 | 24 | 25 | 2 | 7 | 8 | just winging it |
278 | 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. |
281 | 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. |
286 | 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. |
290 | 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. |
295 | 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). |
297 | 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 | 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 | 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 | 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 | 301 | 0 | 6 | 7 | 12 | 12 | 21 | 3 | 31 | 3 | 5 | I used an algorithm to optimize the deployment against the first round entries. |
307 | 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 |
309 | 309 | 0 | 10 | 7 | 10 | 0 | 0 | 10 | 21 | 21 | 21 | Get top 3 + 1 other for 28. |
311 | 311 | 0 | 0 | 0 | 0 | 0 | 10 | 30 | 35 | 10 | 15 | Tried to beat last year's winner |
315 | 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. |
328 | 328 | 0 | 0 | 0 | 0 | 17 | 22 | 23 | 0 | 0 | 38 | Try to hit 28 by winning on 4 numbers. |
333 | 333 | 0 | 0 | 0 | 0 | 18 | 21 | 25 | 0 | 0 | 36 | Sounds good |
335 | 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 | 336 | 0 | 0 | 14 | 0 | 0 | 0 | 26 | 30 | 0 | 30 | picked the easiest looking quartet worth a majority |
339 | 339 | 0 | 0 | 3 | 6 | 13 | 9 | 6 | 35 | 23 | 5 | Random solution meant to help my initial submission. |
351 | 351 | 0 | 4 | 6 | 9 | 12 | 0 | 27 | 32 | 5 | 5 | Crush enemies. |
357 | 357 | 0 | 7 | 8 | 6 | 13 | 9 | 6 | 20 | 26 | 5 | Random solution meant to help my initial submission. |
365 | 365 | 0 | 7 | 8 | 6 | 13 | 9 | 6 | 26 | 20 | 5 | Random solution meant to help my initial submission. |
371 | 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. |
373 | 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. |
378 | 378 | 0 | 0 | 8 | 0 | 23 | 26 | 31 | 0 | 6 | 6 | Poor intelligence |
380 | 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. |
384 | 384 | 0 | 0 | 3 | 6 | 13 | 9 | 6 | 23 | 35 | 5 | Random solution meant to help my initial submission. |
387 | 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. |
394 | 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. |
396 | 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 |
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CREATE TABLE "riddler-castles/castle-solutions-2" ( "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 );