Riddler - Solutions to Castles Puzzle: castle-solutions-3.csv
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
55 rows where Castle 2 = 6
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Suggested facets: Castle 1, Castle 3, Castle 4, Castle 5, Castle 6, Castle 7, Castle 8, Castle 9, Castle 10
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? |
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26 | 26 | 6 | 6 | 7 | 0 | 0 | 0 | 21 | 25 | 0 | 35 | 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. |
27 | 27 | 2 | 6 | 9 | 9 | 12 | 2 | 28 | 27 | 2 | 3 | Just did a pretty similar strategy to Cyrus. |
34 | 34 | 1 | 6 | 6 | 11 | 11 | 16 | 16 | 16 | 11 | 6 | Figure 5x would be a popular number to distribute, so 5x+1 along a skewed curve based on intuition. |
47 | 47 | 1 | 6 | 6 | 6 | 11 | 11 | 6 | 26 | 21 | 6 | Tried to use just above multiples of 5 because that is a human habit when splitting things. |
53 | 53 | 3 | 6 | 9 | 14 | 18 | 22 | 28 | 0 | 0 | 0 | Ignore the top ones, focus on minimum needed for majority of points |
83 | 83 | 3 | 6 | 6 | 11 | 11 | 1 | 27 | 30 | 2 | 3 | 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. |
90 | 90 | 1 | 6 | 14 | 19 | 1 | 15 | 21 | 21 | 1 | 1 | I focused on the 3,4,6,7,8 field, that have good reward, but aren't tied. Put down at least one in the others to surprise my enemies who left castles unattended. By giving my enemy 10,9,5,2,1, I win out by 1. I am weak to attacks on the higher values, as a 7,8,9 30 split with a dump on 10 will destroy my attempt. As long as the enemy doesn't consolidate, then I shall claim victory. |
114 | 114 | 3 | 6 | 9 | 11 | 13 | 14 | 18 | 22 | 2 | 2 | 55 total points and 100 troops means just fewer than 2 troops per point. Assuming opponent uses same math, I will overemphasize the lesser valued castles and hope she goes big. |
191 | 191 | 3 | 6 | 7 | 8 | 2 | 13 | 15 | 1 | 33 | 12 | It's what I submitted last time. I did a bunch of simulations two years ago but I'm not doing any more work today for this glorified rock-paper-scissors match. |
224 | 224 | 3 | 6 | 9 | 12 | 15 | 16 | 15 | 12 | 9 | 3 | I think the middle castles will be where the war is won |
282 | 282 | 5 | 6 | 8 | 10 | 13 | 15 | 5 | 28 | 6 | 4 | Lose the middle, win the ends |
302 | 302 | 5 | 6 | 8 | 5 | 10 | 2 | 2 | 15 | 23 | 24 | How do you know which risks in war are the right ones? You wait to see if you win. |
309 | 309 | 1 | 6 | 5 | 1 | 1 | 1 | 20 | 1 | 32 | 32 | I'm trying to get to 28 points as often as possible. |
320 | 320 | 1 | 6 | 2 | 12 | 2 | 18 | 2 | 24 | 3 | 30 | I wanted a strategy that would defeat any median-style strategy, and chose to win the even-numbered castles. I put a small number of troops in the odds numbered castles to beat those that sent 0 or 1, which was common in the first try, and then allocated the troops to even-numbered castles proportionally to their value. |
338 | 338 | 1 | 6 | 1 | 13 | 1 | 21 | 24 | 1 | 31 | 1 | I chose 5 castles (9,7,6,4,2) to try and win 28 points most often and sorted my troops according to point values per castles. Then I took 1 troop from each castle and allotted to other 5 castles (just in case opponent sent 0 or 1 troops to those castles also). |
394 | 394 | 6 | 6 | 5 | 15 | 20 | 20 | 28 | 0 | 0 | 0 | Seed the top scoring castles and focus heavy on winning the middle ones. The castles worth few pointe I assumed few people would go for |
407 | 407 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 33 | 33 | 28 | I wanted to win 28 point by attacking as few castles as possible. By focusing as many troops as possible on castles 8, 9 and 10 and choosing a low value castle that people typically don’t commit many resources to, I hoped to win the majority of bouts. |
491 | 491 | 5 | 6 | 7 | 8 | 10 | 12 | 13 | 12 | 13 | 14 | Summation x+4, then just added random numbers to make it add to 100 |
537 | 537 | 1 | 6 | 11 | 11 | 12 | 13 | 14 | 15 | 16 | 1 | Assume opponent will load up on the most valuable castle so I will concede it and attempt to dominate the middle values. |
543 | 543 | 0 | 6 | 7 | 8 | 10 | 17 | 20 | 3 | 25 | 4 | I'm guessing 8, 10, and 1 will be the least cost effective castles, based on the previous wars, so I focused my troop deployment on the others. |
576 | 576 | 6 | 6 | 6 | 11 | 6 | 16 | 6 | 6 | 16 | 21 | No round numbers. Try to take castles that would be overlooked by others. |
582 | 582 | 5 | 6 | 7 | 8 | 9 | 11 | 12 | 13 | 14 | 15 | I attempted to give more weight to the more valuable castles, but not neglect the less valuable that could give me the upper-hand. |
590 | 590 | 6 | 6 | 6 | 20 | 20 | 20 | 5 | 5 | 6 | 6 | A lengthy period of psychoanalysis — I pictured some folks committing a ton of troops to collecting 7 to 10, and others committing almost none elsewhere... 5 or 6 was chosen as a number that would defeat those folks that just said 1, 2, or 3. |
605 | 605 | 2 | 6 | 2 | 12 | 2 | 18 | 2 | 28 | 10 | 18 | A very non-sophisticated strategy based on simple logic and even numbers. With 55 points up for grabs, I need 28 to win. 10+8+6+4 is my ideal path to 28 in this strategy. So I put lots of troops into those castles. I picked the exact numbers based on multiplying the averages from previous versions of this by ~1.5. I spent what was left by dropping a couple “just in case” 2s in castles 1, 3, 5 and 7, then the remaining 10 in castle 9. |
614 | 614 | 3 | 6 | 0 | 14 | 0 | 22 | 25 | 30 | 0 | 0 | I figured you need 28 points to win and winning 1-7 will get you there exactly. That means you can reallocate all your points from 8-10 to 1-7 and stand a good chance of winning. Other people might do that too though, so I did some other stuff on a whim to mix it up. |
623 | 623 | 4 | 6 | 11 | 4 | 14 | 6 | 21 | 4 | 24 | 6 | Decided to fight heavily for all of the odd numbered castles - competition for 10 is likely to be high based on the last two rounds having 10 be somewhat low! I might pick up some easy points on the even numbers. Rather than trying to come up with a nice pattern, do the unexpected and be odd! |
644 | 644 | 1 | 6 | 6 | 15 | 6 | 6 | 6 | 6 | 42 | 6 | This strategy focuses on disrupting any focused deployment strategies that players may build based on previous winners. In previous editions of this game, 6 troops win most battles for most castles. So I should win anytime someone chooses to send a small number of troops. I'm also virtually guaranteed to win castles 4 and 9 due to my excessive forces in both locations. The result is that I will steal a castle from all players focused on either high value, or midrange castles, preventing them from winning one of the castles core to their strategy, while taking all of the castles they chose to ignore. |
647 | 647 | 5 | 6 | 10 | 3 | 4 | 5 | 4 | 54 | 4 | 5 | Looked at past battles and picked the inflection point of diminishing returns, had like 50 troops left and threw them all at castle 8 which was highest point value with widest distribution |
677 | 677 | 3 | 6 | 6 | 9 | 11 | 2 | 27 | 31 | 2 | 3 | Trying to bet 1 more than what I believe the majority of people will do based on your historical data. |
700 | 700 | 5 | 6 | 6 | 6 | 11 | 5 | 5 | 6 | 25 | 25 | Performs well against round 2, wins more often than not against round 1... |
708 | 708 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 14 | 15 | 15 | |
717 | 717 | 4 | 6 | 8 | 12 | 17 | 22 | 31 | 0 | 0 | 0 | Focus on the front 7, which adds up to 28, which gives you one more than your opponent, who takes 7,8,9 (total 27) |
719 | 719 | 1 | 6 | 1 | 1 | 41 | 7 | 7 | 34 | 1 | 1 | Starting with the goal of reaching 28 points, I went with a balance of offense and defense. The distribution I was shooting for was winning 2, 5, 6, 7, and 8. Leaving 9 and 10 pretty much open would let my opponent waste much of their capitol on those, leaving only 8 and 5 as 'battles,' but ones in which my opponent would have less to spend. Seeing the distributions of the previous 2 rounds, 6 and 7 seemed pretty safe, so I spent my soldiers on 5 and 8, leaving token 1's to leverage against random strategies with zeros. |
725 | 725 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 19 | Made it up |
774 | 774 | 3 | 6 | 7 | 1 | 2 | 22 | 22 | 2 | 2 | 33 | -Always choose numbers of men above multiples of 5. -Shift focus away from 4 and 5, where large numbers were sent the previous two times -go back to focusing on 1, 2, and 3. -Finally, move focus away from castle 9 to 10. |
786 | 786 | 1 | 6 | 0 | 10 | 0 | 15 | 5 | 19 | 21 | 23 | I try to get the best of both worlds, as much as possible, by sending big battallions to the largest castles while still having a good chance of grabbing the even-numbered lower ones by punting on odd numbered low castles. It's a bizarre strategy that does well against the average strategies from both the other years as well as the winning strategies from those years. I do have to punt on one of the bigger numbers, so I choose 7 since I think people tend to "randomly" select that one a lot, plus 7 is "big enough to be important but not so big that others will get it, so I will". I do still send 5 troops there to avoid losing to other strategies that punt there. |
792 | 792 | 3 | 6 | 6 | 16 | 19 | 12 | 12 | 20 | 3 | 3 | I found the average troop deployment of the top 5 placers from both of the last tournaments, and then I found a strategy that would beat them both on average. |
794 | 794 | 5 | 6 | 8 | 10 | 1 | 16 | 21 | 31 | 1 | 1 | In previous battles the winners took two different approaches. The first round the winners focused on castles 4,5,7,8. In the second the focus was on 4,5,9,10. My idea was to focus on 6/7/8. then capturing as many little castles as I could. |
803 | 803 | 4 | 6 | 8 | 9 | 10 | 11 | 12 | 13 | 13 | 14 | Trying to get win at several castles with an emphasis towards the high point castles. Weighting for each castle proportional to the square root of the value. |
865 | 865 | 1 | 6 | 2 | 16 | 3 | 26 | 8 | 32 | 3 | 3 | I put 3 at 9 & 10, noting how many winners had put 2 there in previous years, and then assuming others would borrow their strategy. I then overloaded on the even numbers to try to eke out victory. |
930 | 930 | 3 | 6 | 7 | 10 | 10 | 18 | 16 | 14 | 1 | 15 | General ramping-up from low to high, leaving out one high to improve the chances on the others |
956 | 956 | 3 | 6 | 2 | 12 | 2 | 18 | 2 | 25 | 28 | 2 | Using java, I found how often flipping a castle would change the outcome of a war (given a random distribution of castles beforehand). This actually is fairly predictive of how many troops the top players sent to the castles they wanted to win. Most winning players picked a selection of targets that added to just more than 27, so thats what I did too. There wasn't much method to the madness, I just picked the ones that I thought would win this time around, not too different from past combinations but not too similar. My targets were 1, 2, 4, 6, 8, 9, adding to 30 points. I am sending an appropriate number of troops to each target, and 2 scouts to the other four castles to maybe win against single scouts or cause ties. Here's a desmos link: https://www.desmos.com/calculator/41xuwxlaeq |
975 | 975 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 14 | 18 | Trying to balance protecting/winning the high-value targets and preventing token squads from picking off the low-value forts |
996 | 996 | 5 | 6 | 6 | 8 | 13 | 22 | 27 | 4 | 4 | 5 | slightly above average plus one on most with choice wins from 5-7 |
1102 | 1102 | 3 | 6 | 9 | 12 | 15 | 0 | 0 | 0 | 26 | 29 | minimize cost/point |
1104 | 1104 | 4 | 6 | 9 | 16 | 21 | 0 | 0 | 0 | 27 | 17 | minimize cost |
1118 | 1118 | 4 | 6 | 12 | 19 | 24 | 7 | 7 | 7 | 7 | 7 | With the notable exception of the linear deployment strategy ( distribute more troops linearly over increasing castle value), almost every strategy depends on securing 2 - 3 spots in castles 6 - 10, and then 2 - 3 in 1 - 5. My strategy should scoop the ignored castles in 6 - 10 and sweep castles 1 - 5 on average. Most pick-4 strategies (where you try to perfectly distribute on 4 castles to hit >=28 points, e.g. 10, 9, 8, 1 or 10, 9, 5, 4 etc) will lose to this strategy by virtue of not allocating enough to secure their least valuable, but critical castle. The pick-4 that my strategy is most vulnerable to (10, 9, 8 ,1) is also likely the least common because of how precarious it is to try to take all 3 of 8 - 10 given those are critical for other pick-4 strategies). 7 is the deployment number for 6 - 10 to counter people who might arbitrarily station 5 at each one and the people putting up 6 to counter that. |
1120 | 1120 | 5 | 6 | 12 | 17 | 25 | 5 | 6 | 7 | 8 | 9 | Collect leftover high-value castles, sweep the low value castles. |
1131 | 1131 | 5 | 6 | 7 | 8 | 9 | 11 | 12 | 13 | 14 | 15 | laziness |
1154 | 1154 | 3 | 6 | 8 | 10 | 13 | 0 | 25 | 29 | 3 | 3 | have to win battle 4 and 5 |
1197 | 1197 | 1 | 6 | 9 | 12 | 15 | 2 | 2 | 2 | 24 | 27 | Targeted ones that were worth the most points per average soldier assigned in previous rounds (2-5, 9-10). |
1253 | 1253 | 5 | 6 | 7 | 8 | 12 | 0 | 19 | 21 | 21 | 1 | |
1298 | 1298 | 4 | 6 | 4 | 12 | 2 | 17 | 18 | 27 | 5 | 5 | I based my numbers on the 2017 distributions, hoping history would repeat and not a ton would pore over the results much. In that data set, there were a lot of clusters in the 1-4 range at the higher and lower castles, so my castles 1-3 and 9-10 all hovered at or around 5 troops to cover. In the middle castles, I figured I'd sacrifice one to put each of the rest in play. |
1300 | 1300 | 4 | 6 | 7 | 1 | 1 | 14 | 17 | 20 | 17 | 13 | Ran a bunch of simulations in Excel |
1315 | 1315 | 4 | 6 | 9 | 11 | 16 | 18 | 0 | 0 | 0 | 36 | Trying to reach 28 points to win and looking at past deployments. Also keep a fairly constant point per soldier ( between 2.75 and 4) |
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CREATE TABLE "riddler-castles/castle-solutions-3" ( "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 );