Riddler - Solutions to Castles Puzzle: castle-solutions.csv
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
1,349 rows sorted by Castle 8
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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 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | because, I am number one! |
11 | 11 | 20 | 12 | 13 | 13 | 14 | 14 | 14 | 0 | 0 | 0 | Get to 28 by conquering the smallest towers |
19 | 19 | 15 | 14 | 14 | 14 | 14 | 14 | 15 | 0 | 0 | 0 | Target to win is 28 points. Concentrating deployment on highest-value castles means I need to capture 10, 9, 8 and 1 to reach target. Highest-value castles are likely to draw most troops by my opponent. So I am going to focus on capturing enough castles from the lowest value upwards until I hit the target, which is castles #1-7 inclusive. Divide troops equally, with the spares focused on 1 (crucial to the 10-9-8-1 strategy set out above) & 7 (because it is the highest value of my targeted castles). |
26 | 26 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | To win a war I need 28 victory points (round up half of the total number of available points). Figure most people are going to try to target the high value targets (8,9,10) which together make 27 points. So if I can capture the rest, I win. |
27 | 27 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | With limited math skills, my basic thinking is that in this 1v1 scenario I just need 28 points to be victorious since the total number of points is 55. 1+2, +7 = 28, where 8+9+10 = 27. So I'm able to capture the first 7 castles while leaving my opponent to deploy most of his troops on the higher value castles (because who wouldn't normally want the highest value castle?) then I have the highest chance of succeeding and capturing 28 points. Hope I won. PS I see that double half-zip. |
28 | 28 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 0 | 0 | 0 | You need 28 points (a majority of 55) to win. I am guessing that it will be easier to do that if I focus all of my troops on 1-7 and none on 8 through 10, because I think the majority of people will overvalue those. |
29 | 29 | 14 | 14 | 14 | 14 | 14 | 14 | 16 | 0 | 0 | 0 | There are 55 points total, and I need 28 to win. Most people will concentrate on the higher numbers. |
34 | 34 | 13 | 7 | 10 | 13 | 16 | 19 | 22 | 0 | 0 | 0 | forfeit on 8,9,10, overweight 1, |
38 | 38 | 12 | 12 | 12 | 12 | 15 | 17 | 20 | 0 | 0 | 0 | I gave up 3 castles and tried to win 7. My hope was that others would try to win the high point bases and I would therefore be able to steal the bottom bases and the win. |
39 | 39 | 12 | 12 | 12 | 12 | 13 | 13 | 26 | 0 | 0 | 0 | I assumed that the most popular strategies would be a distribution close to 10 everywhere, a distribution close to putting a number of solders in each castle equal to (100 * castle # /55) and strategies which only attack castles 7 through 10. This strategy requires that I win castles 1 through 7 so each castle is worth the same to me, except I need to make sure I steal castle 7 from the people only going for 7-10 (and one of the variations there is to play 25 soldiers across the board). |
45 | 45 | 11 | 12 | 13 | 14 | 15 | 17 | 18 | 0 | 0 | 0 | While last few castle have most points, they are also more heavily defended. I am shifting my troops down the order, and give up the big castles. Smaller castles are easily overwhelmed by the extra troops I placed. |
46 | 46 | 11 | 12 | 13 | 14 | 15 | 17 | 18 | 0 | 0 | 0 | There are 55 total points available, so 28 points are necessary to win. I figure a lot of people will focus on winning the high value castles, so I will focus on winning enough low value castles. I didn't think about this strategy very long, but I hope I beat somebody. |
47 | 47 | 11 | 12 | 13 | 14 | 15 | 16 | 19 | 0 | 0 | 0 | Out of 55 points you want 28. You want to put more troops in higher valued castles, however by using only 1-7 (and conceding the highest 3 castles) I can reach the necessary 28 points. I divided it evenly between the castles with a singly increasing importance on each higher castle. The added remainder went to the highest sought after castle. |
48 | 48 | 11 | 12 | 13 | 14 | 15 | 16 | 19 | 0 | 0 | 0 | sum of points for winning castles 1-7 is greater than points for 8-10. i'll let others win those. need to be able to beat people that send 1/10 to every castle, so castle #1 needs at least 11 soldiers. increased by one up to castle #6, then send the rest (19 soldiers) to castle #7 |
49 | 49 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 0 | 0 | 2 | We only need to get 28 of the 55 victory points to win. Castles 1-7 deliver that for us. Let others focus on trying to get Castles 8-10. Put a leftover 2 on 10 to counter anybody else trying a similar strategy of ignoring Castle 10. |
50 | 50 | 11 | 11 | 12 | 14 | 14 | 18 | 20 | 0 | 0 | 0 | The goal is not to win all the castles; the goal is to win the majority of the 55 points possible. I assume that more people will focus on winning the higher point values (7, 8, 9, 10) so I will take the opposite strategy. I can win 28 points if I win castles 1-7, so I split my troops among those castles, more or less equally. I can assume that, if people try a 1/8/9/10 strategy, they will not weight 1 as highly. |
52 | 52 | 11 | 11 | 11 | 13 | 16 | 18 | 20 | 0 | 0 | 0 | I chose to not contest 8, 9, and 10 which may be attractive to go after since they are the highest point value castles, and save my troops for going after castles 1-7. If you are able to win castles 1-7, you automatically will win with a score of 28-27. I chose to at least put greater than 10 soldiers at each castle that I wanted to contend for, such that I would win if my opponent distributes evenly (i.e. 10 soldiers at each castle), that I would still win castles 1-7. I then increased my troop levels for castles 4-7 such that all 100 soldiers were distributed, with castle 7 receiving my most troops, in case my opponent tries to stack all or most of their soldiers at the higher value castles. Additionally, if my opponent also puts 0 troops at castles 8-10, we would split points and I would have a chance for an even larger number of victory points. |
54 | 54 | 11 | 11 | 11 | 11 | 13 | 17 | 26 | 0 | 0 | 0 | Castles 1-7 are enough to get the majority of the points. This allotment defends against putting 10 in every castle and putting 25 in the top 4 castles, and should beat many strategies that focus on seriously competing for the top castles. |
57 | 57 | 11 | 11 | 11 | 11 | 12 | 12 | 26 | 0 | 0 | 6 | I basically tried to come up with a solution that would beat the most common solutions I could think of. Being that I had no idea what others would submit, seemed like the best thing to do. |
58 | 58 | 11 | 11 | 11 | 11 | 11 | 22 | 23 | 0 | 0 | 0 | Over half the points are in 1 - 7 (28) vs (27) in 8, 9, 10. This will beat an even spread of 10 x 10, or 5 x 20 in the top 5 castles. This should beat most strategies that put most points into the top 3 castles. The only strategy it would lose to would be a 6 -10 castle strategy that weighted its troops to castles 6 and 7, not 9 and 10 - which seems an unlikely strategy to take and would lose to the commonsense strategy of putting more troops in 8, 9 and 10. |
62 | 62 | 11 | 11 | 11 | 11 | 11 | 20 | 25 | 0 | 0 | 0 | I'm attempting to maximize my odds of getting 28 points out of a possible 55, this guaranteeing victory. I'm ceding 8-9-10 thinking most people will throw all their troops that way. I'm also thinking there will be enough people who assign 10 troops per castle, which is why I put 11 troops on the lower numbers. |
63 | 63 | 11 | 11 | 11 | 11 | 11 | 19 | 26 | 0 | 0 | 0 | I enjoyed this weekäó»s Riddler. I attacked it, not mathematically, but by brute force and trial näó» error. I learned that the best strategy would involve trying to win a few key battles (i.e. not all of them), loading to ensure victories in those battles, and that it would entail barely winning in the end; i.e. a small margin of victory. My first thought was to look at ways to lock up the highest-value castles. Winning the battles for the top 3 castles is 27 points, only 1 short of victory, so my approach involved throwing a lot of soldiers at the top 3, a chunk at a lower-value one, and deploying 1 soldier at the remaining ones (to win battles against zero soldiers). An example of this approach is 0-2-1-1-1-1-1-30-31-32. This wins against many strategies but fails against a simple one of 10-10-10-10-10-10-10-10-10-10. Loading up on one lower-value castle to 11 (to defeat that strategy) leads to too few soldiers at the higher-value castles. Then I thought of the opposite approach; i.e. concede the battles for the 3 higher-value castles and try to win the remaining 7 (which would yield 28 points, and a win). The best approach I found was 11-11-11-11-11-19-26-0-0-0-. The 26 is necessary to defeat a strategy of deploying Œ_ of oneäó»s soldiers (i.e. 25) to each to the top 4 castles, the 11 is to beat the 10x10 strategy, and assigning the remaining 8 soldiers to the 5th highest castle. This strategy works against almost every strategies, especially the ones that many people likely would choose. It fails against strategies involving loading up on the mid-value castles; e.g. 0-0-1-4-11-20-25-20-15-4. However, as those strategies lose to many other ones I thought people would not choose them. |
79 | 79 | 10 | 11 | 12 | 13 | 15 | 17 | 22 | 0 | 0 | 0 | I think people may gravitate toward locking down high numbers. |
82 | 82 | 10 | 10 | 10 | 15 | 15 | 20 | 20 | 0 | 0 | 0 | I figure castles 1-3 will be lightly deployed while 4-7 will be slightly more defended. But I expect most will focus on the big targets. If I can win castles 1-7 and "sacrifice" 8-10, they will only have 27 points. I will have 28 points and still win the war. |
84 | 84 | 10 | 10 | 10 | 10 | 15 | 20 | 25 | 0 | 0 | 0 | I know I need 28 pts to win. Taking castles 1-7 gives me 28 pts. Many people will likely put a large # of troops on one or more of the bigger point value castles. Of course, many people will think of this and do the opposite, making my theory kaput. |
85 | 85 | 10 | 10 | 10 | 10 | 15 | 20 | 25 | 0 | 0 | 0 | If you win castles 1-7 you win the game. This strategy hopes the enemy will waste all or most of its army's to win 8-10, and not be prepared to win any one of the remaining castles. |
110 | 110 | 8 | 9 | 10 | 10 | 15 | 22 | 26 | 0 | 0 | 0 | You do not need the castles worth 10, 9 and 8 to win the battle, so long as you have all the other castles. Therefore why waste men on the castles which are most likely to be attacked. |
116 | 116 | 7 | 13 | 14 | 15 | 16 | 17 | 18 | 0 | 0 | 0 | Split relatively evenly between less contested castles |
117 | 117 | 7 | 11 | 0 | 14 | 16 | 0 | 23 | 0 | 29 | 0 | I want a winning coalition of 28. |
119 | 119 | 7 | 9 | 11 | 14 | 16 | 19 | 24 | 0 | 0 | 0 | I thought maybe most people would go for the big money, so if I can win the 28 points for the seven smallest castles, that would beat most strategies. |
120 | 120 | 7 | 8 | 11 | 14 | 17 | 20 | 23 | 0 | 0 | 0 | I expect that many others will choose to allocate troops to the highest values (8/9/10). If I can win with just Castles 1-7, it doesn't make sense for me to devote any troops to 8-10 since these troops will usually be completely wasted. The weakness of this strategy is that it gives me an extremely narrow path to victory -- I need all seven castles to win (in the absence of ties from 8-10). Therefore, each is essentially of equal importance to me (losing either 1 or 7 cripples my chances). My troop allocation, then, is more about where other players will choose to allocate troops. Most players will likely choose a proportional strategy, where higher values also have higher troop allocations, so I also have a proportional allocation. After distributing troops proportionally, I am left with two extras. My suspicion is that some players will try to allocate a couple extra troops to 1, thinking that it's an easy way to pick up a win. Because I need castle 1 to win, I have allocated these extra troops to castle 1 to ensure a victory there. |
134 | 134 | 6 | 8 | 10 | 14 | 18 | 20 | 24 | 0 | 0 | 0 | win all 7 and lower, sum = 28, higher than 8+9+10. |
135 | 135 | 6 | 8 | 10 | 12 | 14 | 24 | 26 | 0 | 0 | 0 | Guess from the bottom assuming most will picking from the top |
136 | 136 | 6 | 8 | 9 | 16 | 18 | 21 | 22 | 0 | 0 | 0 | |
137 | 137 | 6 | 7 | 9 | 12 | 16 | 21 | 29 | 0 | 0 | 0 | Triage - concentrate forces to get minimum points to win. Abandoned castles worth most points in hopes opponents would concentrate their forces there and I sneakily win with the lesser valued ones. |
138 | 138 | 6 | 7 | 8 | 10 | 10 | 21 | 38 | 0 | 0 | 0 | There's two basic strategies: quantity(1-7) and quality(7-10). In either case, the 7-point castle is the most important one. I spelled out here a quantity strategy. To do so, I applied a Benford's law curve with the highest value on 7. Why Benford's? No reason, I just felt that a curve like that was a good representation of the quantity strategy. |
146 | 146 | 6 | 6 | 6 | 32 | 32 | 7 | 11 | 0 | 0 | 0 | Win more towers (with lower points each) so that total points compensate for losing highest point towers. Towers 1-7 have 28 of 55 points. Towers 1-5 have 15 of 28 total points among towers 1-7. |
153 | 153 | 5 | 15 | 15 | 15 | 15 | 15 | 20 | 0 | 0 | 0 | I figured that if I won the bottom 7 castles, the total points (28) would outweigh the top three opportunities for points from Castles 8-10 (27). However, knowing the slim difference, I thought that breaking up the 100 soldiers to each Castle 1-7 would be the best strategy, knowing that if my opponent won Castles 8-10 they couldn't take any other Castle or else I would lose. |
156 | 156 | 5 | 10 | 10 | 15 | 15 | 20 | 25 | 0 | 0 | 0 | Assuming most people will try to take at least one of the high-value castles, I send disproportionately high numbers to the lower value castles in an attempt to sweep all 7, and win the war 28-27 |
157 | 157 | 5 | 9 | 15 | 14 | 16 | 16 | 17 | 0 | 0 | 8 | Winning all the castles from 1 through 7 gives you a victory no matter if you win or lose the remaining three castles. So using that I weighed my army heavily on the lower portion figuring most people's gut instinct would be to distribute their troops with powers relative to the VP for a castle. I gambled on people giving up on the lower castles so taking those for free points and putting a good number of troops in the middle range where I expected the most resistance to the strategy. |
161 | 161 | 5 | 7 | 11 | 14 | 17 | 21 | 25 | 0 | 0 | 0 | 28 points to win. ~3.5 troops per point. {10, 1} are focal, as is strategy: max points-per-castle (ie assign in descending order). Current distribution averages troops-per-point over castles least focal, with kinks at 1, 7 to account for bias towards those strategies. |
162 | 162 | 5 | 7 | 10 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | I gave up (zero troops) castles 8, 9, and 10 and their total score (27). I then crossed my fingers and hoped that by heavily weighting the bottom end, I could sweep castles 1 through 7 and receive 28 points. Now that I look at the logic, I see other alternatives. meh. I'll stick with this one. |
163 | 163 | 5 | 7 | 9 | 12 | 15 | 22 | 30 | 0 | 0 | 0 | calculated that as winning castles 1-7 outscores winning 8-10, so I chose to concede castles 8-10 assuming that is where the majority of people chose to put their soldiers allowing me to put more troops where i assume less people put there soldiers |
167 | 167 | 5 | 7 | 8 | 14 | 18 | 23 | 25 | 0 | 0 | 0 | Assuming more people will try and fight for the larger point value castles. By not dedicating any resources to those top 3 point value castles I hope to win the remaining 7 and win each battle with a score of 28-27 |
180 | 180 | 5 | 5 | 10 | 20 | 20 | 20 | 20 | 0 | 0 | 0 | |
181 | 181 | 5 | 5 | 10 | 10 | 20 | 25 | 25 | 0 | 0 | 0 | I assume most would put their soldiers at the higher point castles. I placed mine at the top 7 which would give me the most points. |
183 | 183 | 5 | 5 | 5 | 10 | 15 | 25 | 35 | 0 | 0 | 0 | If my opponent goes for high value, I could possibly win all the low values, which are collectively more points. |
184 | 184 | 5 | 5 | 5 | 5 | 20 | 30 | 30 | 0 | 0 | 0 | I win 28-27 if I win castles 1-7, figuring most people will go for 8, 9, 10 |
208 | 208 | 4 | 8 | 11 | 14 | 17 | 21 | 25 | 0 | 0 | 0 | Needed to get 28 total points to win. Used win probability (number of soldiers allocated vs. the expected distribution) to allocate soldiers in the way that had the highest probability of getting 28 points. |
211 | 211 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | I considered having each soldier is fighting for (roughly as it's rounded) 1% of the total points (e.g. 2-4-5-7-9-11-13-15-16-18) but that seemed to be dominated by more concentrated strategies that ignore some castles. So I doubled up on the lower end to try to win all of 1-7 and ignored the top end where I'm hoping most people will put their soldiers |
212 | 212 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | Castles 1-7 are worth more than 50% of the points. |
213 | 213 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | Concentrate on lower values, expecting others to overplay on higher values. If I win these, I get just enough to win, no matter what happens at the higher value castles. |
214 | 214 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | I yield the 3 juiciest castles to my opponent, and try to win all 7 remaining castles. I deploy my soldiers to each castle in proportion to its prize (rounding to the nearest integer). |
215 | 215 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | Get there firstest, with the mostest! Race to 28 pts. |
216 | 216 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | There are 55 available points, the winner needs 28. Working my way up, I allocated my troops according to the relative value of each castle (1/28 = 3.57% = 4 troops to Castle 1; 2/28 = 7.18% = 7 troops to Castle 2; etc.) until I ran out. |
217 | 217 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | Placed a higher than normal interest in the Castles 1-7 and allowed enemy to capture the three highest valued castles. By capturing the weaker castles, I can earn 28 points, while only surrendering 27 points to the enemy. This is under the prediction that my opponent will target the higher valued castles, which many not be the case. I'm an irrational S.O.B. |
218 | 218 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | Need 28 points to win. 100/28 = 3.5. People are more likely to over allocate to the top value castles. If I win 1-7 victory castles that makes 28 points. Allocate amongst those by the weighted value of each one. |
219 | 219 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | I can win if I take all castles 1-7, so I allocate all troops to those castles proportional to their value... and hope other people allocate to castles proportionately, but allocate at least some to 8-10. |
220 | 220 | 4 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 0 | 0 | To win castles 1-7 (total Victory points 28) |
221 | 221 | 4 | 7 | 11 | 14 | 17 | 21 | 26 | 0 | 0 | 0 | Avoid being beaten by concentrated bets. This strategy is fragile in that it seeks to win with minimum needed (28) while spreading across the most selections to do so. It chooses not to defend the three most valuable castles in an attempt to win all others. Anyone taking a variation of this approach will likely lose close decisive battles for the ultimate margin of victory against me - I hope. |
223 | 223 | 4 | 7 | 10 | 15 | 17 | 22 | 25 | 0 | 0 | 0 | realizing I needed 28 points to win, (55/2 rounded up). I originally was going to put my troops on 4 key castles (9,8,7,4). needing 28 points i realized that i had 3.57 troops per point. I was worried though that was putting too much into on basket, so i spread out over the bottom rung (1 through 7) otherwise known as the lowball strategy. |
228 | 228 | 4 | 6 | 8 | 12 | 16 | 21 | 33 | 0 | 0 | 0 | The winner needs 28 points so I focused all my resources on towers tha will get me 28 points while avoiding the largest castles that most people would focus on. |
231 | 231 | 4 | 5 | 6 | 8 | 11 | 24 | 42 | 0 | 0 | 0 | Trying to win 28-27 |
249 | 249 | 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. |
260 | 260 | 3 | 7 | 11 | 14 | 18 | 21 | 26 | 0 | 0 | 0 | Point weighted distribution of troops for the lowest 7 ranked castles (which constitute the majority of the points in the game). |
269 | 269 | 3 | 6 | 10 | 14 | 18 | 22 | 27 | 0 | 0 | 0 | I focused on winning exactly 28 points against as many likely strategies as possible. |
283 | 283 | 3 | 5 | 8 | 13 | 21 | 25 | 25 | 0 | 0 | 0 | Going for middle ranked castles, and hoping to pick off lower castles for few troops |
284 | 284 | 3 | 5 | 8 | 13 | 18 | 24 | 29 | 0 | 0 | 0 | My approach is not to win as many points as possible, but to take the absolute minimum points to win the majority of the time. In this game you are forced to make assumptions about the enemy. I'm hoping that castles 8, 9 and 10 will be "lucrative traps." With the higher concentration of points, the enemy goes at them with a lot of resources. Instead of trying to take those with my own resources, I will sacrifice those 3 castles to try to pick up the remaining 28 points from the rest of the castles. Essentially, the idea is that the enemy will not have enough resources left for the smaller 7, and I can (hopefully) win them all with small margins. |
303 | 303 | 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. |
315 | 315 | 3 | 3 | 3 | 13 | 25 | 26 | 27 | 0 | 0 | 0 | Ran through a couple of scenarios in a simple model I built in Excel. I liked this one because it leveraged the strategy of keeping the enemy from winning vs the strategy of trying to win. |
341 | 341 | 2 | 17 | 5 | 8 | 13 | 21 | 34 | 0 | 0 | 0 | |
350 | 350 | 2 | 7 | 11 | 14 | 18 | 21 | 25 | 0 | 1 | 1 | The race to 28. Trump's America. |
357 | 357 | 2 | 5 | 8 | 12 | 17 | 24 | 32 | 0 | 0 | 0 | Sum of 1-7 is greater than sum of 8-10, so I'm forgetting those and doing a makeshift exponential function to divvy up the other troops. |
363 | 363 | 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. |
374 | 374 | 2 | 4 | 6 | 16 | 20 | 24 | 28 | 0 | 0 | 0 | Most people I think would go for the castles worth the most points. I chose the opposite route - but who knows? |
383 | 383 | 2 | 4 | 6 | 8 | 10 | 35 | 0 | 0 | 0 | 35 | Guessing that most would shy away from 10 to take 9-8-7-6 and secure the win. I'm trying to take 10 and 6 and then the bottom to slide past them. I only really need 10-6-5-4-3 to win, but it's better to bank the bottom in case of stranger distributions. |
785 | 785 | 1 | 1 | 1 | 13 | 16 | 18 | 22 | 0 | 28 | 0 | I wanted to only go for 28 of the 55 points, but I hedged my bets by bidding 1 for the low values, hoping that I might win easy points. |
914 | 914 | 1 | 1 | 1 | 1 | 0 | 15 | 21 | 0 | 28 | 32 | Each point is worth about 2 soldiers. But like gerrymandering, you want to win a lot of castles by a slim margin and lose a few castles by a large margin. So I didn't compete for castles 8 and 5 and hope to use those soldiers to win the other big castles by a little. |
919 | 919 | 1 | 0 | 0 | 39 | 0 | 60 | 0 | 0 | 0 | 0 | I assume a lot of people are going to go all out on Castle 10. I just am trying to avoid confrontation and maximize my chances of beating people who went all on ten. |
923 | 923 | 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. |
924 | 924 | 0 | 25 | 25 | 25 | 25 | 0 | 0 | 0 | 0 | 0 | HUNGER! |
925 | 925 | 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! |
937 | 937 | 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. |
947 | 947 | 0 | 10 | 30 | 60 | 0 | 0 | 0 | 0 | 0 | 0 | swag |
955 | 955 | 0 | 9 | 11 | 0 | 0 | 19 | 21 | 0 | 0 | 40 | I didn't work the math out precisely, but I first established that I only wanted to deploy troops to win 28/55 victory points to avoid spreading myself thin. Next, I gave some thought as to which Castles I felt would be least likely to have troops deployed. This is primarily guesswork, but I went with 2, 3, 6, 7, and 10. For the distribution of troops, I put more eggs in the higher values castles but didn't calculate too much beyond that. |
958 | 958 | 0 | 8 | 0 | 14 | 0 | 21 | 25 | 0 | 32 | 0 | Instead of comparing all options, I compared all combinations that sought to defend 4 castles and promoted the best 10 combinations to an 'a-league'. These combinations were subject to constraints: the total points being defended by at least one army was 28 or more and the armies were allotted to the castles proportional to the number of available victory points for the number of castles I decided to defend. I then did the same for all combinations that sought to defend 5 castles, 6 castles, and 7 castles, 8 castles, and 9 castles. I then ran these a-league combinations (60) against each other and found that this combination won 43 fights, tied 16 fights, and lost none. http://imgur.com/a/TUJmZ. Interestingly, this wins at most 28 points and is thus vulnerable to 0 7 0 14 0 21 25 0 32 1 and the like. I suck at game theory and I'm counting on not everyone coming up with this optimization and having one person specifically beat it. |
966 | 966 | 0 | 7 | 0 | 14 | 0 | 21 | 25 | 0 | 33 | 0 | Ranked by troop efficiency points by expected value, all-in |
973 | 973 | 0 | 6 | 0 | 12 | 0 | 23 | 26 | 0 | 33 | 0 | the maximum point in this game is 55, so to win in any 1 on 1 match up i only need to get 28 points. so focusing on specific castle(s) with total points of 28, i could distribute 100 troops in only 5 castles to guaranteed a control. this strategy can also works if i decide to put 100 troops in 4 castles e.g 1, 8, 9, 10. However majority of people tends to contest "high-value" castle(s) (castle 7, 8, 9, 10) so it would be a safer pick if i just distribute the troops in less-contested castles. |
1014 | 1014 | 0 | 2 | 0 | 9 | 4 | 1 | 20 | 0 | 28 | 36 | I generated a few hundred random teams, tested them against a few base deployments (10 in each castle, 11 in castles 2 - 10, etc) and each other, and this one appears to be the best. |
1015 | 1015 | 0 | 2 | 0 | 2 | 22 | 0 | 26 | 0 | 12 | 36 | Simple simulation among randomly generated strategies https://github.com/mattinbits/fivethirthyeight_riddler_war_game |
1062 | 1062 | 0 | 0 | 15 | 15 | 15 | 15 | 0 | 0 | 0 | 40 | It beat my previous strategy |
1065 | 1065 | 0 | 0 | 15 | 0 | 0 | 15 | 0 | 0 | 35 | 35 | It beat my previous strategy |
1069 | 1069 | 0 | 0 | 12 | 16 | 20 | 24 | 28 | 0 | 0 | 0 | Since the sum of 1-10 is 55, it's really a race to 28 points. I figured most people will try to evenly distribute their answers, sacrificing the guarantee of winning a 9 or 10, in order to ensure they *could* win something. I figured I should stack all my marbles to try and guarantee winning 4-5 castles equalling 28 points, which would do well against a balanced distribution. I figured 3-7 was the best way to do this, because people will still weight their answers towards the higher numbers, so 3-7 is a nice sneaky way to ensure I get all of them (if I put 28 on the 10 square, there is a good chance someone with a more even distribution could still beat me on that one). |
1070 | 1070 | 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! |
1081 | 1081 | 0 | 0 | 11 | 11 | 11 | 11 | 11 | 0 | 34 | 11 | Beats some of the simpler strategies, and is beaten only by strategies with more obvious flaws. |
1087 | 1087 | 0 | 0 | 10 | 20 | 30 | 40 | 0 | 0 | 0 | 0 | Went for middle of the road, figuring most would deploy larger troops at the higher values |
1092 | 1092 | 0 | 0 | 10 | 0 | 20 | 0 | 30 | 0 | 40 | 0 | Higher points are worth more, so have more troops. |
1093 | 1093 | 0 | 0 | 10 | 0 | 0 | 22 | 0 | 0 | 32 | 36 | This deployment was optimised to contain the fewest castles required to reach the minimum needed points to win (28). Specifically, I wanted the deployment to have the most "bang for your buck," and to that end I looked for the most efficient castle. The metric I used was troops per point per point, which produced castle number 3, leaving only 2 selections for the castle, 3, 6, 9 and 10 or 3, 7,8 and 10. I chose the combination with the fewest points per troop, and then weighted troop placement by the number of troops I'd expect someone who had placed them based on value alone would have placed them. |
1099 | 1099 | 0 | 0 | 8 | 11 | 19 | 22 | 0 | 0 | 0 | 40 | A proportionate distribution across one combination of must-win castles for the minimum number of points to win. Then less a few soldiers from the lower point castles and re-allocated to the higher value castles, which was guesswork. |
1100 | 1100 | 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. |
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JSON shape: default, array, newline-delimited
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 );