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
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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? |
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1349 | 1349 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | YOLO |
1348 | 1348 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | Go big or go home. |
1347 | 1347 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 75 | Because you told me to |
1346 | 1346 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | I figure many will put all 100 in #10 and thus have lots of ties |
1345 | 1345 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 50 | My last and final submission! I ran every distribution of 30 troops / 4 castles to find that [0 7 8 15] performed the best against all others. For 12 troops / 5 castles = [0 0 3 3 6]. For 10T, 6C = [0 0 1 2 3 4]. I'm extrapolating / guessing that 100T,10C looks like this. |
1344 | 1344 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 13 | 26 | 51 | This is kind of a variation on (n/2)+1, with a few extra troops thrown in to defeat a potentially like-minded enemy. |
1343 | 1343 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 20 | 30 | 40 | Trying to win the top 4 castles should outscore all be all who use equal deployment over any 4 or more castles. Also will outscore anyone who just goes for top castle. Will lose to anyone who goes for only top 1, 2 or 3, but they will lose to all equal allocations to more than 3 castles |
1342 | 1342 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 20 | 30 | 40 | 1st 6 castles are worth an average of 2 2/3 points. The last 4 are worth an average of 8 1/2 points. Any 2 of the last 4 gets more than the first 6 combined. |
1341 | 1341 | 0 | 0 | 0 | 0 | 0 | 0 | 11 | 20 | 27 | 42 | I'm not convinced of my strategy's effectiveness, so I'm going to submit a few answers to this riddler. In this one I abandoned all of the low value castles and concentrated them all in the highest value castles. I'm not convinced this will work... |
1340 | 1340 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 24 | 26 | 30 | Started with a points weighted distribution of troops and created successively better strategies by shifting troops from lower ranked castles to higher ranked castles. |
1339 | 1339 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 24 | 26 | 29 | Against a random opponent, assigning soldiers in proportion to the value of each castle is a winning strategy. Unfortunately it loses to anyone who focuses troops on a smaller number of castles. Since it is impossible to win without at least one of the four strongest castles, I sent a number of troops proportional to value to each of the four strongest castles, totally neglecting the smallest castles. (I got lazy when trying to calculate the Nash Equilibrium and stopped here.) |
1338 | 1338 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 24 | 26 | 28 | I gave up on the smallest three - and then tried to optimally place the others. Not much math involved, honestly. |
1337 | 1337 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | The top four castles are more valuable than the descending 6 combined |
1336 | 1336 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | Submission #3. A variation on my first submission. Here, however, I gave an equal number to each of the castles I defended. |
1335 | 1335 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | defend the top scoring castles |
1334 | 1334 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | you need the last four to win |
1333 | 1333 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | Win at least one of the higher value castles |
1332 | 1332 | 0 | 0 | 0 | 0 | 0 | 1 | 12 | 12 | 34 | 41 | Base strategy of 37,33,11,11,1 form castles 10 to 6 with remaining 7 soldiers distributed to give 'optimal' result. |
1331 | 1331 | 0 | 0 | 0 | 0 | 0 | 6 | 16 | 21 | 26 | 31 | I anticipated a couple strategies (10 all, proportional distribution, 25 on the top 4, 30-25-20-15-10, etc.) and I tried to come up with a simple strategy that would beat them. I anticipated that many players would use multiples of 5, so I used number that had a remainder of 1 when divided by five to get a slight edge over them. |
1330 | 1330 | 0 | 0 | 0 | 0 | 0 | 10 | 15 | 20 | 25 | 30 | the biggest numbers are the most important x |
1329 | 1329 | 0 | 0 | 0 | 0 | 0 | 10 | 20 | 30 | 39 | 1 | You need 28 points to the war. The fewest castles this can be achieved in is 4, but I can go for #6 instead of #10 and still meet the goal. I'm hoping others overvalue castle 10 and I'm able to win 6-9 for 30 points. If they ignore 10 and contest one of the others integral to my plan I have 1 soldier at 10 to avoid splitting those points |
1328 | 1328 | 0 | 0 | 0 | 0 | 0 | 10 | 25 | 65 | 0 | 0 | I didn't put too many at the top, I instead put them in the middle where people are less likely to go, but I'll still earn a sizable number of points. |
1327 | 1327 | 0 | 0 | 0 | 0 | 0 | 11 | 11 | 26 | 26 | 26 | Winning the highest 5 together is far more important than the lower five. |
1326 | 1326 | 0 | 0 | 0 | 0 | 0 | 11 | 14 | 20 | 25 | 30 | Get the big ones! |
1325 | 1325 | 0 | 0 | 0 | 0 | 0 | 14 | 15 | 21 | 21 | 29 | I figure if i can deploy enough troops to win at least 4/5 of the 10,9,8,7,6 castle combination and i can win so i am going to guess most other people will put troops in every castle (mistake) so i wanted to fortify my higher level castles with more than most other people might be comfortable with and sacrifice the points for castles 1-5 (15 points) to try to obtain 6-10 (40 points) so even if i lose one of them including a higher number like 10 or 9 i would most likely win the others but i am banking on winning 4/5 of them and if not then i lose but it will be a valiant effort |
1324 | 1324 | 0 | 0 | 0 | 0 | 0 | 15 | 15 | 20 | 22 | 28 | |
1323 | 1323 | 0 | 0 | 0 | 0 | 0 | 16 | 20 | 30 | 30 | 4 | Winning the top three castles alone isn't enough. You need at least four castles to win. So it seems wise to concentrate troops on four castles that together can take the prize. I figure 10 will be in high demand so I concentrate on 6-9, which together combine for 30 points, more than the 28 points needed to win. I put together a program with my son that simulates lots of tournaments of randomly selected deployments and outputs the average of the winners. I was surprised to see a pattern emerge, proving there is some merit to my earlier analysis. Winners tended to put lots of troops in 6, 7, 8, and 9, but fewer in 10. I then picked a deployment similar to my final answer and ran it head-to-head against a million random selections, and carefully tweaked it, moving one soldier at a time to find the best possible strategies. I'm not sure there aren't better strategies -- this may be a local maximum -- but it's good enough. Also, the best strategy really depends on how others play the game. This one does pretty well against soldiers deployed randomly (and another algorithm that assigns soldiers randomly with a preference for the higher valued castles), but it may not be the best against strategies that are actually employed in this game. |
1322 | 1322 | 0 | 0 | 0 | 0 | 0 | 18 | 19 | 20 | 21 | 22 | I can lose one castle and still win a battle |
1321 | 1321 | 0 | 0 | 0 | 0 | 0 | 18 | 19 | 20 | 21 | 22 | I can lose one castle and still win a battle |
1320 | 1320 | 0 | 0 | 0 | 0 | 0 | 19 | 21 | 25 | 35 | 0 | I'll give them castle 10 if it means I'll win castles 9,8,7, and 6. Winning those castles should end with a higher point total. |
1319 | 1319 | 0 | 0 | 0 | 0 | 0 | 19 | 22 | 27 | 32 | 0 | Focused on 6-9 pat castles only |
1318 | 1318 | 0 | 0 | 0 | 0 | 0 | 19 | 23 | 27 | 31 | 0 | There is no one answer that can beat everyone. I decided to focus on 4 castles that would get enough points to win, but I chose not to go for castle 10, because I figured lots of people would try to get 10 or 7-10. I assigned my troops roughly proportional to the number of points in these four castles. |
1317 | 1317 | 0 | 0 | 0 | 0 | 0 | 20 | 20 | 20 | 20 | 20 | Need 28 points to win. Assuming that the points happened to coincide with the castle number, I can lose at most one of the castles i bet on and still win. |
1316 | 1316 | 0 | 0 | 0 | 0 | 0 | 20 | 20 | 20 | 20 | 20 | |
1315 | 1315 | 0 | 0 | 0 | 0 | 0 | 20 | 20 | 20 | 20 | 20 | First five = 15 PT's, next five equal 40 PTs so that deploy troops proportionately bcse average value is 8. |
1314 | 1314 | 0 | 0 | 0 | 0 | 0 | 20 | 23 | 27 | 30 | 0 | I ran a bunch of simulations to get a feel for winning strategies. It quickly became clear that winning strategies ignore castles of lower value. It took longer for me to notice, but every once in a while a strategy that ignored Castle 10 also showed up and did well. Putting these two together I decided to amass my troops at four castles This is the smallest number of castles that can ensure you get more than half the available points. Doing so at Castles 6-9 hopefully gives me an advantage over people that expend troops on Castle 10. I the exact distribution because it worked the best in my simulations (though those are biased based on the mechanism I used to create them). I also note that this distribution gives me the evenest expected points per troop when I win all four castles. |
1313 | 1313 | 0 | 0 | 0 | 0 | 0 | 20 | 25 | 25 | 30 | 0 | I previously submitted a solution that was created by a genetic algorithm. Though it was good, I think this is better. (And I created it myself.) There are 55 points possible, so one needs to score 28 points to win. Since the biggest score with just 3 castles is 10+9+8=27<28, any solution needs to dominate four castles. I'm guessing that most people will try to conquer 10 -- so I don't want to dominate that castle. This is just spreading my troops among the next four castles in a fashion that I hope works well. Thanks for an amazing competition. I'm looking forward to seeing how well my two solutions fare! |
1312 | 1312 | 0 | 0 | 0 | 0 | 0 | 21 | 22 | 28 | 29 | 0 | I only need to conquer castles 6,7,8, and 9 to win a battle. |
1311 | 1311 | 0 | 0 | 0 | 0 | 0 | 21 | 23 | 27 | 29 | 0 | This is a moneyball strategy. If I can consistently win castles 6,7,8, and 9, I win every war. I am placing my bets that opponents will not fortify these 4 castles enough, and am giving up the rest of them in the process. While I realize that if I lose or tie any of these 4 battles, I lose the war, I think it is a chance. |
1310 | 1310 | 0 | 0 | 0 | 0 | 0 | 21 | 25 | 25 | 29 | 0 | You only need 4 castles (excluding 10) to get more points |
1309 | 1309 | 0 | 0 | 0 | 0 | 0 | 24 | 24 | 24 | 24 | 4 | There are a total of 55 points in play here. Assuming no drawn battles, I need to get 28 points (at least) to win. There are 4.2634215e+12 number of solutions to x1 + x2 + ... + x10 = 100. Before I saw this number, I thought for a minute about brute forcing it by finding all solutions and doing a one-vs-one across them all to find the winner. So, I ended up brute-force searching over all solutions of x1+x2+x3+x4 = 20 to get best candidate (0, 5, 5, 10). I ran again for x1+x2+x3+x4=24 to get best candidate (0, 6, 6, 12) and for x1+x2+x3+x4+x5=20 to get best candidate (0, 2, 4, 6, 8). Extrapolating it for the problem of 10 castles with 100 soldiers, I get (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). This (I think/hope/believe) wins on average against the set of all possible solutions but my concern is that I lose against a top-heavy strategy (10, 0, 0, 0, 0, 0, 0, 20, 30, 40) and a bottom-heavy strategy (8, 10, 12, 14, 16, 18, 22, 0, 0 ,0). I ended up going with a middle-heavy strategy giving up on 25 points for castles 1-5+10. |
1308 | 1308 | 0 | 0 | 0 | 0 | 0 | 24 | 24 | 25 | 27 | 0 | If I manage to win 9, 8, 7, and 6, then I'd win the game. 10 seems like the sort of place people might expend a lot of resources over, and the other castles can be forfeited for the sake of those key four. This might backfire against an unexpected number of troops on any of the four, though. |
1307 | 1307 | 0 | 0 | 0 | 0 | 0 | 25 | 24 | 25 | 25 | 1 | A majority is won with only castles 9, 8, 7 and 6, so I deployed 25 to each. Winning these four only will guarantee victory. However, if somebody takes the same approach, they'd beat me. So I reassigned one soldier from castle 7 to castle 10. |
1306 | 1306 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | Maximizes points I could win |
1305 | 1305 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | |
1304 | 1304 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | It's a wild guess at a strategy |
1303 | 1303 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | If I take Castles 6, 7, 8 and 9, I defeat someone who gets the other 6. It would work, too, with 7 to 10, but I think most people would send many soldiers to 10, and so, I am going to render those moot and enhance my chances of taking 6 through 9. |
1302 | 1302 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | Guessing -- hoping the odds are in my favor |
1301 | 1301 | 0 | 0 | 0 | 0 | 0 | 25 | 25 | 25 | 25 | 0 | Winning 6,7,8,9 will win the battle regardless of the results at the other castles |
1300 | 1300 | 0 | 0 | 0 | 0 | 0 | 26 | 0 | 35 | 39 | 0 | Winning by higher margins is useless in this game. The only thing that matters is getting 23 points. I figured that I could either spread the risk and provide multiple ways to get 23 points or put all my eggs in one basket. With these "multiple simulation" games, using a risk spreading strategy basically guarantees you will be in the middle of the pack. I went with a high risk / greater variability strategy to either win outright, or crash spectacularly. |
1299 | 1299 | 0 | 0 | 0 | 0 | 0 | 29 | 0 | 34 | 37 | 0 | 55 points total. 23 points to win. In order to get 23 points, you need to win at least 3 castles. choose 3 and go ham to win them. |
1298 | 1298 | 0 | 0 | 0 | 0 | 0 | 33 | 33 | 34 | 0 | 0 | Spooky magic |
1297 | 1297 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | Any selection higher than 6, if a tie, will result in, at most, 5 pts, therefore 6 will win. |
1296 | 1296 | 0 | 0 | 0 | 0 | 1 | 10 | 16 | 20 | 24 | 29 | Ran a lot of simulated tournaments and picked a top choice from those. |
1295 | 1295 | 0 | 0 | 0 | 0 | 1 | 17 | 19 | 20 | 21 | 22 | Emphasized larger castles. |
1294 | 1294 | 0 | 0 | 0 | 0 | 3 | 5 | 16 | 22 | 27 | 27 | I wrote some Python scripts to generate random deployments, and compared them against sorted versions, as well as against balanced versions, and I played several rounds where the best ones went on ... not sure if this makes sense as a strategy but it was fun |
1293 | 1293 | 0 | 0 | 0 | 0 | 4 | 11 | 21 | 31 | 31 | 2 | I have the all the best strategies. |
1292 | 1292 | 0 | 0 | 0 | 0 | 5 | 6 | 6 | 11 | 31 | 41 | To win |
1291 | 1291 | 0 | 0 | 0 | 0 | 5 | 12 | 17 | 25 | 23 | 18 | Didn't waste any on the lower scoring castles. Didn't decide to put a ton on castle 10 either, since it's worth the most and likely will have a lot of soldiers from everybody else. I put almost all of my soldiers at castles 7-10. Almost half of my soldiers are dedicated to 8 and 9, hoping to win either of those plus maybe either 6 or 7 too. Trying to spread out among the higher scoring castles without focusing too hard on one of them, but also prioritizing 8 & 9. |
1290 | 1290 | 0 | 0 | 0 | 0 | 7 | 21 | 0 | 31 | 41 | 0 | I am trying to allocate such that I get 28 points in a manner unlikely to be matched by others (passing on 10). Any splits are bonus. I worry that I may have over-allocated to 8 and 9, but am trying to outdo, by 1, any 40-30-20-10 split. |
1289 | 1289 | 0 | 0 | 0 | 0 | 8 | 15 | 20 | 25 | 30 | 2 | Because it beat my son. äÖ_ |
1288 | 1288 | 0 | 0 | 0 | 0 | 8 | 16 | 18 | 18 | 20 | 20 | Trial and error led me to think that protecting higher value castles outweighs collecting multiple smaller numbers |
1287 | 1287 | 0 | 0 | 0 | 0 | 10 | 14 | 16 | 18 | 20 | 22 | I figured many people would do the "optimal" 13 5 7 9 11 13 15 17 19, and picked a top heavy strategy to beat it. |
1286 | 1286 | 0 | 0 | 0 | 0 | 10 | 20 | 20 | 20 | 30 | 0 | Conceded the low point castles because tier low point value doesn't make them worth defending when 28 needs to be a winning score. Conceded Castle 10 and instead fortified Castle 9, figuring that most players would go for the top point castle. Then effectively evenly weighted the remainder of the castles in the hopes that I'd win 3 of the remaining 4 ... and enough points to clear a "no tie" threshold. |
1285 | 1285 | 0 | 0 | 0 | 0 | 11 | 11 | 21 | 26 | 31 | 0 | |
1284 | 1284 | 0 | 0 | 0 | 0 | 11 | 13 | 15 | 18 | 20 | 23 | 60% of the castles have 82% of the victory points. I just allocated from there. Each one has at least 10, and the specific numbers were pretty random. |
1283 | 1283 | 0 | 0 | 0 | 0 | 11 | 21 | 0 | 34 | 34 | 0 | All you need are 4 castles totalling 28 (out of 55). My thought would be that most that recognize this would take the 8-9-10 and any 1 other (most going for either 7 or 1). But 5+6+9+8 also = 28. Sending 34 troops each to #8 & #9 would beat those who'd use a 33-33-33-1 deployment with that 8-9-10-x strategy; Sending 11 troops to #5 beats those going for a 10-straight strategy as well as what I call the "Prevent" Strategy [of sending (2n-1) troops to each castle with n being the value of each castle]. 21 Troops to #6 helps against the 20-even strategy for 6-10, but admittedly fails against a 25-even 4-6-8-10 strategy. |
1282 | 1282 | 0 | 0 | 0 | 0 | 11 | 29 | 30 | 30 | 0 | 0 | Forfeited 1,2,3,4,9,10 so my max score is 26. decided to distribute evenly across 6,7,8 and throw 10 on 5. Changed from 10 on 5 to 11 in case the highest value is 10's across the board. This is a dumb strategy, but hey we'll see. |
1281 | 1281 | 0 | 0 | 0 | 0 | 12 | 14 | 16 | 21 | 35 | 2 | This layout beats a lot of typical strategies I could image: i) 10 on every city ii) 11-13 on most cities iii) linear weight on each city (proportional to city strength) iv) 34-33-33 on any 3 castles v) 40-30-30 or 35-35-30 on castles 10, 9, 8 We want to either just win a castle, or lose by a lot (so the opponent "wasted" a lot of troops). I'm guessing most people will weight castle 10 the most so deploying 2 there feels like it will either just win, or lose by a lot most of the time. |
1280 | 1280 | 0 | 0 | 0 | 0 | 14 | 16 | 20 | 23 | 27 | 0 | Focused strategy: fighting only for the lowest number of castles required for victory. Not playing for the most sought-after castle allows more equitable distribution. |
1279 | 1279 | 0 | 0 | 0 | 0 | 14 | 20 | 25 | 2 | 2 | 37 | Main strategy is to go big on winning castles 5, 6, 7 and 10. But I've got a side bet on a few people leaving 8 and 9 either totally undefended or with only 1 soldier. |
1278 | 1278 | 0 | 0 | 0 | 0 | 15 | 16 | 0 | 33 | 34 | 2 | I'm trying to pick my battles, and 9+8+6+5 wins the war. I hope this beats most people who focus on the top three castles, it makes someone pay for abandoning castle 10, and it should beat people who distribute evenly among the bottom 7 castles. |
1277 | 1277 | 0 | 0 | 0 | 0 | 15 | 17 | 0 | 34 | 34 | 0 | Trying to win minimum number of castles to win 28 points. if people go for 10,9,8, they would put roughly 1/3 into each, saving a point to win castle 1. |
1276 | 1276 | 0 | 0 | 0 | 0 | 15 | 18 | 0 | 30 | 37 | 0 | Chose 28 points worth of castle, tried to win those. |
1275 | 1275 | 0 | 0 | 0 | 0 | 15 | 19 | 0 | 30 | 36 | 0 | The easiest way to get to 28 points (the lowest winning score) is to deploy at castles 1, 8, 9, 10. I assume that most puzzlers will figure this out, and so designed a strategy that effectively wins against the "obvious" strategy. |
1274 | 1274 | 0 | 0 | 0 | 0 | 15 | 20 | 0 | 30 | 35 | 0 | |
1273 | 1273 | 0 | 0 | 0 | 0 | 16 | 16 | 17 | 17 | 17 | 17 | I played around in Excel with an evolutionary alogrithm, although I'm still not sure it's optimized. |
1272 | 1272 | 0 | 0 | 0 | 0 | 16 | 17 | 0 | 29 | 38 | 0 | Picked the smallest group of castles which if all are won gives victory (four castles). Split them to allow for victories in smaller castles (5 and 6) and give up 10 point castle as a hopeful over extension on the enemies behalf. Then split troups, favoring higher point castles. |
1271 | 1271 | 0 | 0 | 0 | 0 | 16 | 21 | 0 | 31 | 32 | 0 | I assume there will be 2 common strategies. Strategy A is to send to each castle soldiers proportional to the amount of points available at the castle, if not a bit skewed toward the higher castles. Something like 24-19-16-13-10-7-5-3-2-1. Strategy B is going all in on just 28 points worth of castles. Something like 40 on Castle 10, 28 on Castle 8, 19 on Castle 6, and 13 on Castle 4. There is little room for error with Strategy B, as losing just 1 of your targets guarantees a loss, but the big advantage here is that all soldiers are warring at the required castles and none are wasted. I need to figure out a way to beat both of these strategies consistently ---- if I can, I figure I will win enough wars against these two to ignore any other strategies (strategies geared to beat these 2, strategies geared to beat mine, or other "optimal if both are playing completely logically" strategies I cannot come up with.) My first idea is to concede Castle 10, giving me more soldiers to play with in the rest of the 9 castles and hopefully proving to be a key advantage going forward. If I was to then proportion my soldiers out similar to Strategy A, but just on the back 9, I would clean up house against Strategy A. However, this will usually doom me against Strategy B. There are so many alterations of Strategy B: 10+9+8+1, 10+9+7+2, 10+9+6+3...39 different ones by my count. Moreover, each castle shows up in 19 to 20 of these different strategies. So I am going to make an assumption that most people who choose Strategy B will choose a 4-castle strategy as that contains the least room for error. The 4-castle strategies are as follows: 10+9+8+1 10+9+7+2 10+9+6+3 10+9+5+4 10+8+7+3 10+8+6+4 10+7+6+5 9+8+7+4 9+8+6+5 10 shows up 7 times, 9 shows up 6, 8 shows up 5, 7 - 4, 6 - 4, 5 - 3, 4 - 3, 3 - 2, 2 - 1, 1 - 1. Still wanting to avoid the assumed-to-be-hotly-contested 10 castle, and noting that all but one contain either a 9 or an 8, I am going to choose my own 4-castle, 28-point strategy that is front-loaded on 9 and 8: 9 + 8 + … |
1270 | 1270 | 0 | 0 | 0 | 0 | 16 | 21 | 1 | 28 | 32 | 2 | 4 castles are highly contested castles picked to add up to 28 points. Troop deployment numbers for these castles are near the 3.57 troop/point ratio that is the maximum number of troops that be deployed to win a point and still win the battle. Chose not to contest lowest 4 point castles at all and put very small amounts in castle 7 and 10 to potentially "steal" the points if uncontested or only contested with 1 troop. |
1269 | 1269 | 0 | 0 | 0 | 0 | 16 | 21 | 1 | 29 | 32 | 1 | Focus on minimum number of castles four. Focus on the least valued of those. 9,8,6,5 proportionally. Then adding a little bit back for possible 10,7. Little tricky because not working against random troop assignments but working against visitors of 538. |
1268 | 1268 | 0 | 0 | 0 | 0 | 17 | 17 | 17 | 0 | 0 | 49 | Optimizer. |
1267 | 1267 | 0 | 0 | 0 | 0 | 17 | 17 | 17 | 17 | 16 | 16 | I assume most people will send more troops to the first castles, and I only need 6 castles to win so If I deploy as many troops as possible to the last 6 and forfeit the first 4 castles I will hopefully dominate the last 6 while opponents waste soldiers on castles I didn't attempt to win in the first place. |
1266 | 1266 | 0 | 0 | 0 | 0 | 17 | 19 | 20 | 21 | 22 | 1 | Ten's not worth blowing all your troops for. Hopefully they wasted too much on ten to match us for 5-9 |
1265 | 1265 | 0 | 0 | 0 | 0 | 17 | 21 | 0 | 26 | 36 | 0 | Same as before, different case. |
1264 | 1264 | 0 | 0 | 0 | 0 | 17 | 21 | 0 | 29 | 33 | 0 | This is a go for broke strategy attempting to secure a 28-27 victory by taking only 4 castles. Each contested castle receives a number of armies proportional to its value, with the extra 2 units sent to the highest value castles rather than based on simple rounding. |
1263 | 1263 | 0 | 0 | 0 | 0 | 17 | 21 | 0 | 29 | 33 | 0 | Focusing all on winning 5+6+8+9=28, which is more than half of 1+2+3+4+5+6+7+8+9+10=55 |
1262 | 1262 | 0 | 0 | 0 | 0 | 18 | 0 | 19 | 9 | 24 | 30 | I made 500 "random" strategies and picked the winner from each. Then repeated that 500 times, resulting in 500 "first-round" winners, and then submitted the winner from among those. The 500 first-round winners hopefully somewhat approximate real strategies that real people might pick, and then the winner from among those might approximate an actual winning strategy for the overall game. Three comments on my solution: (1) the strategy has its simplicity to recommend it, but doesn't think through the psychology much at all; (2) I'm curious but have no idea if this process converges; (3) the two parameters -- 2 rounds, each with 500 entires -- are totally arbitrary, and I wonder how they affect the outcome. |
1261 | 1261 | 0 | 0 | 0 | 0 | 18 | 21 | 0 | 29 | 32 | 0 | I picked the smallest number of castles to get 28 points, avoided 10 since I figure a proportion will garrison that heavily, and otherwise picked numbers as low as possible to hopefully face less opposition. I fortified the ones I picked roughly in proportion to their value, as a guess at how well each will be protected. |
1260 | 1260 | 0 | 0 | 0 | 0 | 18 | 21 | 0 | 29 | 32 | 0 | Minimum number of castles and points required and least popular numbers, weighing the number of troops to the value of the chosen castles. |
1259 | 1259 | 0 | 0 | 0 | 0 | 18 | 22 | 0 | 28 | 32 | 0 | Concentrated on winning 28 points (more than 1/2 of the available 55) with the fewest number of castles. Likely popular strategies will be equal mix or some thing with a little on each castle (more on higher values); this should beat most such strategies. It would take a big bet on the few castles I made big bets on to beat this. |
1258 | 1258 | 0 | 0 | 0 | 0 | 19 | 22 | 1 | 28 | 29 | 1 | Consider the populations of strategies that will be submitted. Naive strategies include allocating 10 per castle or point weighting the allocation across all 10. Less naive strategies include targeting exactly enough castles to obtain 28/55 points. Some will go after 10-7 with 25 each or point weighted, others will target 7-1, likely point weighted. I put enough on 5-6 to win against the 7-1 point weighted strategy and enough on 9-8 to win against people targeting the large numbers. Of course, this strategy must win against all naive strategies, but probably does not have to beat strategies that would lose to a naive strategy. |
1257 | 1257 | 0 | 0 | 0 | 0 | 19 | 23 | 23 | 2 | 0 | 33 | Wrote a program to choose a random assortment of soldiers, then 'improve' the assortment by moving a soldier from one castle to another, and checking to see if that beats all previous soldier assortments. It's somewhat surprising that after 244 different deployments of soldiers, it was impossible to come up with a deployment that beat even 55% of the previous deployments with less than 10 million random deployments. It does appear that deploying soldiers to a few castles is the right thing to do. Using 33 to try to get the 10th castle, and trying to get castles 5, 6, and 7 with many other soldiers, should be a good plan. |
1256 | 1256 | 0 | 0 | 0 | 0 | 20 | 20 | 20 | 20 | 20 | 0 | |
1255 | 1255 | 0 | 0 | 0 | 0 | 20 | 23 | 0 | 27 | 30 | 0 | out of 55 victory points, i only need 28 to win the battle. so i only allot soldiers to castles 5+6+8+9=28. |
1254 | 1254 | 0 | 0 | 0 | 0 | 20 | 50 | 30 | 0 | 0 | 0 | Obviously the castles with the small points do not make a big difference and it makes sense to focus on the larger point castles but at the same time, most people would put more soldiers on the larger castles. So would choose to go where most others would not and still get enough number of points. Assuming that the middle ones do not get enough attention, putting a large number of soldiers here gives a real good chance. |
1253 | 1253 | 0 | 0 | 0 | 0 | 21 | 21 | 0 | 26 | 31 | 1 | 9 + 8 + 6 + 5 = 28. left 1 in 10 for all the people that left it empty |
1252 | 1252 | 0 | 0 | 0 | 0 | 21 | 21 | 0 | 26 | 31 | 1 | |
1251 | 1251 | 0 | 0 | 0 | 0 | 22 | 22 | 0 | 27 | 29 | 0 | 28 is the threshold, and there's a lot of ways to make this sum. Any that uses 4 castles must include 9 or 10, so I picked 9 + . Picking the "less desirable after this for other sum sequences seems to favor 8+6+5. Any troops on castles not needed for victory are wasted. I propped up 9/8 a little because I figured they'd be more contended, but all 4 castles are equally required for victory. |
1250 | 1250 | 0 | 0 | 0 | 0 | 22 | 24 | 0 | 26 | 28 | 0 | I decided to ignore ties, since any strategy depending on that relies too much on precisely predicting the opponent's strategy. Given that, winning requires winning a minimum of 4 castles with a minimum value of 28. Thus, the objective was to target only this minimum threshold and not allocate any resources to back-ups, contingencies, or disrupting the opponent's strategy. This means assigning soldiers to four towers, and 0 to 6 others. The 10 tower was ignored because it opens up so many options for winning, which also presumes that it will be contended for often. Thus the scenario of taking towers 9, 8, 6, and 5 was chosen. From there, the soldiers were nearly evenly distributed, with a slight bias toward the higher value towers. |
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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 );