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 7 descending
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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? |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1333 | 1333 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | Win at least one of the higher value castles |
1201 | 1201 | 0 | 0 | 0 | 10 | 20 | 20 | 50 | 0 | 0 | 0 | Trying to win the mid castles |
231 | 231 | 4 | 5 | 6 | 8 | 11 | 24 | 42 | 0 | 0 | 0 | Trying to win 28-27 |
1131 | 1131 | 0 | 0 | 1 | 11 | 12 | 14 | 41 | 21 | 0 | 0 | There are 55 points available so I need to get 28 to win. If i take a top down approach i need to take castles 10,9,8 and 7. A bottom up i need to take all castles from 1-7. middle of the road Castles 8-5 and either 2 or 3 or 4. 7 is the most important in stopping either a top down or bottom up wins so this is the one most needed followed by 8 and 6. This method will beat simple approaches like 10 troops on all or 20 troops on the top 5 but may not work against any players opting to take 5 and 6 decisively. SUBMIT |
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. |
1105 | 1105 | 0 | 0 | 6 | 11 | 18 | 27 | 38 | 0 | 0 | 0 | I did (C-1)^2 + 2 for 2< C < 8 |
160 | 160 | 5 | 8 | 8 | 10 | 13 | 16 | 37 | 1 | 1 | 1 | There's two main strategies: 7 8 9 10, and 1 2 3 4 5 6 7. Castle seven is, then, the most important castle. My strategy seeks to prey upon the first strategy, with a miser's troop in each expensive castle, to try to prey upon the second strategy. |
866 | 866 | 1 | 1 | 1 | 1 | 1 | 21 | 36 | 36 | 1 | 1 | 9 and 10 are too obvious, and people will deploy way too many to take them. 6, 7, 8 are more likely higher yield targets, 1-5 are worthless. I put one in them, just in case someone put 0. |
145 | 145 | 6 | 6 | 7 | 8 | 10 | 25 | 35 | 1 | 1 | 1 | The ancient chariot race story |
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. |
241 | 241 | 4 | 4 | 4 | 4 | 4 | 4 | 34 | 34 | 4 | 4 | No specific reason. |
341 | 341 | 2 | 17 | 5 | 8 | 13 | 21 | 34 | 0 | 0 | 0 | |
1028 | 1028 | 0 | 1 | 3 | 4 | 5 | 6 | 34 | 36 | 5 | 6 | I am hoping that by fortifying 7 and 8, I can ruin the strategies of people hoping to win a minimum number of high value castles (4 is the minimum number of castles you must win). By throwing slightly more than a minimum number of soldiers at 9 and 10 I hope to have dedicated enough so that people that wanted them wasted way more soldiers then they needed and people that just committed as an after thought would lose because they didn't commit enough. |
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. |
442 | 442 | 2 | 3 | 6 | 11 | 16 | 26 | 33 | 1 | 1 | 1 | -Worth leaving 1 point at every castle, in case opponent leaves 0 -People will waste troops on high point castles -Many people will use round numbers (10, 15, 20), so putting 1 extra point will mean a few free victories. -The goal isn't to beat the *best* players, but to beat the *most*, and this strat should be decent against a lot of comps |
1298 | 1298 | 0 | 0 | 0 | 0 | 0 | 33 | 33 | 34 | 0 | 0 | Spooky magic |
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. |
863 | 863 | 1 | 1 | 1 | 1 | 1 | 31 | 32 | 32 | 0 | 0 | I'm trying to take advantage on the bottom 5 of people leaving those as 0. I'm also trying to beat people who put high amounts in 9 and 10. 8 7 6 are worth more combined than 9 and 10 |
322 | 322 | 3 | 3 | 3 | 3 | 3 | 21 | 31 | 31 | 1 | 1 | I suspect many people will place great weights on Castles 9 and 10, so I prioritized the next few highest castles. Further, I anticipate many people only awarding one troop to the smaller castles, and some placing two troops to counter that strategy, so I reasoned that placing three troops at Castles 1-5 would let me win some portion of those castles. |
366 | 366 | 2 | 5 | 0 | 0 | 0 | 21 | 31 | 41 | 0 | 0 | give up the high points castles to win the middle castle points with a small attempt to win the bottom two |
509 | 509 | 2 | 2 | 2 | 11 | 0 | 21 | 31 | 31 | 0 | 0 | 28 points requires 4 or more castles, I wanted to avoid the competition for the top spots as much as possible so chose a wider distribution assuming that fewer opponents would go for the 1/2/3 point castles. This is probably strong against 4 castle solutions (competing strongly for 8 and 7, then challenging at a weaker level for 6 and 4 should hit a weak spot in most 4/5 castle solutions). Probably weakest against larger spreads, and a bit of a crap shoot against other 6/7 castle solutions, just depends where you load up. Fun one, thanks. |
893 | 893 | 1 | 1 | 1 | 1 | 1 | 1 | 31 | 31 | 31 | 1 | Always have at least 1 at each castle to claim points in case the enemy does not show up. Go strong for the 9-8-7 castles; people tend to fixate on the 10, so let them have it. The goal is 28 points. This is not all that different from the electoral college, only more arrows, battering rams and boiling oil. |
1003 | 1003 | 0 | 3 | 3 | 3 | 17 | 3 | 31 | 35 | 3 | 2 | Need to get to 28 points. Focus on 3 to get me to 20, then deploy a few everywhere else to pick up 8 points on poorly defended castles. |
1048 | 1048 | 0 | 1 | 1 | 2 | 10 | 11 | 31 | 41 | 1 | 2 | Other players are likely to target the highest point value castles most heavily. By targeting mid tier castles it is possible to get to 28 without having to compete for the highest value castles. 1-2 troops are sent to the remaining castles to pick up any that are uncontested. |
1104 | 1104 | 0 | 0 | 6 | 16 | 21 | 26 | 31 | 0 | 0 | 0 | (10+9+8) < (7+6+5+4+3+2+1), so the top three castles are negligible if I can win the bottom seven castles. Since winning the 6th castle once is the same as winning all three of the 1st, 2nd, and 3rd castles, it makes the most sense to load up troops in the middle four castles. Also assuming people naturally group numbers into multiples of five, I used a distribution of (multiples of 5)+1. |
94 | 94 | 10 | 8 | 8 | 13 | 8 | 20 | 30 | 1 | 1 | 1 | There are a maximum of 55 Points available, so 28 is a Winning score. My strategy is to win the first 7 castles to get 28 points, hoping my opponents over commit solders to the last 3 castles. I have also overcommitted to castle 1 as Castle 1,8,9,10 is a winning strategy same applies to castle 4 as 4,7,8,9 is a winning combination. |
112 | 112 | 8 | 8 | 9 | 9 | 13 | 20 | 30 | 1 | 1 | 1 | with a total of 55 points available, i conceded the higher level castles and focused on the smaller castles to win the majority(spoiler: like how the electoral college went lol) |
113 | 113 | 8 | 8 | 8 | 8 | 8 | 25 | 30 | 3 | 1 | 1 | I thought 7 was most important |
149 | 149 | 6 | 2 | 2 | 15 | 19 | 23 | 30 | 1 | 1 | 1 | Only need 23 to win. Everyone will go for 8-10, so I will go strong for 4,5,6,7 and #1 to get my 23. |
150 | 150 | 6 | 1 | 8 | 12 | 10 | 1 | 30 | 30 | 1 | 1 | attempt to win the minimum number of points concentrating on lower values that should be less competitive, leaving 1 troop to pick up any undefended castles |
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 |
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 |
192 | 192 | 5 | 5 | 5 | 5 | 5 | 5 | 30 | 30 | 5 | 5 | Fortune favors the brave! |
193 | 193 | 5 | 5 | 5 | 5 | 5 | 5 | 30 | 30 | 5 | 5 | Fortune favors the brave! |
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. |
295 | 295 | 3 | 5 | 6 | 10 | 20 | 23 | 30 | 1 | 1 | 1 | There are 55 pts in the game -- if I have 28, the game is done (and I the winner). Thus I hope to win castles 1äóñ7 ... that results in 28 pts. I abandon castles 8, 9, 10 äóñ the sum of three totaling 27 pts äóñ assuming most players will seek the big numbers first. I do send one (unfortunate) solo man in the case the castle is indeed empty. If so, free pts for me! It is my hope I win out across the bottom 7 castles. Little room for error, but such is the case for most wars. |
297 | 297 | 3 | 4 | 8 | 0 | 20 | 0 | 30 | 35 | 0 | 0 | to not deploy forces to the most valuable castles where there would likely be the most competition. Place strength on mid value and low value targets to reach goal of 26 |
310 | 310 | 3 | 3 | 5 | 5 | 7 | 7 | 30 | 30 | 5 | 5 | Conquer the low castles, spam a few higher ones. |
575 | 575 | 2 | 1 | 1 | 1 | 15 | 2 | 30 | 2 | 44 | 2 | Focus on three high value castles, and put in token force on others. I hope is that other players will also have low-commitment castles ( 0 or 1 ) that I can take will minimal commitment. No statistical backing for this, just hunch. |
604 | 604 | 1 | 7 | 1 | 1 | 15 | 15 | 30 | 30 | 0 | 0 | I tried to find a "path of least resistance" to 28 points, choosing to cluster my troops in the mid to upper value castles and leave the highest point castles alone since it would take the most troops (theoretically) to win those points. I also stuck 1 troop in the remaining lower castles to stock pile points in the event that the other player left those castles empty, which would allow me to lose on of the other castles and still win. |
706 | 706 | 1 | 2 | 2 | 2 | 11 | 15 | 30 | 2 | 2 | 33 | I figured that some people would focus on castles 7-10, because you can win with just them, and that others would focus on 1-7, because they also give enough points to win. The people who aim for 7-10 will be beaten by my strategy because they will most likely lose 7 and 10, or at least be tied. People who aim for 1-7 will almost certainly lose 7, and perhaps tie for 6. People who put 10 in every castle will lose 5, 6, 7, and 10, which makes me get 28. People who allocate their soldiers like 1-3-5-7-9-11-13-15-17-19 will also lose 5, 6, 7, and 10. |
708 | 708 | 1 | 2 | 2 | 2 | 2 | 29 | 30 | 30 | 1 | 1 | I think if I can secure 6, 7, 8 plus some of 1-5 I will beat out those who go all in on 8, 9, 10. |
764 | 764 | 1 | 1 | 2 | 2 | 2 | 2 | 30 | 30 | 30 | 0 | |
821 | 821 | 1 | 1 | 1 | 1 | 30 | 35 | 30 | 1 | 0 | 0 | Luck. |
860 | 860 | 1 | 1 | 1 | 1 | 3 | 30 | 30 | 30 | 0 | 3 | Gut feeling |
917 | 917 | 1 | 0 | 5 | 5 | 0 | 24 | 30 | 35 | 0 | 0 | Just get to 28. Leave 9 and 10 alone because they are too enticing. |
957 | 957 | 0 | 9 | 0 | 0 | 0 | 26 | 30 | 35 | 0 | 0 | We have to keep in mind, our goal is to beat other people, not randomness. My feeling is that most of the analytical riddler minds will modify proportional distribution, giving slight edges to certain castles to try to win them by slight margins, as this seems like the optimal plan. So let's turn that on it's head, and beat a lot of people who smoothly allocate their points. There are 55 total points, so 23 total points win. There are many ways to get this with only three castles, but let's keep in mind people will tend to try to do sneaky things to steal high number castles (particularly #9, as that seems "sneaky" to ignore 10 and steal 9). My first reaction was: just win 7,8,9. Put all your points in and win those. This gives 24 and a sure win. But again, 9 seems like a very highly contested castle. So I decided instead, 6,7,8,2. Surely 2 and 6 should be more guaranteed than 9! Now just how to distribute. Well, I should mirror how others will be distributing their points here. (obviously 25 troops to each could lose me 7,8 somewhat frequently). While it seems like I MUST win all four to win, many people will likely assign 0 to some castles, so tie points may come into effect. So even losing 6 can be repaired by a tie in 10 and 3. So I aim to get 23 total points, so let's assign proportionally: {0,2/23*100, 0,0,0,6/23*100, 7/23*100, 8/23*100, 0, 0} = {0,9,0,0,0,26,30,35,0,0}. I need to win every one of these four I've chosen (unless other people elect 0 on some castles... very possible?), but I think in the long run, I've overvalued weird castles that aren't likely to be beaten in general. |
1047 | 1047 | 0 | 1 | 1 | 7 | 1 | 25 | 30 | 35 | 0 | 0 | There are 55 points at stake, so we need 28 to win. While the optimal strategy likely involves some randomness, letäó»s go with a simple deterministic strategy (looking at the submission form itäó»s deterministic strategies only). A lot of people will target the high numbers, so weäó»ll pass on those -- hopefully most people will allocate a lot to 9 and 10 and we can make that up elsewhere. Since we have 100 soldiers to use to get 28 points we need a return of slightly over 1/4 points per soldier. Some people might use this as a benchmark, so for the larger numbers letäó»s overshoot this (because losing one of those battles dooms us). Rather than pass completely on some of the battles we donäó»t intend to win (namely 5) letäó»s throw out a single soldier for a chance at great point per soldier value. Pts Sldrs Ratio 8 35 4.375 7 30 4.286 6 25 4.167 5 1 0.2 4 7 1.75 3 1 0.333 2 1 0.5 We need to win those top three battles to put us at 21, leaving us with 7 more to get. Winning 4 puts us at 25, and we then need 3 total points between all of our 1 and 0 soldier battles. We want to be able to match up against some simple strategies, so letäó»s consider a few. 10, 9, 8, 1 with most soldiers at first three -- Seems like we should beat it since we have more than 1/3 of our soldiers at 8 10 soldiers to each castle -- We lose with 21 points, but I donäó»t expect this to be common Approximately 2x at each castle -- We probably lose, depending how the low ones fall Ignoring 8, 9, 10 -- Depends on allocation, but if we take 6 and 7 we win after splitting 9 and 10. If we lose 6 or 7 then it will be close, depending on 4 All even (or odd) numbers -- Depending on allocation this could go either way |
1051 | 1051 | 0 | 1 | 1 | 1 | 15 | 18 | 30 | 34 | 0 | 0 | There's a limited number of possible winning combinations, and with scarce troops any deployment needs to be concentrated in one or two places. Based on possible allocations, this deployment interferes with as many other deployment styles as possible. |
1064 | 1064 | 0 | 0 | 15 | 0 | 0 | 20 | 30 | 35 | 0 | 0 | There are 55 points to win, I need 28. I don't need to win every round, just the majority so if I deploy to win exactly 28 points in some of the less likeable castles, I should win more often then not. |
1079 | 1079 | 0 | 0 | 11 | 12 | 0 | 16 | 30 | 31 | 0 | 0 | Cede 9 and 10, concentrate power on 6,7,8 with remaining forces allocated to ensure a point victory is possible |
1092 | 1092 | 0 | 0 | 10 | 0 | 20 | 0 | 30 | 0 | 40 | 0 | Higher points are worth more, so have more troops. |
1156 | 1156 | 0 | 0 | 0 | 15 | 25 | 30 | 30 | 0 | 0 | 0 | Collect mid-range castle with high concentration of troops. |
1215 | 1215 | 0 | 0 | 0 | 10 | 0 | 0 | 30 | 30 | 30 | 0 | If I usually overwhelm the opponents on 4, 7, 8, and 9, I'll get 28 points, which is enough to win the war. |
1236 | 1236 | 0 | 0 | 0 | 2 | 2 | 2 | 30 | 30 | 32 | 2 | Get 9/7/8 and then hope the 2 on some other castle is enough |
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. |
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. |
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. |
244 | 244 | 4 | 1 | 1 | 16 | 21 | 25 | 29 | 1 | 1 | 1 | |
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. |
765 | 765 | 1 | 1 | 2 | 2 | 2 | 2 | 29 | 29 | 29 | 3 | Evolutionary algorithm. I made 15 sets, and then kept replacing the worst performing one with one that would beat the best one. |
1196 | 1196 | 0 | 0 | 0 | 11 | 0 | 0 | 29 | 29 | 31 | 0 | I looked at different ways to get 28 points and thought that committing to 3 big numbers hard and one small number that makes the total 28 could be a good strategy. I debated between 9,8,7,4 and 10,9,8,1 and in the end decided skipping out on the 10 fight is probably worthwhile. 11 on the 4 beats the 10 across the board plan and the 29 on 7 beats the even split across the lower 7 numbers plan. |
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? |
376 | 376 | 2 | 4 | 6 | 15 | 19 | 23 | 28 | 1 | 1 | 1 | Assuming most other ranked the castles by placing a ratio of soldiers to victory points, you would end up with 1=1.8, 2=3.6, 3 =5.5, 4=7.3, 5=9.1, 6=10.9, 7=12.7, 8=14.5, 9 =16.4, 10=18.1. Given that there are ways to attack this strategy, assume most people have developed something more strategic. My plan is to start with 1 soldier on each castle so that you claim any castle where someone else put zero. With the remaining 90 soliders, you want to capture at least 23 victory points assuming no ties, keeping in mind the above ratios. If you went after only castles 4-7 you could get 22 victory points by doubling the standard attack and having 10 soldiers left over plus your original 10. This now gives you 15 on 4, 19 on 5, 23 on 6, 27 on 7 and one the other six. Given the other 10 soldiers are likely wasted on the higher numbers, space them out on castles 1-3 proportionately to get you some time breakers, i.e. 13 total solider (initial 3 plus 10) across 6 VPs means 2=1, 4=2, 6=3 with one left over. He will attack 7 just to give the assist on our most important as losing 4-6 could be made up with our tie-breakers in the 1-3. |
605 | 605 | 1 | 7 | 1 | 1 | 11 | 11 | 28 | 38 | 1 | 1 | Basically give up on 9 and 10 and try to get 5, 6, 7, and 8...and then 2. If I win those all, the other guy can't win. I let a 1 for each of the others in case I oppose some zeroes. |
805 | 805 | 1 | 1 | 1 | 5 | 11 | 16 | 28 | 29 | 3 | 5 | Because my buddy Tony showed me his plan and this one beat it. |
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. |
950 | 950 | 0 | 10 | 0 | 0 | 25 | 25 | 28 | 12 | 0 | 0 | Just hoping I get lucky, if I'm being honest, Ollie. |
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). |
1107 | 1107 | 0 | 0 | 6 | 10 | 1 | 22 | 28 | 31 | 1 | 1 | Attempt to get 28, and only 28 points. |
1237 | 1237 | 0 | 0 | 0 | 2 | 0 | 0 | 28 | 34 | 34 | 2 | 28 out of 55 points are required to win (it's like 270 out of 538!). Since 8+9+10 = 27, no 3 castles will guarantee a win. So, rather that contest the 3 most valuable castles, I chose to try to assure winning castles 7, 8, and 9 for a total of 24 points. Then I need to win 4 more points. I chose to do this by making a play to win castle 4 or win or split castle 10. I chose 34 soldiers for castles 8 and 9 in case my opponent was dividing his soldiers nearly equally among 8, 9, and 10. I chose 28 soldiers for castle 7 in case my opponent was trying to win castles 1-7 for 28 points and divided his soldiers nearly equally among these castles. By the way, my first thought was to try to formulate a strategy that would ensure at least a tie, but computer experiments with a few castles suggested that this was not possible. |
53 | 53 | 11 | 11 | 11 | 12 | 12 | 13 | 27 | 1 | 1 | 1 | Half of available points is 27.5. If I win castles 1-7, that is 28. If someone distributed evenly I want more than 10 on the lower castles. If they try for the top 4 I want to have more than 25 on castle 7. If they try for a relative expected value strategy I want more than 12 on castle 6. If they try my strategy (bottom 7) I want to steal castles 8-10 with the minimum number of troops. |
194 | 194 | 5 | 5 | 5 | 5 | 5 | 5 | 27 | 30 | 6 | 7 | Updated. Fortune favors the brave! |
210 | 210 | 4 | 8 | 10 | 10 | 15 | 20 | 27 | 2 | 2 | 2 | Giving up 27 points to hopefully win the remaining 28. I stuck two troops in the big three in case anyone else had a similar idea. |
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. |
279 | 279 | 3 | 6 | 7 | 9 | 11 | 2 | 27 | 31 | 2 | 2 | I suspect that many strategies will have castles with either 0 or 1 armies and will focus their armies on castles worth about 28 points. Other strategies will distribute their armies more evenly. If one distributed the 100 armies evenly by the points of the castle, one would get the following: 2, 4, 5, 7, 9, 11, 13, 15, 16, 18. If one distributed the 100 armies according to castle points but focused on just castles worth 28 points, the armies would be some combination zero values and numbers like: 4, 7, 11, 15, 18, 22, 25, 29, 33, 36 (with slight variations due to rounding). In general, I will win over a given opponent if I tend to win castles by having only slightly more armies than my opponent, but lose castles by having much less than my opponent. Each of my 10 castles will have armies designed to slightly beat one of the following opposing strategies for that castle: an essentially undefended castle (castles 6, 9 & 10), an equally distributed castle (castles (1, 2, 3, 4 & 5), or a focused attack castle (castles 7 & 8). This gives the following values: 3, 6, 7, 9, 11, 2, 27, 31, 2, 2. |
296 | 296 | 3 | 4 | 11 | 13 | 16 | 21 | 27 | 2 | 2 | 1 | Scoring 1 to 7 |
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. |
753 | 753 | 1 | 1 | 2 | 4 | 14 | 21 | 27 | 27 | 2 | 1 | Assuming some will split evenly and others load up high, I am trying to make sure also possible castles that remain unguarded can be one, but focus on higher side below most highly picked choices and those of little value. |
775 | 775 | 1 | 1 | 1 | 15 | 18 | 1 | 27 | 1 | 34 | 1 | Put just over (castle VP number)/(28 points needed to win) at four locations totaling 25 VP with expectations of getting the remaining 3 VP from tying or winning another castle where the opponent has not placed troops |
792 | 792 | 1 | 1 | 1 | 11 | 1 | 1 | 27 | 28 | 28 | 1 | Picked a simple route to 28 and defended it without leaving any uncontested. |
918 | 918 | 1 | 0 | 4 | 10 | 20 | 26 | 27 | 10 | 1 | 1 | Assuming most people would enter their highest numbers in castles 9 and 10, I tried to win the lower groups to win the majority of the lower numbered castles |
941 | 941 | 0 | 11 | 0 | 0 | 16 | 17 | 27 | 29 | 0 | 0 | |
943 | 943 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
944 | 944 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
945 | 945 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
946 | 946 | 0 | 11 | 0 | 0 | 12 | 15 | 27 | 35 | 0 | 0 | I went for the minimum number needed to win (28). Guessing that most people might want to try to lock down 10,9,8, I bet more than 1/3 of my total men on 8, then enough on 7 to lock out other competitors, and then enough on 6, 5, and 2 to beat out people just playing the average. |
956 | 956 | 0 | 9 | 0 | 5 | 8 | 5 | 27 | 12 | 31 | 3 | I let a computer evolve the strategy. I started with 100 random deployments, then used a Monte Carlo algorithm to develop a deployment that would defeat as many of these as possible. I repeated this procedure until I had a new collection of 100 deployments, each one able to defeat (nearly) every deployment of the original 100. I then repeated the entire process 100 times (100 is a nice round number), each time creating a collection of 100 strategies that were all good at defeating the previous collection. I then selected from these 100 strategies the one that would win when these 100 went up against one another. |
975 | 975 | 0 | 6 | 0 | 0 | 15 | 21 | 27 | 31 | 0 | 0 | If I win the five castles I put troops at I win by one. |
985 | 985 | 0 | 5 | 0 | 0 | 16 | 21 | 27 | 31 | 0 | 0 | As 55 total points are available, 28 are needed for a victory. Castles 8, 7, 6, 5, and 2 combine for 28 points and will avoid the significant troop commitments likely required to capture castles 9 and 10. Gambling that Castle 2 will not be heavily contested does allow for additional troop allocation among castles 5-8. |
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. |
1102 | 1102 | 0 | 0 | 8 | 9 | 10 | 14 | 27 | 32 | 0 | 0 | Just need 28 to win. Tossed out 9 and 10 hopping to win the rest, need just 2 out of 3 from the 3:4:5 group. Tried to put more on 8 and 7 to protect against 10:9:8:1 and 10:9:7:2 strategies. |
1106 | 1106 | 0 | 0 | 6 | 11 | 0 | 22 | 27 | 32 | 0 | 2 | I need 28 points to beat any opponent. I figure most strategies out there will be of several forms: (1) get all the high point castles, so 10-9-8 plus something small; (2) skip the 10 and try to get something like 9-8-7-4 or 9-8-6-5; (3) get all the small castles, 7-6-5-4-3-2-1, and (4) some general "what-is-each-castle-worth?" strategy that has a declining point value for each castle. To triangulate against them, I went with a very specific 8-7-6-4-3 strategy to try to get to exactly 28. I also assume some human bias toward numbers ending in 0 or 5, so my numbers are 1 or 2 above those values. Finally, I put 2 points in castle 10 to cover against those putting 0 or 1 in there. Note that winning castle 10 would cover against losses three different ways: 8 or 7-3 or 6-4. I don't expect to win, but I'm hoping that I'll place pretty high with this strategy, with an outside shot at winning. |
1233 | 1233 | 0 | 0 | 0 | 2 | 19 | 23 | 27 | 29 | 0 | 0 | Get to 28! |
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). |
41 | 41 | 12 | 12 | 12 | 12 | 12 | 12 | 26 | 1 | 1 | 0 | Beat the 10x10 strategy or any that over values the last 3 castles. If you win 7 you have 28/55 pts. |
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. |
56 | 56 | 11 | 11 | 11 | 11 | 12 | 12 | 26 | 2 | 2 | 2 | To win each round, you only need to win 28 points. Winning any more than 28 points doesn't do you any good - a win is a win, whether by 1 point or 10 points. I identified what I believe will be popular strategies, and developed one that can beat them. I suspect the most popular strategies will be the Even All Strategy, the Top 4 Strategy, and the Bottom 7 Strategy. I also believe some players will employ versions of the Marginal Strategy, which I employ here. I am playing what I call the Marginal-Low Strategy. This troop deployment is susceptible to a variation of the Even Strategy that evenly distributes forces to a smaller number of castles, rather than 10 across the board. |
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. |
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. |
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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 );