riddler-castles/castle-solutions

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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?
101 10 0 0 0 0 0 0 30 30 30 Tried to choose the fewest number of castles (and in the case of #1' the least likely to be attacked) to attack that would give me a majority of the points.
102 10 0 0 0 0 0 0 30 30 30 Deploying hopefully overwhelming force at castles 8 through 10, and a token force to capture 1. It doesn't allow any room for failure, but hopefully will be strong enough at the one point to ensure victory.
103 9 12 13 14 15 16 17 1 1 2 I attempt to concede castles 8-10 to win 1-7 in order to scrape by with a total win. I moved one extra soldier from 1 to 10 in case someone puts 1 in the last 3 castles, but otherwise uses the same strategy.
104 9 11 11 11 11 11 11 23 1 1 I tried a ton of different variants of a number of strategies, which I ran against each other using python code. I came to a point of realization that any strategy could be beaten by another strategy, but that it would probably be advantageous to choose a strategy which eschewed the top two values completely and beefed up where others would not think to invest but would add up assuming over-investment in the highest values. The particular distribution I chose, while simple, performed the best overall against top-heavy distributions.
105 9 11 9 11 9 11 9 11 9 11 I thought I'd have the most wins by splitting up my troops almost evenly.
106 9 10 10 10 10 10 10 10 10 11 Wanted to get the most possible free points from people who are just skipping out on castles, so I figure just send troops everywhere. You miss all the shots you don't take. Slightly altered the troop deployment for Castle 1 and Castle 10 so as to beat anyone else using this strategy.
107 9 9 9 11 9 12 9 11 10 11 The goal of a battle is to get to 28. For simplicity's sake, I ignored ties (likely a fatal omission). So I considered all 36 partitions of 28 into distinct parts less than 11. Each of these partitions represents a winning coalition of castles that will get me to 28. Then I counted how often each castle was in a winning coalition and used that to get a percentage of my troops to send to that castle. After truncating some percentages I had one trooper left over, so I put him in castle 6, which is the highest value part that appears the most. In hindsight this leads to a very uniform distribution of soldiers, which makes me question my methodology, but let's see how it does.
108 9 9 9 9 9 11 11 11 11 11 I just want to beat the person that deploys them evenly to every castle!
109 8 10 12 14 16 17 19 2 1 1 My plan is to try to pick up all of the lesser value castles that others have hopefully ignored. If I can get castles 1-7, then that is enough to win. I've reserved 1-2 extra troops for the remaining castles just in case the opponent's strategy involved abandoning one of those altogether.
110 8 10 11 11 12 13 14 6 7 8 Somewhat even distribution for people who include lots of low numbers and some slightly higher ones for the people who include near totally even distribution.
111 8 9 12 14 16 18 20 1 1 1 For the most part, I gave up on the top 3 value castles (total points 27), to focus on the bottom 7 value castles (total points 28), as I thought most people would commit a lot of resources to the top value castles, and I could win all of the lesser battles. However, I left 1 army at each of the top value castles to combat a similar strategy to mine, except where they left the top castles completely undefended.
112 8 9 10 12 15 18 25 1 1 1 I figured people would go for the larger numbers.
113 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.
114 8 8 10 10 10 10 11 11 11 11 Strategy A: Concentrate your forces as much as possible, taking more than half the victory points while holding the minimum number of forts required. (forts 10, 9, 8, x). Likely choose fort 1 for x since it's sufficient and unlikely to be hotly contested. Strategy B: Beat A by focusing on forts 8, 7 ,6, 5, y. Where y is not 9, 10, or x. Since "Strat A" will likely put 32 or fewer soldiers in each of forts 8, 9, and 10, Strat B puts 33 soldiers in fort 8. It then picks up 20+ victory points from forts 7, 6, 5, y. Likely to choose fort 2 for y since it's sufficient and probably not hotly contested. My chosen strategy (C: fully distributed) is likely to beat simple variants of A and B (as well as many other random or semi-random distributions). Since I expect those strategies to be most common, that's what I'm going with. Basically, this puzzle is much like the Riddler Express puzzle; both come down to the player's estimation of other player's strategies.
115 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)
116 8 8 8 8 8 25 30 3 1 1 I thought 7 was most important
117 8 2 11 12 17 2 21 21 2 2 55 points are available, common strategies to get 28 may involve attempting to getting a few high scoring or many low scoring castles. 8,7,5,4,3,1 gets 28, with 2 soldiers minimum to each castle in case of uncontested/1 soldier chosen by an opponent, and avoids relying on the highest castles or too many castles
118 8 2 4 11 8 14 13 9 14 17 https://goo.gl/qwoylN wrote this code to randomly generate 1000 'setups' then battled each setup against eachother and only returned the 'setup' with the most wins a general strategy is to try and accumulate 28 points total to guarantee yourself a win. This can be done with a minimum of 4 wins (on the 10,9,8 and 1 point castles).
119 8 0 1 1 2 5 11 24 10 38 evolutionary programming
120 7 13 14 15 16 17 18 0 0 0 Split relatively evenly between less contested castles
121 7 11 0 14 16 0 23 0 29 0 I want a winning coalition of 28.
122 7 10 12 14 16 18 20 1 1 1 I am "punting" the top three castles, hoping my opponents waste troops. Therefore, I can win the bottom seven castles to secure victory (28 pts).
123 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.
124 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.
125 7 8 10 12 15 20 25 1 1 1 I figured everyone would fight over the top three castles, so I'm making a risky gambit by ignoring them and hoping to sweep the bottom 7.
126 7 8 9 11 12 13 14 15 5 6 I know that everyone would likely (on average) assign increasing numbers based on the value of the castle. My goal is to be out of 'phase' with those values in order to be 'slightly' higher than the most castles that I can...
127 7 8 9 10 11 12 13 14 16 0 I decided to sacrifice points at the highest value castle (10 point castle) and provide myself with a higher probability of winning the remaining castles. I then deployed troops in descending order from castle nine down to castle one. Jon Snow had to sacrifice Castle Black (or at least it's tenant's ideals) to (hopefully) regain the North, so I was inspired to do the same!
128 7 7 15 15 15 16 16 3 3 3 It is the opposite of my other strategy
129 7 1 1 1 16 19 23 1 30 1 Focused on 5 castles (1,5,6,7,9) that would yield 28 victory points - just enough to win. No hard and fast rule on choosing castles - just what I thought would be an interesting way of achieving it - didn't want to be too overweight in high value or low value castles so chose a mix. Sent 1 troop to remaining castles (2,3,4,8,10) in case opponent had similar strategy / didn't send troops. Split remainder of troops roughly equivalent to weight of castle in terms of victory points (approximately 3 troops per VP).
130 7 0 14 15 10 17 16 18 2 1 STRATEGY! Banking on the little guys!
131 7 0 0 0 0 0 0 31 31 31 28 or bust.
132 7 0 0 0 0 0 0 31 31 31 There are 55 points total to be won between the 2 warlords if all castles are fought for, so whoever gets 28 or more wins in that case. In that case there are 14 ways to get at least 28 points, by winning one of the following specific groups of castles: {10,9,8,7}, {10,9,8,6}, {10,9,8,5}, {10,9,8,4}, {10,9,8,3}, {10,9,8,2}, {10,9,8,1}, {9,8,7,6}, {9,8,7,5}, {9,8,7,4}, {8,7,6,5,4}, {8,7,6,5,3}, {8,7,6,5,2}, {7,6,5,4,3,2,1}. I would like to try to win the fewest number of castles yielding at least 28 points and including a castle that fewer warlords would desire if possible so I can win it with a light deployment and concentrate in the others. From the above, it appears that a 4-castle group of {10,9,8,1} satisfies that, so those are my targets and I have concentrated the soldiers in the higher values castles as desired.
133 7 0 0 0 0 0 0 31 31 31 Well i was in the armed forces for about 27 years soooooo i think i know what I'm talking about pfffff
134 7 0 0 0 0 0 0 23 30 40 There are a total of 55 victory points available, so 28 are needed to win each war. Winning is not necessarily about getting the most victory points -- it's about getting to 28 victory points as often as possible. Thus I dumped almost of my troops in the 8,9, and 10 victory point castles, since winning those three is a total of 27 victory points. Unfortunately, I needed one more victory point, so I put 7 in the 1 victory point castle, hoping that it would be virtually ignored by most people. If one were to distribute troops to castles proportional to their victory points, only (1*(100/55))= 1.818 (which rounds to 2) would be sent there, so I hoped 7 would be enough to take care of that.
135 6 12 9 15 15 0 0 21 21 1 Picked favorite numbers.
136 6 8 11 14 16 18 21 2 2 2 Concentrate on the smaller ones.
137 6 8 11 11 16 21 21 2 2 2 Focus on the mid-valued castles
138 6 8 10 14 18 20 24 0 0 0 win all 7 and lower, sum = 28, higher than 8+9+10.
139 6 8 10 12 14 24 26 0 0 0 Guess from the bottom assuming most will picking from the top
140 6 8 9 16 18 21 22 0 0 0  
141 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.
142 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.
143 6 7 8 9 10 13 14 15 18 0 Concede the big prize, deploy those available soldiers to hopefully win the rest!
144 6 7 8 9 10 11 12 13 14 10 Worth plus 5 except for the 10 point castle
145 6 7 8 9 10 10 11 12 13 14 Jdnd
146 6 6 10 12 14 15 16 17 2 2 Focus on a large group of middle value targets.
147 6 6 8 15 20 15 10 8 6 6 Concentrate in the middle
148 6 6 7 11 16 21 26 3 3 1 Since the high value castles I'm intending to fight somewhere else. By ignoring the place where (I hope) most players are spending their resources, I hope I have the forces to win across the board on 1 through 7. Overspending slightly on the low numbers to counter strategies which try to spend high on one or two low numbers to pick up an edge. Oh, and playing 6's and 1's to come in just over anyone sending forces in round numbers.
149 6 6 7 8 10 25 35 1 1 1 The ancient chariot race story
150 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.
151 6 6 6 11 20 21 21 3 3 3 Let people fight for the big ones.
152 6 6 6 6 6 7 15 16 16 16 This deployment is what I think has the highest number of troops that need to be correctly to defeat it, with 56 out of the 100. Additionally, although two other deployments also have that minimum (one troop from 8->5, and from 6->7), this has the fewest possible ways of reaching that number, with two (as opposed to four for the 8->5 and six for 6->7). This is the maximin for the problem, so that's why I'm choosing this for my deployment. The minimum deployment to beat this is 6 to either castle 4 or 5, 16 to castle 7, and 17 to castles 9 and 10, which gets 2+7+9+10=28 or 2.5+7+9+10=28.5
153 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.
154 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
155 6 1 1 1 1 1 1 21 21 46 Because the optimal strategy should be to win with the fewest castles
156 6 0 0 0 0 0 0 26 27 41  
157 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.
158 5 12 17 13 13 11 13 5 4 7 monte carlo simulation of 100,000 placements.
159 5 10 20 10 5 5 20 10 5 10 Expecting to crush people who put 0 a lot or overdo #10
160 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
161 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.
162 5 9 12 14 16 19 22 1 1 1 I need to win 28 points- there is no prize for winning all the points. So- rather than go after Castle 9/10 which will be heavily contested, I'll aim for capturing 1 through 7 to earn 28 points. I shouldn't completely neglect the higher castles- if they're undefended I might as well capture them (because they must've stationed their troops elsewhere!)
163 5 8 12 15 18 22 5 5 5 5 This beats the vast majority of strategies that do the following: focus attention on a subset of castles totaling >=28 points, assigning soldiers proportional to points for castles in the subset, and zero elsewhere.
164 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.
165 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.
166 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.
167 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
168 5 7 9 12 13 14 18 20 1 1 Ideally, I want to beat my opponent by as little as possible in as many castles as possible. The obvious plan is to assign many troops to high-value castles, and fewer and fewer for each castle down the road. I plan to surrender the 10 and 9 pointer, only assigning 1 troop to each on the chance that someone assigns zero. From there, I have a decreasing amount of troops from castle 8 to castle 1. Hopefully I will massively lose the battle for 9 and 10, but win the war for the remaining castles.
169 5 7 9 11 15 21 25 2 2 3 Winning the lower 7 gives you more than half the points, so the top 3 values are largely ignored save for a scouting force of 2-3 to prevent a lone scout of the opponent from stealing. Then starting at 7 we deploy in force and curve down from there.
170 5 7 9 11 12 15 17 19 1 4 Just tried to defeat what I thought might be a few popular strategies.
171 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
172 5 7 5 7 12 11 15 13 13 12 I wrote an R script to generate random arrangements of troops, and then I compared them against each other. My program ran very slowly, and this was the best arrangement of troops it came up with.
173 5 6 10 10 10 10 15 30 2 2 Focus on getting more low-value castles without totally ceding 9 & 10
174 5 6 7 8 12 13 14 15 20 0 I sacrificed Castle 10, predicting that my opponent would heavily fortify it. Then I was able to increase the troops at all the other castles.
175 5 6 7 8 10 14 15 15 15 0 meh
176 5 6 7 8 9 11 12 13 14 15 This should perform well on average but is far from optimal.
177 5 6 7 8 9 11 12 13 14 15 It seemed to me that the optimal strategy would be to take advantage of each weakness in my opponent's line, so something like 10 at each castle makes some sense, but I also wanted to weight the more valuable castles more heavily, so I started with a base of 5, and distributed the remaining 50 across the rest, weighted by castle value.
178 5 6 7 8 9 11 12 13 14 15 It's a bit of a weighted average. I first deployed 1-10 soldiers based on point values, one to Castle 1, two to Castle 2, et cetera. That left 45 soldiers. I then distributed the rest evenly, sending 4 more soldiers to each castle, and then sending the last 5 to the top 5 castles. I figure some adversaries will be more top-heavy, and this way I might win some of the middle and lower castles and make it a close contest. This distribution would also beat those who went for a pure average 10-man-per-castle deployment.
179 5 6 7 8 9 11 12 13 14 15 this will defeat those who use an even distribution and those who give slight preference to higher value castles.
180 5 6 7 8 9 11 12 13 14 15 By giving more clout to the larger castles, while still packing a punch with the castles of fewer points, this set up guarantees at least something to walk away with.
181 5 6 6 15 15 25 25 1 1 1 thinking im gonna do something like this: 1 on 10 1 on 9 1 on 8... and distrubte 97 more from 7-1...if you can win 7-1 (28 total) over 10-8 (27) total, you are in good shape. so ignoring top 3 and focusing on lower 7-1 is a better strat. if others feel the same as me, it will feel be sweet to perhaps steal one of the "top 3" with only one soldier each.
182 5 6 4 5 24 20 20 10 3 3 cuz I'm a legend boi go to the outsider website
183 5 5 15 15 15 15 15 15 0 0 I don't have to beat everyone, just a lot of people. I figure most people will put a lot of emphasis on castles 9 and 10, so I'm just ignoring those two, in hopes of winning all of 1-7 or 8 and most of 1-7. I was originally gonna distribute evenly between castles, but thought that might be common so I decided to put slightly more than an even distribution in most castles, and leave fewer in 1 and 2, which I could lose if I win 8.
184 5 5 11 17 4 7 25 10 11 5 Random
185 5 5 10 20 20 20 20 0 0 0  
186 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.
187 5 5 10 10 15 15 20 20 0 0 I figured a lot of people would load up on 9-10 so I focused on lower value, but easier to win (I hope) castles
188 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.
189 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
190 5 5 5 5 15 15 15 25 5 5 Al achunte
191 5 5 5 5 11 12 13 14 15 15 lose the first five but get the rest
192 5 5 5 5 10 20 2 2 30 16 I seeded the competition with some sensible strategies, then added other strategies that tended to do well against those, then added others and so on.
193 5 5 5 5 10 10 15 25 19 1 if I can win 1-7, I win. Figured many people will try to spend a lot of resources on 8,9 and 10.
194 5 5 5 5 10 10 10 15 15 20 Intuitive
195 5 5 5 5 5 18 25 1 30 1 To get the 28 points needed to win, you need to win at least 4 castles. I figured many people would devise a strategy to focus on winning 4 or 5 mid-to-high valued castles (meaning they'd split their troops into 4-5 main groups of roughly 20-25 troops) with maybe a few left for smaller valued castles. I, instead, decided to focus on 3 main targets (9, 7, and 6) and try to make up the difference by winning several of the lower-valued castles by sending 5 troops each to castles 1-5 (assuming most people will be willing to sacrifice several of them).
196 5 5 5 5 5 8 15 30 15 7 not very good at game theory, but I wanted something where I could leave enough to clean up on some low value targets if people ended up being too concentrated, focus on some powerful hitters, and not waste too much on folks who wanted to hold hard to the top castle, but catch anyone who does a complete pump fake on ten. Let's see if it works!
197 5 5 5 5 5 5 30 30 5 5 Fortune favors the brave!
198 5 5 5 5 5 5 30 30 5 5 Fortune favors the brave!
199 5 5 5 5 5 5 27 30 6 7 Updated. Fortune favors the brave!
200 5 5 5 5 5 5 5 5 5 55 Played 20 test rounds with some friends and this one won the most frequently. Strong chance of winning 10 and at least 18 leftover points (17.5 for the tie). Prevents the 1 and 2 strategy on not desirable numbers.

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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
);
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