riddler-castles/castle-solutions-2: 78
Data license: CC Attribution 4.0 License · Data source: fivethirtyeight/data on GitHub · About: simonw/fivethirtyeight-datasette
| 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? |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 78 | 1 | 6 | 9 | 16 | 5 | 15 | 9 | 12 | 15 | 12 | I chose it based on an intuition that a certain number of people would pick the winning strategy from last time, a certain number of people would pick a strategy which beats that one, a certain number would pick a strategy which beats THAT one, and so on and so forth. Like with a Keynesian beauty contest game, you want to be exactly one step ahead of most other people; no more, no less. And, in my experience, people usually go around 2-3 levels deep on these things. So, I generated a data set which took the original strategy and added a lot of the winning strategy, and one which beats the winning strategy, and one which beats that, etc. Then, I calculated the expected number of net points you can get, based on this dataset, for each number of people in each castle. After that, it's a simple evolving function to find a strategy where taking away from any one castle would cause more harm than the good of adding someone to another castle. The remainder of my answer is a copy of the R code which I made to find this answer: library(foreign) setwd("~/Voting data") previousanswers <- read.csv("castle-solutions.csv") previousanswers <- previousanswers[,-11] #I'm not using the text comments, and they just make things harder to read. #Need 28+ points to win. previouswinner <- c(3,5,8,10,13,1,26,30,2,2) #I'm going to make a "predicted" dataset, baesd on the previous answers, the previous winner, and winning strategies against the previous winner and so on #The idea is that some people will copy the winner, some people will anticipate that and make a strategy which beats the winner #some people will anticipate that and make a strategy which beats the winner beater, etc., etc. #I'm going 4 layers deep on winner beating. I'm guessing a peek around 2-3. #Winning strategies should be able to soundly beat the strategy they are set against, while retaining #2+ in each castle. #There is some subjectivity going into these winnerb1 <- c(4,6,9,11,14,5,5,31,6,9) #This will beat the previous winner in castles 1,2,3,4,5,6,7,9,10, giving 47 points winnerb2 <- c(6,8,11,13,16,10,8,7,10,11) #This will beat b1 in all but castle 8 and beat the previous winner in all but 7 and 8. winnerb3 <- c(2,2,13,15,4,12,12,9,12,15) winnerb4 <- c(2,2,3,17,6,14,14,11,14,17) #Now to combine them together into one big data matrix previouswinnermatrix <- t(matrix(rep(previouswinner),10,nrow(previousanswers) * 0.20)) winnerb1matrix <- t(matrix(rep(winnerb1),10,nrow(previousanswers) * 0.15)) winnerb2matrix <- t(matrix(rep(winnerb2),10,nrow(previousanswers) * 0.22)) winnerb3matrix <- t(matrix(rep(winnerb3),10,nrow(previousanswers) * 0.20)) winnerb4matrix <- t(matrix(rep(winnerb4),10,nrow(previousanswers) * 0.10)) colnames(previouswinnermatrix) <- colnames(previousanswers) colnames(winnerb1matrix) <- colnames(previousanswers) colnames(winnerb2matrix) <- colnames(previousanswers) colnames(winnerb3matrix) <- colnames(previousanswers) colnames(winnerb4matrix) <- colnames(previousanswers) datamatrix <- rbind(previousanswers, previouswinnermatrix, winnerb1matrix, winnerb2matrix, winnerb3matrix, winnerb4matrix) #Now that I have my data, it's time to figure out what the expected number of points I can expect #from each castle, for each number of soldiars at that castle. expectedmatrix <- matrix(0,100,10) colnames(expectedmatrix) <- colnames(datamatrix) #Only 100 rows. I'm precluding strategies that include 0 people at any castle. #Now, to go by for each castle... for (i in 1:ncol(expectedmatrix)) { #...and go through each number of soldiers in that castle... for (j in 1:nrow(expectedmatrix)) { #And replace that value with the expected number of net wins with that number of people #+1 if win, 0 if tie, -1 if lose. expectedmatrix[j,i] <- (length(datamatrix[(datamatrix[,i] < j),i]) - length(datamatrix[(datamatrix[,i] > j),i])) / length(datamatrix[,i]) } #Multiple each column by the value of that castle, to get expected # of points expectedmatrix[,i] <- expectedmatrix[,i] * i } #Now, to make a looped function to continue taking away from the castle with the lowest expected loss #And giving to the castle with the highest expected gain #Until lowest loss > greatest gain strategy <- c(10,10,10,10,10,10,10,10,10,10) losses <- strategy gains <- strategy keepgoing <- TRUE while (keepgoing) { for (i in 1:10) { #calculte losses if (strategy[i] == 1) { losses[i] <- 10 } else { losses[i] <- expectedmatrix[strategy[i],i] - expectedmatrix[strategy[i]-1,i] } #calculate gains if (strategy[i] == 100) { gains[i] <- 0 } else { gains[i] <- expectedmatrix[strategy[i]+1,i] - expectedmatrix[strategy[i],i] } } #If the biggest gain and smallest loss are the same castle, break if (which.max(gains) == which.min(losses)) { keepgoing <- FALSE } else { #If the biggest gain is less than the smallest loss, break if (max(gains) < min(losses)) { keepgoing <- FALSE } else { #Otherwise, evolve the strategy. strategy[which.max(gains)] <- strategy[which.max(gains)] + 1 strategy[which.min(losses)] <- strategy[which.min(losses)] - 1 } } } #Cool, that was quick. #How many expected points can we get? expectednetpoints <- 0 for (i in 1:10) { expectednetpoints <- expectednetpoints + expectedmatrix[strategy[i],i] } #Based on the datamatrix I generated (which is dubious), this strategy will get 8.18 points more than a given opponent, on average. |