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| -rw-r--r-- | goat.R | 72 |
1 files changed, 72 insertions, 0 deletions
@@ -0,0 +1,72 @@ +# goat.R +# a numerical approach to the monty hall paradox +# http://en.wikipedia.org/wiki/Monty_hall_problem +# SJP 25 Oct 2007 +# +# consts +NUMDOORS <- 3 # +GOAT <- 0 +PRIZE <- 1 +ITERATIONS <- 100 +# FUNCTIONS +############################################################### +# select a door +getDoor <- function(d=NUMDOORS){ + z <- rep(1, d) # vector of 1s + z <- cumsum(z) / sum(z) # vector of props a..1 + my_door <- which.min(z < runif(1)) # which door is chosen + return(my_door) +} +############################################################### +# put the prize behind a door +allocPrize <- function(d=NUMDOORS){ + door <- rep(GOAT, d) # vector of goat doors (0) + door[getDoor()] <- PRIZE # put the prize behind a door + return(door) +} + +############################################################### +# game() function +# call game(T) to switch, game(F) to not swap +# put a prize behind a door +game <- function(swap_decision, iter=ITERATIONS){ + wins <- 0 # counter for winning trials + for(i in 1:iter){ + doors <- allocPrize() + # the contestant chooses a door + guess_door <- getDoor() # could be the same as the prize door + + # Monty Hall opens a goat door + while(T){ + host_door <- getDoor() # Monty chooses a door + if(host_door == guess_door) next # Monty not very smart + if(doors[host_door] == PRIZE) next # oops not that one either + break + } + # extra bit: add in 'toss a coin' + swap <- ifelse((class(swap_decision)=='logical'), swap_decision, pr()) + # test the original guess + #! 1: I guessed right AND I swap: win <- 0 + #! 2: I guessed right AND I DON'T swap: win <- 1 + #! 3: I guessed wrong AND i swap: win <- 1 + #! 4: I guessed wrong AND I DON'T swap: win <- 0 + win <- (xor(doors[guess_door]==PRIZE, swap)) + wins <- wins + win + } + return(sprintf('Iterations: %i Swap: %5s Wins: %3.1f%%', iter, swap_decision, wins/iter*100)) +} + +cat('\n========== SWAP or not, to win a car =============\n') +print(game(swap=T)) +print(game(swap=F)) +print(game(swap='TOSS')) +cat('===================================================\n\n\n') + + +# ###################################### +junkYard() # stop() silently +# test functions +# have we got a fair distribution of prizes? +x <- t(replicate(1000, allocPrize())) +colsum <- apply(x, 2, sum) +barplot(colsum) |