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The Monty Hall Problem @mathiasverraes

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Don't use thinking when you can use programming — Alan Turing1 1 Supposedly

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data Door = Goat | Car deriving (Eq, Show) type Game = [Door]

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newGame :: MonadRandom m => m Game newGame = shuffleM [Car, Goat, Goat] newGames :: MonadRandom m => m [Game] newGames = replicateM 100 newGame

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(|>) = flip ($) play :: Strategy -> Game -> Door play strategy game = game |> pickDoor |> revealGoat |> strategy

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pickDoor :: Game -> Game pickDoor = id -- Assume we always pick -- the first door, it -- doesn't matter anyway.

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revealGoat :: Game -> Game revealGoat [choice, Goat, x] = [choice, x] revealGoat [choice, x, Goat] = [choice, x]

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type Strategy = Game -> Door stay :: Strategy stay [firstChoice, alternative] = firstChoice switch :: Strategy switch [firstChoice, alternative] = alternative

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do game <- newGame return $ play stay game) -- Goat do game <- newGame return $ play switch game -- Car

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playAll :: Strategy -> [Game] -> Int playAll strategy games = map (play strategy) games |> filter (==Car) |> length

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do gs <- newGames return $ playAll stay gs -- 32 do gs <- newGames return $ playAll switch gs -- 68

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module MontyHall where newGame :: MonadRandom m => m Game newGame = shuffleM [Car, Goat, Goat] import System.Random.Shuffle newGames :: MonadRandom m => m [Game] import Control.Monad.Random.Class newGames = replicateM 100 newGame import Control.Monad pickDoor :: Game -> Game (|>) = flip ($) pickDoor = id data Door = Goat | Car deriving (Eq, Show) revealGoat :: Game -> Game type Game = [Door] revealGoat [choice, Goat, x] = [choice, x] type Strategy = Game -> Door revealGoat [choice, x, Goat] = [choice, x] play :: Strategy -> Game -> Door stay, switch :: Strategy play strategy game = stay [firstChoice, alternative] = firstChoice game switch [firstChoice, alternative] = alternative |> pickDoor |> revealGoat main :: IO() |> strategy main = do (stayCnt, switchCnt) <- do playAll :: Strategy -> [Game] -> Int gs <- newGames playAll strategy games = return (playAll stay gs, playAll switch gs) map (play strategy) games print ("Stay: " ++ show stayCnt) |> filter (==Car) print ("Switch: " ++ show switchCnt) |> length

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Full source code: https://gist.github.com/mathiasverraes/ 3a31c912c6efb496566d55ee077dad6f Diagram: Curiouser http://www.curiouser.co.uk/monty/montyhall2.htm Images: AsapScience http://youtube.com/watch?v=9vRUxbzJZ9Y Inspiration: F# Monty Hall problem by Yan Cui http://theburningmonk.com/2015/09/f-monty-hall-problem/

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Thanks :-) @mathiasverraes