The Monty Hall Problem with Haskell

5min lightning talk for the SoCraTes Belgium meetup.

Transcript

1. The Monty Hall Problem
   @mathiasverraes
   

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

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

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

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

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

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

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

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14. do
    game return $ play stay game)
    -- Goat
    do
    game return $ play switch game
    -- Car
    

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

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16. do
    gs return $ playAll stay gs
    -- 32
    do
    gs return $ playAll switch gs
    -- 68
    

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18. 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) playAll :: Strategy -> [Game] -> Int gs 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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19. 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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20. Thanks :-)
    @mathiasverraes
    

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