hpastetwo

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module LetsMakeADeal where

{- Fairly naive attack on
   http://programmingpraxis.com/2009/07/24/lets-make-a-deal/

> ghci LetsMakeADeal.hs
*LetsMakeADeal> rounds 100000
0.66252

-}

import Control.Monad
import Data.List
import System.Random

-- Pick a random element from a list.  Maybe there's a nicer way?
chooseFrom :: [a] -> IO a
chooseFrom xs = do which <- getStdRandom $ randomR (0, length xs-1)
                   return $ xs !! which

-- Play one round of the game.  Returns True if player should switch.
play :: IO Bool
play = do car <- chooseFrom doors -- Place the car.
          guess <- chooseFrom doors -- Player makes a first guess.
          -- Show them a goat.  It can't be behind the door hiding the
          -- car, and it can't be the door they picked.
          shown <- chooseFrom $ delete guess $ delete car doors
          -- Player should switch if the other (non-guessed,
          -- non-shown) door is the right one.
          return $ car == head (delete guess $ delete shown doors)
    where doors = [0,1,2]

-- Play n rounds of the game and work out how many times switching was
-- the right thing to do.
rounds :: Int -> IO Double
rounds n = do outcomes <- replicateM n play
              let shouldHave = filter id outcomes
              return (fromIntegral (length shouldHave) / fromIntegral n)

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