prob_xkcd.hs

import Control.Monad.Random
import Control.Monad.Writer

type Sim = Rand StdGen

-- returns the series of rolls, with the final 6 omitted (implied)
simGame :: Sim [Int]
simGame = do
    roll <- getRandomR (1,6)
    if roll == 6
        then return []
        else fmap (roll:) simGame

-- bob wins if there were an odd number of rolls before a 6
bobWins :: [Int] -> Bool
bobWins = odd . length

bobWinsSecondTurn :: [Int] -> Bool
bobWinsSecondTurn rolls = length rolls == 3

-- returns a list of ever-refining probabilities
simulate :: Sim [Double]
simulate = execWriterT (go 0 0)
    where
    go tries successes = do
        tell [successes/tries]
        game <- lift simGame
        go (inc (bobWins game) tries) (inc (bobWinsSecondTurn game) successes)

    -- converts a bool into an incrementor function 
    -- (if true, adds one, else leaves alone)
    inc True = (+1)
    inc False = id

main = mapM_ print =<< fmap (evalRand simulate) newStdGen