cardChances.hs

import Text.Printf


test :: IO ()
test = do
  return ()

hyper possibleWins actualWins actualDraws  = (winPerms * lossPerms) / totalPerms
 where
   winPerms = binomial possibleWins actualWins
   lossPerms = binomial possibleLosses actualLosses
   totalPerms = binomial possibleDraws actualDraws
   possibleDraws = 30
   possibleLosses = possibleDraws - possibleWins
   actualLosses = actualDraws - actualWins
binomial :: Integer -> Integer -> Double
binomial n k = fromIntegral (fact n) / fromIntegral (fact k * fact (n - k))
fact = product . enumFromTo 1
atLeast1 :: Integer -> Integer -> Double
atLeast1 poss draws = sum [hyper poss i draws | i <- [1..poss]]
drawDarkest d = atLeast1 4 d * atLeast1 2 d
drawPlotTwist d = atLeast1 2 d * atLeast1 2 d
drawDorian d = atLeast1 2 d * atLeast1 1 d
anyOf a b = a * (1-b) + b * (1-a) + a * b
main :: IO ()
main = do
    putStrLn "      | Darkest Hour:| PlotTwist:   | Either:      | Dorian: "
    forM_ [3..24] $ \i -> do
        let 
          d = (drawDarkest i) 
          p = (drawPlotTwist i)
        printf "%5i | %.10f | %.10f | %.10f | %.10f\n" i d p (anyOf d p) (drawDorian i)