# patperry/hs-monte-carlo

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 module Main where import Control.Monad import Control.Monad.MC import Data.List import Data.Map( Map ) import qualified Data.Map as Map import Text.Printf -- | Data types for representing cards. An Ace has 'number' equal to @1@. -- Jack, Queen, and King have numbers @11@, @12@, and @13@, respectively. data Suit = Club | Diamond | Heart | Spade deriving (Eq, Show) data Card = Card { number :: Int , suit :: Suit } deriving (Eq, Show) -- | The number values of the aces and face cards. ace, jack, queen, king :: Int ace = 1 jack = 11 queen = 12 king = 13 -- | Get a list of cards that make up a 52-card deck. deck :: [Card] deck = [ Card i s | i <- [ ace..king ] , s <- [ Club, Diamond, Heart, Spade ] ] -- | A type for the various poker hands. data Hand = HighCard | Pair | TwoPair | ThreeOfAKind | Straight | Flush | FullHouse | FourOfAKind | StraightFlush deriving (Eq, Show, Ord) -- | Determine the hand corresponding to a list of five cards. hand :: [Card] -> Hand hand cs = case matches of [1,1,1,1,1] -> case undefined of _ | isStraight && isFlush -> StraightFlush _ | isFlush -> Flush _ | isStraight -> Straight _ | otherwise -> HighCard [1,1,1,2] -> Pair [1,2,2] -> TwoPair [1,1,3] -> ThreeOfAKind [2,3] -> FullHouse [1,4] -> FourOfAKind where (x:xs) = (sort . map number) cs (s:ss) = map suit cs isStraight | x == ace && xs == [ 10..king ] = True | otherwise = xs == [ x+1..x+4 ] isFlush = all (== s) ss matches = (sort . map length . group) (x:xs) -- | Deal a five-card hand by choosing a random subset of the deck. deal :: (MonadMC m) => m [Card] deal = sampleSubset deck 5 -- | A type for storing the frequencies of the various hands. type HandCounts = Map Hand Int -- | An empty frequency count. emptyCounts :: HandCounts emptyCounts = Map.empty -- | Update the count of the hand corresponding to a list of five cards. updateCounts :: HandCounts -> [Card] -> HandCounts updateCounts counts cs = Map.insertWith' (+) (hand cs) 1 counts main = let seed = 0 reps = 100000 counts = foldl' updateCounts emptyCounts \$ replicateMC reps deal `evalMC` mt19937 seed in do printf "\n" printf " Hand Count Probability 99%% Interval \n" printf "-------------------------------------------------------\n" forM_ ((reverse . Map.toAscList) counts) \$ \(h,c) -> let n = fromIntegral reps :: Double p = fromIntegral c / n se = sqrt (p * (1 - p) / n) delta = 2.575829 * se (l,u) = (p-delta, p+delta) in printf "%-13s %7d %.6f (%.6f,%.6f)\n" (show h) c p l u printf "\n"
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