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4-7-17 Riddler
{-# LANGUAGE GADTs #-}
data Slot = S1 | S2 | S3 | S4
deriving Eq
data Start
data Player
data Deck
data GameMove a where
Start :: [GameMove Deck] -> GameMove Start
DeckMove :: Int -> [GameMove Player] -> GameMove Deck
PlayerMove :: Slot -> [GameMove Deck] -> GameMove Player
End :: GameMove Deck
type Board = (Int,Int,Int,Int)
-- Enumerate the full game tree.
gameTree :: GameMove Start
gameTree = Start $ goDeck allSlots allDigits
where
allSlots = [S1,S2,S3,S4]
allDigits = [0..9]
goDeck slots remainingDigits =
map
(\digit ->
DeckMove digit $
goPlayer slots (filter (/= digit) remainingDigits))
remainingDigits
goPlayer [lastSlot] _ = [PlayerMove lastSlot [End]]
goPlayer remainingSlots digits =
map
(\slot ->
PlayerMove slot $
goDeck (filter (/= slot) remainingSlots) digits)
remainingSlots
-- Setter function for the game board.
setValue :: Slot -> Int -> Board -> Board
setValue S1 v (_,x,y,z) = (v,x,y,z)
setValue S2 v (w,_,y,z) = (w,v,y,z)
setValue S3 v (w,x,_,z) = (w,x,v,z)
setValue S4 v (w,x,y,_) = (w,x,y,v)
average :: [Double] -> Double
average xs = sum xs / fromIntegral (length xs)
-- Given a way to find the expected value of a player's chosen move
-- from a list of all possible alternatives, compute the expected
-- value of a move.
scoreMove :: ([Double] -> Double) -> Board -> GameMove a -> Double
scoreMove strategy board (Start nextMoves) =
average $ map (scoreMove strategy board) nextMoves
scoreMove strategy board (DeckMove card nextMoves) =
strategy . flip map nextMoves $
(\move@(PlayerMove slot _) ->
scoreMove strategy (setValue slot card board) move)
scoreMove strategy board (PlayerMove _ nextMoves) =
average $ map (scoreMove strategy board) nextMoves
scoreMove _ (w,x,y,z) End = fromIntegral $ (w*10+x)*(y*10+z)
blankBoard :: Board
blankBoard = (undefined,undefined,undefined,undefined)
randomEV = scoreMove average blankBoard gameTree
-- randomEV = 2339.3
optimalEV = scoreMove minimum blankBoard gameTree
-- optimalEV = 1056.8
skillAdvantage = randomEV / optimalEV
-- skillAdvantage = 2.2135
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