Question

The following code should evaluate every possible game in tic tac toe and return the results as a list

data Piece = Naught | Cross deriving (Show, Eq)
data Result = Win | Lose | Draw deriving (Show, Eq)
type Board = Array Integer (Maybe Piece)

emptyBoard :: Board
evaluateBoard :: Board -> (Maybe Result)
allPossibleMoves :: Board -> [Board]

walkPaths :: Bool -> Board -> [Result]
walkPaths inv b = 
    if result /= Nothing
        then [fromJust result]
        else concat $ map (walkPaths (not inv)) (allPossibleMoves $ invertBoard b)
    where 
        result = if inv then invertResult evald else evald
        evald = evaluateBoard b 

allGamesResults = walkPaths False emptyBoard

This is giving me (wins/loss for first to move):

• Total: 255168
• Wins: 77904
• Lose: 131184
• Draw: 46080

Providing these results are correct (I can’t find any data to verify mine with), why doesn’t the first to move have more wins?

UPDATE:
Source code can be found here

Answer 1

Thanks to scree from #haskell on freenode for the answer:

if result /= Nothing
    then [fromJust result]
    else concat $ map (walkPaths (not inv)) (map invertBoard $ allPossibleMoves b)