Sicherman Dice

Main.hs

{-# LANGUAGE QuasiQuotes #-}

import Data.Foldable
import Data.List
import PyF

f = ([1, 2, 2, 3, 3, 4] !!) . pred

g = ([1, 3, 4, 5, 6, 8] !!) . pred

x (i, j) = i + j
y (i, j) = f i + g j

combs fun tot = [(i, j) | i <- [1 .. 6], j <- [1 .. 6], fun (i, j) == tot]

-- >>> combs x 5
-- [(1,4),(2,3),(3,2),(4,1)]

-- >>> combs y 5
-- [(1,3),(2,2),(3,2),(6,1)]

main = do
  for_ [2 .. 12] $ \tot -> do
    let xCombs = combs x tot
        yCombs = combs y tot
        lengthX = length xCombs
        lengthY = length yCombs
        disp = intercalate ", " . map (show @(Int, Int))
    putStrLn [fmt|\\P(X = {tot}) &= \\P(\\set{{{disp xCombs}}}) &= {lengthX}/36 \\\\\\P(Y = {tot}) &= \\P(\\set{{{disp yCombs}}}) &= {lengthY}/36 \\\\|]

  -- Check that the distributions actually are the same
  print $ all (\tot -> length (combs x tot) == length (combs y tot)) [2 .. 12]