DieProb.hs

--
-- calculate sequence of die rolls needed to hit some probability target;
-- most useful in conjunction with take, e.g. 
--
-- take 25 (dieProb 12 1%7)
--
-- originally written by me @ http://guyblade.livejournal.com/159423.html, and archived here
--
module DieProb where

import Ratio

dieProb sides target         = map numerator $ dp sides target 1 1
dp sides target power count  =
  let weight = 1 % (sides ^ power) in
    if target == 0 then
      []
    else
      if (target <= (count * weight)) && (target > ((count - 1) * weight)) then
        let newWeight = (count * weight) - target
            newPower = power + 1
        in count:(dp sides newWeight newPower 1)
      else
        dp sides target power (count + 1)

isFailure seq sides target = any (uncurry (>)) $ zip seq (dieProb sides target)
isSuccess = ((.).(.).(.)) not isFailure