tuesday puzzle 4

from fractions import Fraction

def max_chance(blacks, reds):
  stand = Fraction(blacks, blacks + reds)
  if not blacks or not reds: return stand
  draw = (stand * max_chance(blacks - 1, reds) +
          (Fraction(1,1) - stand) * max_chance(blacks, reds - 1))
  print '%d\t%d\t%s\t%s\t' % (blacks, reds, stand, draw),
  if draw == stand: print 'TIE'
  if draw > stand: print 'DRAW'
  if draw < stand: print 'STAND'
  return max(stand, draw)

class Memoize:
  def __init__(self, f):
    self.f = f
    self.memo = {}
  def __call__(self, *args):
    if not args in self.memo:
      self.memo[args] = self.f(*args)
    return self.memo[args]

max_chance = Memoize(max_chance)

print 'blacks\treds\tstand\tdraw\tchoice'
print max_chance(26, 26)