My friend, Dan Coffman, posed a game on his Facebook...

card-game.py

#
# My friend, Dan Coffman, posed a game on his Facebook. Some people answered. I
# didn't believe that one of them was wrong.
#
# A game (reworded to remove misleading 'i.e.'):
#
# The dealer shuffles a deck of cards and reveals them face up one at a time.
# At any time, you can interrupt the dealer and bet that the next card will be
# red. If the card is red, you win. If it is black, you lose. Is there a
# strategy that will allow you to win more than half your games?
# 
# Can you explain why/why not?
#

import random


# I don't know shit about statistics, so I don't actually know how many runs is statistically valid.
RUNS = 1000


class Card:
    def __init__(self, value):
        self.value = value

    def is_red(self):
        return (self.value % 2) == 0


class Deck(list):
    def __init__(self):
        self.extend([Card(v) for v in range(52)])
        random.shuffle(self)


def test(guess):
    seen = []
    won, lost = 0, 0

    for c in Deck():
        if guess(seen):
            if c.is_red():
                won += 1
            else:
                lost += 1

        seen.append(c)

    if (won + lost) > 0:
        return won / float(won + lost)
    else:
        return None


def guess_bias(seen):
    number_reds = len(filter(lambda c: c.is_red(), seen))
    number_blacks = len(seen) - number_reds
    return number_blacks > number_reds


def guess_when_certain(seen):
    number_blacks = len(filter(lambda c: not c.is_red(), seen))
    return number_blacks == 26


def main():
    guessers = [('Always guess red', lambda seen: True),
                ('Guess when biased', guess_bias),
                ('Guess when certain', guess_when_certain)]

    for title, guess in guessers:
        # I'm dropping runs in which a guess is never taken. But they could
        # also be 100% wins or 100% loses?
        tests = filter(None, [test(guess) for x in xrange(RUNS)])
        print "%s: %.4f" % (title, sum(tests) / len(tests))


if __name__ == '__main__':
  main()