A simple simulation of the Monty Hall Problem.

monty_hall.py

#!/usr/bin/env python
# coding=utf-8

from __future__ import division

import itertools as it
import random as r
from sys import argv

def play_round(switch_choice=True):
    doors = [1, 2, 3]
    player_pick = r.choice(doors)
    master_pick = r.choice(doors)
    reveal_pick = r.choice(filter(
        lambda d: d != player_pick and d != master_pick,
        doors
    ))
    if switch_choice:
        player_pick = filter(
            lambda d: d != player_pick and d != reveal_pick,
            doors
        )[0]
    return player_pick == master_pick


if __name__ == "__main__":
    N_rounds = 1000000
    if len(argv) > 1:
        N_rounds = int(argv[1])
    print("Playing {} rounds for each strategy.".format(N_rounds))
    result_switch = len(filter(
        lambda play: play(),
        it.repeat(play_round, N_rounds))
    )/N_rounds
    result_stay = len(filter(
        lambda play: play(switch_choice=False),
        it.repeat(play_round, N_rounds))
    )/N_rounds
    print("Switch: {:.0%}".format(result_switch))
    print("Stay  : {:.0%}".format(result_stay))