# This program simulates the Monty Hall game show.
# The setup is as follows: There are three closed
# doors. Behind one of the doors is a car, and behind
# the other two are goats. You pick one of the doors.
# The game show host then opens one of the two doors
# that you didn't pick. You then have the option
# to switch your guess to the third door. Assume that
# your goal is to win the car. In this program, we test 
# the proportion of times you win by choosing to switch
# after one of the doors is revealed.

import random

def montyhall():
    car = random.randint(0,2)
    guess = random.randint(0,2)
    if guess != car:
        opendoor = 3-car-guess
    else:
        while True:
            opendoor = random.randint(0,2)
            if opendoor != car:
                break
    switch = 3 - guess - opendoor
    return (switch == car)

def propwins(n):
    count = 0.
    for _ in range(n):
        if montyhall():
            count += 1
    return count/n

print propwins(100)