Let's solve the Monty Hall problem using Monte Carlo!

monty_hall.py

"""
Modeling the Monty Hall Problem

https://en.wikipedia.org/wiki/Monty_Hall_problem

Suppose you're on a game show, and you're
given the choice of three doors: Behind one
door is a car; behind the others, goats. You
pick a door, say No. 1, and the host, who
knows what's behind the doors, opens another
door, say No. 3, which has a goat. He then
says to you, "Do you want to pick door No. 2?"
Is it to your advantage to switch your choice?

Let's solve the Monty Hall problem using Monte Carlo!

https://en.wikipedia.org/wiki/Monte_Carlo_method
"""
from random import randint


def main():
    n = 10000

    print(f"\nIf you play the Monte Hall game {n} times")
    print(f"{monty_hall_monte_carlo(n, False)}% of the time you win if you don't switch,")
    print(f"{monty_hall_monte_carlo(n, True)}% of the time you win if you switch.\n")


def monty_hall_monte_carlo(n, switch=True):
    """Let's solve the Monty Hall problem with Monte Carlo!

    Parameters
    ----------
    n : int
        How many times should we play the game?
    switch : bool (defaults True)
        Should we switch or keep our first guess?

    Returns
    -------
    What percentage of the N times did we win?
    """
    successes = 0

    # Let's play the Monty Hall game N times
    for _ in range(n):
        # We will set up 3 doors, with one random winner.
        doors = [0, 0, 0]
        doors[randint(0, 2)] = 1

        # You pick one door at random.
        your_pick = randint(0, 2)

        # Every time, you either keep your first guess, or switch.
        if switch:
            # If you DO switch...
            if doors[your_pick] == 1:
                # If your first guess was correct, you lose.
                continue
            else:
                # If your first guess was wrong, you win.
                successes += 1
        else:
            # If you don't switch, we just test your first guess.
            if doors[your_pick] == 1:
                successes += 1

    # return the percentage of times you succeeded
    return 100 * float(successes) / n


if __name__ == "__main__":
    main()