Simulation: Mythbusters and the Monty Hall paradox

In episode 177, “Wheel of Mythfortune” of the Mythbusters show, Jamie and Adam explore the Monty Hall paradox. I wrote a small python script to simulate the problem past the break.

Simple simulator for the Mythbusters Pick-A-Door.
This simulates the results of the Monty Hall paradox.

It turns out that it is always advantagous to switch. Here is why:

Picking a door means 1/3 chance of wining and a 2/3 chance that one of the
one of the other doors is the winner. The show host opens one
of the other two doors that is empty. The probability that the non-picked
doors wins is still in effect. That means that the existing non-picked
closed door has a 2/3 chance of being a winner.

Just run and look at the numbers...

- Leo Tindle 

This script is released in to the public domain. Do as you wish with it.
import random

stick_score = 0
switch_score = 0
for x in xrange(1000):
    # Pick the door that really has the prize
    actual = random.randint(1,3)

    # Take the first guess (player)
    pick = random.randint(1,3)

    # Find empty doors that we can open
    show_doors_avail = set((1,2,3))
    # Rule out the actual winning door
    # Rule out the door the player picked
    # Randomly choose a door from available options
    # This will be either one (if the first guess was wrong)
    # or two (if the first guess was right)
    show = list(show_doors_avail)[
        random.randint(0, len(show_doors_avail)-1)]

    # Randomly choose whether we stick
    stick = random.randint(0,1) and True or False

    if stick:
        # If we do stick, our new pick is the same as the original
        new_pick = pick

        # If we don't stick, find the other door we can open
        new_pick_avail = set((1,2,3))
        new_pick = list(new_pick_avail)[0]

    # We win if our new pick matches the actual prize door
    win = actual == new_pick
    if win:
        if stick:
            stick_score += 1
            switch_score += 1

    print("{!r}: Actual: {!r}, Pick: {!r}, Shown: {!r}, Stick: {!r}, "
          "New Pick: {!r}, Win: {!r}"
          .format(x, actual, pick, show, stick, new_pick, win))

print("Switch Score: {!r}, Stick Score: {!r}".format(switch_score, stick_score))