A simulation, in Python, of the Variable Change problem as explained in the movie "21".

VariableChangeSimulation.py

import random
 
def get_choices():
    '''Generates a list of size 3 that represents the doors. 0 is a loss (goat)
    while 1 is a win (car). 1 door will have a 1 in it, the other two will have
    0s.'''
    choices = [0, 0, 0]
    choices[random.randint(0, 2)] = 1
    return choices
 
def remove_choice(doors, choice):
    '''Takes the list of doors and the players current choice and returns a
    door number that is neither the players current choice or the right
    door.'''
    index = random.randint(0, 2)
    while (doors[index] == 1 or index == choice):
        index = random.randint(0, 2)
    return index
 
def switch_choice(choice, removed):
    '''Takes the players current choice and the door that has already been
    opened and revealed to have nothing behind it and returns the last remaining
    door. Hence a switched choice.'''
    if 0 != choice and 0 != removed:
        return 0
    if 1 != choice and 1 != removed:
        return 1
    if 2 != choice and 2 != removed:
        return 2
 
 
wins = 0
losses = 0
 
for i in range(0, 10000):
 
    doors = get_choices()
    #print "Doors: " + str(doors)
 
    choice = random.randint(0, 2)
    #print "Initial choice: " + str(choice+1)
 
    opened = remove_choice(doors, choice)
    #print "Host opened door: " + str(opened+1)
 
    choice = switch_choice(choice, opened)
    #print "Choice switched to: " + str(choice+1)
 
    if doors[choice] == 1:
        wins += 1
    else:
        losses += 1
 
print "Wins: " + str(wins) + "\tLosses: " + str(losses)