This python program simulates the simplest Monty Hall 3-door problem. No optimization, but can be easily extended to count for many-door situations.

MontyHall.py

# Monty Hall simulation

import numpy as np

winningdoor = -1  # ordinal numbers
firstChoice = -1  # both first pick and final pick
closedDoor = -1
finalChoice = -1


# called at every loop to initialize result
def initialize():
    """
    This gets an array of 3 elements
    then we choose the first as winner, the rest as loser
    """
    global firstChoice
    global closedDoor
    global winningdoor
    global finalChoice

    firstChoice = -1
    closedDoor = -1
    winningdoor = -1
    finalChoice = -1

    choice = np.random.choice(3)
    winningdoor = choice


# initial pick
def firstPick():
    global firstChoice
    firstChoice = np.random.choice(3)


# host closes the door
def hostChoice():
    """
    not allowed to close winning door or door first pick is picked
    """
    global closedDoor
    choices = []
    for i in range(0, 3):
        if (i != winningdoor) and (i != firstChoice):
            choices.append(i)
    closedDoor = np.random.choice(choices)  # choose a door to close


# switch: true = switch door; false = stay
def finalDecision(switch):
    global firstChoice
    global finalChoice
    if switch:
        for i in range(0, 3):
            if (i != closedDoor) and (i != firstChoice):
                finalChoice = i  # pick the other door
    else:
        finalChoice = firstChoice


# determine who wins by comparing two arrays
def determineWinner():
    if finalChoice == winningdoor:
        return True
    else:
        return False


def strategyRun(switch, times):
    winningStatistics = 0.0
    totalGame = 0.0
    for x in range(0, times):
        totalGame += 1
        initialize()
        firstPick()
        hostChoice()
        finalDecision(switch)
        if determineWinner():
            winningStatistics += 1

    print("total game: " + str(totalGame))
    print("winning #: " + str(winningStatistics))
    print("prob of winning: " + str(winningStatistics / totalGame))

if __name__ == '__main__':

    strategyRun(True, 1000)
    strategyRun(False, 1000)