Monty Hall problem

Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.

A well-known statement of the problem was published in Parade magazine:

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? (Whitaker 1990)

Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.

Python

<python> I could understand the explanation of the Monty Hall problem but needed some more evidence

References:

 http://www.bbc.co.uk/dna/h2g2/A1054306
 http://en.wikipedia.org/wiki/Monty_Hall_problem especially:
 http://en.wikipedia.org/wiki/Monty_Hall_problem#Increasing_the_number_of_doors

from random import randrange, shuffle

doors, iterations = 3,100000 # could try 100,1000

def monty_hall(choice, switch=False, doorCount=doors):

 # Set up doors
 door = [False]*doorCount
 # One door with prize
 door[randrange(0, doorCount)] = True

 chosen = door[choice]

 unpicked = door
 del unpicked[choice]

 # Out of those unpicked, the alterantive is either:
 #   the prize door, or
 #   an empty door if the initial choice is actually the prize.
 alternative = True in unpicked

 if switch:
   return alternative
 else:
   return chosen

print "\nMonty Hall problem simulation:" print doors, "doors,", iterations, "iterations.\n"

print "Not switching allows you to win", print [monty_hall(randrange(3), switch=False)

       for x in range(iterations)].count(True),

print "out of", iterations, "times." print "Switching allows you to win", print [monty_hall(randrange(3), switch=True)

       for x in range(iterations)].count(True),

print "out of", iterations, "times.\n" </python> Sample output:

Monty Hall problem simulation:
3 doors, 100000 iterations.

Not switching allows you to win 33337 out of 100000 times.
Switching allows you to win 66529 out of 100000 times.