monty hall

The other day I was introduced to the Monty Hall problem. I had never heard it before and my first guess at the answer was wrong. After some thought (and some reading), it's obvious to me why I was wrong. Being a geek, I wanted to prove it myself with code so I wrote a quick Python class to model the problem.

import random

class Monty:
  "The Monty Hall problem"

  def __init__(self):
      print "init"
      iterations = 100
      # keep track of how often the keepers and changers win
      countKeepers = 0
      countChangers = 0
      for i in range(iterations):
          countKeepers += self.doit(1)
          countChangers += self.doit(0)
      print "of the %s iterations, the keepers won %s and the changers won %s" % (iterations, countKeepers, countChangers)

  def doit(self, keepSelection):
      print random.randrange(1,4)
      # setup the doors
      doors = [0,0,0,0]
      # pick one for the car
      doorWithCar = random.randrange(1,4)
      print "door %s has the car" % doorWithCar
      doors[doorWithCar] = 1
      # pick one as a contestant
      userChoice = random.randrange(1,4)
      print "the user chose door", userChoice
      # if the contestant is a keeper, then we can stop here
      if (keepSelection):
          if (userChoice == doorWithCar):
              return 1
          else:
              return 0
   
      # reveal a door
      for i in range(1,4):
          if (i != userChoice and doors[i] == 0):
              revealedDoor = i
              print "revealing that door %s has a goat behind it" % revealedDoor
              break
   
      # determine if the contestant wins when they change their selection
      if (userChoice != doorWithCar):
          return 1
      else:
          return 0

m = Monty()