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Monty Hall problem

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A proof of the Monty Hall problem written in Python.

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  1. #---------------------------------
  2. # The Monty Hall Problem
  3. #---------------------------------
  4.  
  5. import random
  6.  
  7. pickcount = 0
  8. newpickcount = 0
  9. i = 0
  10. counter = 100000
  11.  
  12. def pick1of3():
  13.     pick=random.randint(0,2)
  14.     return pick
  15.  
  16. while i < counter:
  17. # Prize assignment
  18.     doors = ['goat','goat','goat']
  19.     car = pick1of3()
  20.     doors[car] = 'car '
  21.  
  22. # Contestant choice
  23.     firstchoice = pick1of3()
  24.     pick = doors[firstchoice]
  25.  
  26. # Monty's reveal
  27.     reveal=random.random()
  28.  
  29.     if firstchoice == 0:
  30.         if pick=='car ' and reveal < 0.5: Montyshows=doors[1]
  31.         elif pick=='car ': Montyshows=doors[2]
  32.         elif pick=='goat' and doors[1]=='goat': Montyshows=doors[1]
  33.         else: Montyshows=doors[2]
  34.  
  35.     elif firstchoice == 1:
  36.         if pick=='car ' and reveal < 0.5: Montyshows=doors[0]
  37.         elif pick=='car ': Montyshows=doors[2]
  38.         elif pick=='goat' and doors[0]=='goat': Montyshows=doors[0]
  39.         else: Montyshows=doors[2]
  40.  
  41.     elif firstchoice == 2:
  42.         if pick=='car ' and reveal < 0.5: Montyshows=doors[0]
  43.         elif pick=='car ': Montyshows=doors[1]
  44.         elif pick=='goat' and doors[0]=='goat': Montyshows=doors[0]
  45.         else: Montyshows=doors[1]
  46.  
  47.  
  48. # The Switch
  49.     if pick==doors[0]:
  50.         if Montyshows==doors[1]: newpick=doors[2]
  51.         else: newpick=doors[1]
  52.  
  53.     elif pick==doors[1]:
  54.         if Montyshows==doors[0]: newpick=doors[2]
  55.         else: newpick=doors[0]
  56.  
  57.     else:
  58.         if Montyshows==doors[0]: newpick=doors[1]
  59.         else: newpick=doors[0]
  60.  
  61.     if pick == 'car ':
  62.         pickcount = pickcount + 1
  63.  
  64.     if newpick == 'car ':
  65.         newpickcount = newpickcount + 1
  66.  
  67.     i = i + 1
  68.  
  69. print 'Original Pick is a Car: ',"{0:.3f}%".format(float(pickcount)/counter * 100)
  70. print 'Switched Pick is a Car: ',"{0:.3f}%".format(float(newpickcount)/counter * 100)

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