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README

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+A simulation of the Monty Hall problem in python.

monty_hall.py

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+#!/usr/bin/env python
+
+import random
+
+class MontyHall:
+    "Simulate a game in the Monty Hall problem."
+
+    def __init__(self):
+        self.rng = random.Random()
+        self.setupDoorPermutations()
+
+    def setupDoorPermutations(self):
+        "Permutations of goat1, goat2, and car used in the game."
+        self.doorPermutations = (
+            ('goat1', 'goat2', 'car'),
+            ('goat1', 'car',   'goat2'),
+            ('goat2', 'goat1', 'car'),
+            ('goat2', 'car',   'goat1'),
+            ('car',   'goat1', 'goat2'),
+            ('car',   'goat2', 'goat1')
+        )
+
+    def setupDoors(self):
+        "Setup the doors containing the goats and car." 
+        # use random number generator to pick one of the door permutations
+        rand_door_permutation = self.rng.randint(0,5)
+        self.doors = self.doorPermutations[rand_door_permutation]
+
+    def door(self, ind):
+        "Return a door number given an index."
+        return ind+1
+
+    def ind(self, door):
+        "Return an index given a door number."
+        return door-1
+
+    def isWinner(self, door):
+        "Return true when the player has won the game."
+        return self.doors[self.ind(door)] == 'car'
+
+    def winningDoor(self):
+        "Return the door number containing the car."
+        return self.door( self.doors.index('car') )
+
+    def switchDoor(self, door):
+        "Switch the door selected by the player."
+        if self.isWinner(door):
+            # since the user is switching away from the winning door,
+            # randomly choose between one of the two available goats
+            choices = [ (2,3), (1,3), (1,2) ]
+            choose = choices[self.ind(door)]
+            # use random number generator to pick one of the door choices
+            rand_choice = self.rng.randint(0,1)
+            door = choose[rand_choice]
+        else:
+            # the host will never show the door containing the car,
+            # so the user will always select the door containing the car
+            door = self.winningDoor()
+        return door
+
+    def game(self, door, switch_door):
+        "Play a single game and return the outcome."
+        self.setupDoors()
+        if switch_door:
+            door = self.switchDoor(door)
+        return self.isWinner(door)
+
+    def randDoor(self):
+        "Help the user by picking a random door to start."
+        return self.rng.randint(1,3)
+
+def pcnt(num, denom, scale=100.0):
+    "Return number as percent from [0.0, scale]"
+    return num*scale/denom
+
+def main():
+    switch_door = True
+    games = 10000
+    monty_hall = MontyHall()
+    outcomes = [None] * games   # history of game outcomes
+    picked = [None] * games     # history of doors picked by user
+    winning = [None] * games    # history of winning door
+    verbose = True
+
+    for g in range(games):
+        # use random number generator to pick a door (not strictly necessary)
+        door = monty_hall.randDoor()
+        outcomes[g] = monty_hall.game(door, switch_door)
+        if verbose:
+            picked[g] = door
+            winning[g] = monty_hall.winningDoor()
+
+    won = sum(outcomes)
+    lost = games - won
+    print('games\n count=%-5d\n won=%-5d(%3.1f)\n lost=%-5d(%3.1f)' % 
+        (games, won, pcnt(won,games), lost, pcnt(lost,games)))
+
+    if verbose:
+        reports = [ ('picked', picked), ('winning', winning) ]
+        for name,raw in reports:
+            counts = [raw.count(door) for door in range(1,4)]
+            pcnts  = [pcnt(count, games) for count in counts]
+            print('%s\n door1=%-5d(%3.1f)\n door2=%-5d(%3.1f)\n door3=%-5d(%3.1f)' %
+                (name, counts[0], pcnts[0], counts[1], pcnts[1], counts[2], pcnts[2]))
+
+if __name__ == '__main__':
+    main()
+