Testing the Monty Hall Problem

monty.py

"""As much as I understood the theorems of the monty hall problem 
my brain simply refused to take it in and accept, so I wrote a very quick (and dirty) script to just test it out.
The script randomly generates two goats (designated as 0) and a car (designated by 1) for three doors (stored in a dictionary. I don't know why I
chose that. Anyway. Here's the script... And it works. Funnily enough when writing the program I kept having snippets of thoughts on how staying
with your old choice would leave you at 33% anyways since you didn't take advantage of the situation of knowing one door which had a goat behind it
That prompted me to write the normal test where based on intuition, you'd stick with the door you picked originally. And yes, everything checks out.

Edit: I also thought of the case of what if the game host reveals a door behind which there is a goat BEFORE you make your first pick.
Isn't that like the first scenario but the order just reversed? Apparently not. The results move down to 50-50. My mind has been blown. 
In the face of math, trust not your intuition I guess. Oh, and I included results at the bottom.
"""

import random

"""this is the standard monty test. Works as follows
Pick a random door.
Host reveals a door behind which there is a goat
You are mathematical genius so you switch doors

Resulted in ~66% win ratio
"""
def montyTest():
  wins = 0
	losses = 0
	for i in range(0,100000):
		random.seed()
		doors = {1:0,2:0,3:0}
		doors[1] = random.randint(0,1)
		if doors[1] == 1:
			doors[2] = doors[3] = 0
		else:
			doors[2] = random.randint(0,1)
			doors[3] = 1 - doors[2]
		
		#print ('door 1: %d , door 2: %d, door 3: %d' % (doors.get(1),doors.get(2),doors.get(3)))
		#logic for picking the door here

		#randomly pick the first door
		pick = random.randint(1,3)
		

		"""if doors[pick] == 1:
			print 'first door was car'
		else:
			print 'first door was goat'"""

		#since the monty hall problem means we discard our first choice anyway, we pop it out of the list	
		doors.pop(pick)

		#search for a door with a goat behind in and remove that door (the host of the show does this in the monty hall problem)
		for k in doors.keys():
			if doors[k] == 0:
				doors.pop(k)
			break

		#which leaves us with the only door remaining. For all we know we could have discarded a car in the first one. 
		if doors.get(doors.keys()[0]) == 1:
			wins += 1
		else:
			losses += 1
	
	print 'wins: ' + str(wins)
	print 'losses: ' + str(losses)

"""This is the monty hall test for non mathematicians
Pick a door at random
Host revelas a door behind which there is a goat
You are stubborn and don't switch because of your intuition

Resulted in ~33% win ratio
"""
def normalTest():
	wins = 0
	losses = 0
	for i in range(0,100000):
		random.seed()
		doors = {1:0,2:0,3:0}
		doors[1] = random.randint(0,1)
		if doors[1] == 1:
			doors[2] = doors[3] = 0
		else:
			doors[2] = random.randint(0,1)
			doors[3] = 1 - doors[2]
		
		#print ('door 1: %d , door 2: %d, door 3: %d' % (doors.get(1),doors.get(2),doors.get(3)))
		#logic for picking the door here

		#randomly pick the first door
		pick = random.randint(1,3)
		

		"""if doors[pick] == 1:
			print 'first door was car'
		else:
			print 'first door was goat'"""

		#in this one, since we are going to stick with the door choice anyway, we stop the test here.	
		if doors.get(pick) == 1:
			wins += 1
		else:
			losses += 1

	print 'wins: ' + str(wins)
	print 'losses: ' + str(losses)

"""This may or may not fall under a monty hall scenario but it was an interesting discussion. Scenario is as follows
Before you pick at random, the host reveals a door behind which there is a goat
You pick a door at random

Resulted in ~50% win ratio 

Note - Even if you changed logic where if you randomly picked a door behind which there was a goat then you win and vice versa (the equivalent of picking 
two doors... sort of) you'd still end up with ~50% win ratio. 
"""
def abnormalTest():
	wins = 0
	losses = 0
	for i in range(0,100000):
		random.seed()
		doors = {1:0,2:0,3:0}
		doors[1] = random.randint(0,1)
		if doors[1] == 1:
			doors[2] = doors[3] = 0
		else:
			doors[2] = random.randint(0,1)
			doors[3] = 1 - doors[2]

		for k in doors.keys():
			if doors[k] == 0:
				doors.pop(k)
			break

		if doors.get(doors.keys()[random.randint(0,1)]) == 1:
			wins += 1
		else:
			losses+= 1
	
	print 'wins: ' + str(wins)
	print 'losses: ' + str(losses)
  
"""results of the tests are as follows. 

Python 2.7.2 (default, Jun 12 2011, 14:24:46) [MSC v.1500 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import monty
>>> monty.montyTest()
wins: 66598
losses: 33402
>>> monty.abnormalTest()
wins: 50253
losses: 49747
>>> monty.abnormalTest()
wins: 50070
losses: 49930
>>> monty.abnormalTest()
wins: 49719
losses: 50281
>>> monty.abnormalTest()
wins: 49791
losses: 50209
>>> monty.normalTest()
wins: 33317
losses: 66683
>>>

"""