Monty Hall Problem -- Statistical Analysis

README

This utility is meant for educational purposes. Please, on the honor system, don't use it as your own homework!

Otherwise, it is under this license: http://sam.zoy.org/wtfpl

ANALYSIS

Strategy 1, which is "stay every time" predictably won 33.33% of the time.

Strategy 2, "switch every time" won 66.67% of the time.

Strategy 3, "switch 33% of the time randomly" won 44.44% of the time.

If you can come up with a strategy that, after immense amounts of trials, is above 66.67% win rate, you may want to contact the makers of Let's Make a Deal, and then contact us to let us know.

DISCLAIMER: I don't think such a strategy exists, so don't lose sleep over finding it.

monty.py

#!/usr/bin/python
'''

monty.py - find the probability of winning "Let's Make a Deal" given a constant strategy

Usage: monty.py <strategy> <iterations>

<strategy> is either 1, 2 or 3: 1 is 'always switch' and 2 is 'always stay'. 3 is 'switch 33% of the time'.
<iterations> is the number of times to try.

'''

import sys, random

def switch(one, two):
    if one == two:
        raise ValueError('You can\'t use this method with two of the same value.')
    choice = 3 - one - two
    return choice

strategy = int(sys.argv[1])
number = int(sys.argv[2])

wins = 0
total = 0

for i in range(number):
    door = random.randrange(3)
    choice = random.randrange(3)
    if door == choice:
        if choice == 0:
            remove = random.randrange(1,3)
        elif choice == 2:
            remove = random.randrange(0,3,2)
        else:
            remove = random.randrange(0,2)
    else:
        remove = 3 - door - choice

    if strategy == 1:
        choice = switch(choice, remove)
    elif strategy == 2:
        choice = choice
    elif strategy == 3:
        if random.randrange(0,3) == 0:
            choice = switch(choice, remove)
    else:
        raise ValueError('The strategy must be 1, 2, or 3!')

    if choice == door:
        wins += 1
    total += 1

print "Out of %i games, your strategy won %i times." % (total, wins)
print "That is a win probability of %.2F percent." % ((float(wins) / float(total)) * 100)

monty.py line 17, quote consistency.

Bugger all, I need to test when I change things. Sorry!