Simulation to prove answer to monty hall problem

montyhall.py

import numpy as np

# returns a numpy array of n doors with the prize range 0-2
def simulate_prizedoors(n):
    return np.random.random_integers(0, 2, size=n)

# returns a numpy array of n contestant guesses with range 0-2
def simulate_guesses(n):
    return np.random.random_integers(0, 2, size=n)

# returns a numpy array of doors the host would show with the goat
def goatdoors(guesses, prizedoors):
    return [np.setdiff1d([0, 1, 2], [prizedoors[i], guesses[i]])[0] for i in range(len(prizedoors))]

# switches guess based on the goat door shown
def switch_guess(guesses, goatdoors):
    return [np.setdiff1d([0, 1, 2], [guesses[i], goatdoors[i]])[0] for i in range(len(guesses))]

# returns percentages of wins
def win_percentage(guesses, prizedoors):
    count = 0
    for i in range(len(guesses)):
        if guesses[i] == prizedoors[i]:
            count += 1
    return 100.0 * count / float(len(guesses))

N = 10000

prizedoors = simulate_prizedoors(N)
guesses = simulate_guesses(N)

print "Wins without switching %f" % win_percentage(guesses, prizedoors)

prizedoors = simulate_prizedoors(N)
guesses = simulate_guesses(N)
goatdoors = goatdoors(guesses, prizedoors)

print "Wins with switching: %f" % win_percentage(switch_guess(guesses, goatdoors), prizedoors)

output.txt

Wins without switching 31.880000
Wins with switching: 67.630000