Python implementation of a Monte Carlo simulation of the famous "cars and goats" problem. Yes it is a mess.

monte_carlo_hall.py

# USAGE just copy/paste this in to a Python interpreter and invoke it with try_doors_with_strategy(), e.g.

# >>> num_trials, found_cars, found_goats = try_doors_with_strategy()
# >>> print 'car rate: {}'.format(str(1.0 * found_cars / num_trials))
# car rate: 0.338

# >>> num_trials, found_cars, found_goats = try_doors_with_strategy(num_trials = int(1e6), strategy='switch')
# >>> print 'car rate: {}'.format(str(1.0 * found_cars / num_trials))
# car rate: 0.666569

import os
# os.urandom()

def bytes2int(str):
    return int(str.encode('hex'), 16)

def pick_door(doors=3):
    return bytes2int(os.urandom(1)) % doors


goat_str = 'G'
car_str = 'C'

def fill_doors(num_doors=3):
    car_door = pick_door(num_doors)
    doors = []
    for d in range(num_doors):
            if d is car_door:
                    doors.append(car_str)
            else:
                    doors.append(goat_str)
    return doors



# total_count = 0
# car_count = 0
# goat_count = 0

# for trial in range(2000):
#     total_count += 1
#     if fill_doors(3)[pick_door(3)] is car_str:
#             car_count += 1
#     else:
#             goat_count += 1


# def try_doors(num_trials=2000):
#     total_count = 0
#     car_count = 0
#     goat_count = 0
    
#     for trial in range(num_trials):
#         total_count += 1
#         if fill_doors(3)[pick_door(3)] is car_str:
#                 car_count += 1
#         else:
#                 goat_count += 1
    
#     return total_count, car_count, goat_count

def try_doors_with_strategy(num_trials=1000, num_doors=3, strategy='stay'):
    total_count = 0
    car_count = 0
    goat_count = 0
    
    for trial in range(num_trials):
        total_count += 1
        doors = fill_doors(num_doors)
        chosen_door = pick_door(num_doors)
        
        shown_door = -1
        offered_door = -1
        
        unchosen_goat_doors =[]
        
        # find the remaining goats!
        for door in range(num_doors):
            if (door is not chosen_door) and (doors[door] is goat_str):
                unchosen_goat_doors.append(door)
        
        # pick a goat and show him
        shown_door = unchosen_goat_doors[pick_door(len(unchosen_goat_doors))]
        
        remaining_doors = []
        
        # offer the remaining door
        # there has to be a better way
        for door in range(num_doors):
            if (door is not chosen_door) and (door is not shown_door):
                remaining_doors.append(door)
        
        # choose your destiny
        if strategy is 'stay':
            pass
        else:
            chosen_door = remaining_doors[pick_door(len(remaining_doors))]
        
        # let's see what they won!
        if doors[chosen_door] is car_str:
            car_count += 1
        else:
            goat_count += 1
    
    return total_count, car_count, goat_count