Monty Hall Problem Monte Carlo simulation

simulation.py

# A simulation to settle a Twitter argument:
# https://twitter.com/brenorb/status/1213898659752038400

import random
random.seed(42)  # For reproducible results

# We have four possible scenarios we can simulate, based on these two bools.
# The first determines whether it's permissible for the host to reveal the car
# on the first door-opening. The second determines whether the contestant is
# using an "always swap" strategy or an "always stick" strategy.
CAN_REVEAL_CAR_EARLY = True
ALWAYS_SWAP = True  # if False, always stick

# Let's just have three doors, as in the classic version of the problem:
DOORS = ['A', 'B', 'C']

wins = 0
losses_on_first_reveal = 0  # (Only possible if car can be revealed early)
losses_on_final_reveal = 0

for _ in range(1000):
    # Location of the car:
    car = random.choice(DOORS)

    # We could just as well go for a hard-coded choice here, but let's have the
    # contestant choose an initial door randomly:
    contestant_choice = random.choice(DOORS)

    if CAN_REVEAL_CAR_EARLY:
        # The host randomly chooses a door out of the two the contestant didn't
        # pick and opens it, potentially revealing the car.
        host_choice = random.choice([
            door for door in DOORS
            if door != contestant_choice
        ])
        if host_choice == car:
            # The car was revealed early. The contestant loses immediately.
            losses_on_first_reveal += 1
            continue
    else:
        # The host "randomly" chooses a door out of the set of either one or
        # two doors that are neither the contestant's choice nor the door
        # hiding the car. (Scare quotes since this may only leave one choice!)
        host_choice = random.choice([
            door for door in DOORS
            if door != contestant_choice and door != car
        ])

    remaining_door = next(door for door in DOORS
                          if door not in (host_choice, contestant_choice))
    if ALWAYS_SWAP:
        contestant_choice = remaining_door

    if contestant_choice == car:
        wins += 1
    else:
        losses_on_final_reveal += 1

print("RULES: the host",
      ("CAN" if CAN_REVEAL_CAR_EARLY else "CANNOT"),
      "reveal the car when they first open a door.")
print("STRATEGY: the contestant will always",
      ("SWAP" if ALWAYS_SWAP else "STICK"))
print("Wins:", wins)
print("Early losses (before contestant gets a chance to swap):",
      losses_on_first_reveal)
print("Losses after the contestant chooses whether to swap:",
      losses_on_final_reveal)

# Results observed for each of the four possible scenarios:

# RULES: the host CANNOT reveal the car when they first open a door.
# STRATEGY: the contestant will always SWAP
# Wins: 661
# Early losses (before contestant gets a chance to swap): 0
# Losses after the contestant chooses whether to swap: 339

# RULES: the host CANNOT reveal the car when they first open a door.
# STRATEGY: the contestant will always STICK
# Wins: 339
# Early losses (before contestant gets a chance to swap): 0
# Losses after the contestant chooses whether to swap: 661

# RULES: the host CAN reveal the car when they first open a door.
# STRATEGY: the contestant will always SWAP
# Wins: 333
# Early losses (before contestant gets a chance to swap): 328
# Losses after the contestant chooses whether to swap: 339

# RULES: the host CAN reveal the car when they first open a door.
# STRATEGY: the contestant will always STICK
# Wins: 339
# Early losses (before contestant gets a chance to swap): 328
# Losses after the contestant chooses whether to swap: 333