run monty hall simulations to see if is better to switch door or not

monty_hall.py

import random

def monty_hall_trial(switch: bool) -> bool:
    """
    Run a single Monty Hall trial.
    Returns True if the player wins the car, False otherwise.
    """
    doors = [0, 1, 2]

    prize = random.choice(doors)      # door hiding the prize
    choice = random.choice(doors)     # player's initial pick

    # Host opens a goat door that's neither the prize nor the player's choice
    possible_opens = [d for d in doors if d != prize and d != choice]
    opened = random.choice(possible_opens)

    # The only remaining closed door that's not the player's initial choice or opened by host
    remaining_closed = next(d for d in doors if d != choice and d != opened)

    final_choice = remaining_closed if switch else choice
    return final_choice == prize

def run_simulations(n_trials: int = 1000):
    stay_wins = sum(monty_hall_trial(switch=False) for _ in range(n_trials))
    switch_wins = sum(monty_hall_trial(switch=True) for _ in range(n_trials))

    stay_rate = stay_wins / n_trials * 100.0
    switch_rate = switch_wins / n_trials * 100.0

    print(f"Trials: {n_trials}")
    print("----- Results -----")
    print(f"Stay with original choice: {stay_wins} wins ({stay_rate:.1f}%)")
    print(f"Switch door:               {switch_wins} wins ({switch_rate:.1f}%)")

if __name__ == "__main__":
    run_simulations(1000)