import random

def simulate_n_door_monty_fall(num_doors, num_runs):
    if num_doors < 3:
        print("You need at least 3 doors for this to be a Monty Hall problem!")
        return

    stay_wins = 0
    switch_wins = 0
    monty_opened_car = 0
    valid_games = 0

    for _ in range(num_runs):
        doors = list(range(num_doors))
        car_door = random.randint(0, num_doors - 1)

        # 1. Player makes an initial choice
        player_choice = random.randint(0, num_doors - 1)

        # 2. Monty chooses (N - 2) doors at random from the ones NOT chosen by player
        available_to_monty = [d for d in doors if d != player_choice]
        doors_to_open = random.sample(available_to_monty, num_doors - 2)

        if car_door in doors_to_open:
            # Result -> Monty accidentally revealed the car
            monty_opened_car += 1
        else:
            valid_games += 1

            # Result -> Keep door
            if player_choice == car_door:
                stay_wins += 1

            # Result -> Switch door
            remaining_door = [d for d in doors if d != player_choice and d not in doors_to_open][0]
            if remaining_door == car_door:
                switch_wins += 1

    print(f"Results for {num_runs} Runs with {num_doors} Doors")
    print(f"Monty opened the car: {monty_opened_car}")
    print(f"Valid games (Only goats revealed): {valid_games}")
    print("-" * 40)
    if valid_games > 0:
        print(f"Wins by Staying: {stay_wins} ({(stay_wins/valid_games)*100:.1f}%)")
        print(f"Wins by Switching: {switch_wins} ({(switch_wins/valid_games)*100:.1f}%)")
    else:
        print("Monty opened the car every single time!")

if __name__ == "__main__":
    simulate_n_door_monty_fall(num_doors=100, num_runs=10000)