import random


def simulate_monty_hall(switch, num_trials=100000):
    """
    模拟三门悖论（蒙提霍尔问题）

    参数:
    - switch: bool, 是否在主持人打开门后选择换门
    - num_trials: int, 模拟次数（默认10万次）

    返回:
    - 获胜次数
    - 胜率
    """
    win_count = 0
    doors = [1, 2, 3]  # 三扇门

    for _ in range(num_trials):
        # 随机放置汽车（1 表示汽车，0 表示山羊）
        car_door = random.choice(doors)

        # 参赛者初始选择
        player_choice = random.choice(doors)

        # 主持人要打开一扇门：不能是参赛者选的，也不能是有车的
        remaining_doors = [d for d in doors if d != player_choice and d != car_door]
        host_opens = random.choice(remaining_doors)

        # 换门逻辑
        if switch:
            # 换到剩下的那一扇未被选、未被开的门
            final_choice = [d for d in doors if d != player_choice and d != host_opens][0]
        else:
            # 不换，保持原选择
            final_choice = player_choice

        # 判断是否获胜
        if final_choice == car_door:
            win_count += 1

    win_rate = win_count / num_trials
    return win_count, win_rate


# === 运行模拟 ===
if __name__ == "__main__":
    num_trials = 100000

    print(f"模拟 {num_trials} 次三门问题：\n")

    # 情况1：坚持不换门
    wins_stay, rate_stay = simulate_monty_hall(switch=False, num_trials=num_trials)
    print(f"坚持原选择（不换门）:")
    print(f"  获胜次数: {wins_stay}")
    print(f"  胜率: {rate_stay:.4f} ({rate_stay * 100:.2f}%)\n")

    # 情况2：总是换门
    wins_switch, rate_switch = simulate_monty_hall(switch=True, num_trials=num_trials)
    print(f"总是换门:")
    print(f"  获胜次数: {wins_switch}")
    print(f"  胜率: {rate_switch:.4f} ({rate_switch * 100:.2f}%)\n")

    print("理论值对比:")
    print("  不换门胜率: 1/3 ≈ 33.33%")
    print("  换门胜率: 2/3 ≈ 66.67%")