66 lines
2.0 KiB
Python
66 lines
2.0 KiB
Python
import random
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def simulate_monty_hall(switch, num_trials=100000):
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"""
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模拟三门悖论（蒙提霍尔问题）
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参数:
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- switch: bool, 是否在主持人打开门后选择换门
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- num_trials: int, 模拟次数（默认10万次）
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返回:
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- 获胜次数
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- 胜率
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"""
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win_count = 0
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doors = [1, 2, 3] # 三扇门
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for _ in range(num_trials):
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# 随机放置汽车（1 表示汽车，0 表示山羊）
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car_door = random.choice(doors)
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# 参赛者初始选择
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player_choice = random.choice(doors)
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# 主持人要打开一扇门：不能是参赛者选的，也不能是有车的
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remaining_doors = [d for d in doors if d != player_choice and d != car_door]
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host_opens = random.choice(remaining_doors)
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# 换门逻辑
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if switch:
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# 换到剩下的那一扇未被选、未被开的门
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final_choice = [d for d in doors if d != player_choice and d != host_opens][0]
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else:
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# 不换，保持原选择
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final_choice = player_choice
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# 判断是否获胜
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if final_choice == car_door:
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win_count += 1
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win_rate = win_count / num_trials
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return win_count, win_rate
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# === 运行模拟 ===
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if __name__ == "__main__":
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num_trials = 100000
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print(f"模拟 {num_trials} 次三门问题：\n")
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# 情况1：坚持不换门
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wins_stay, rate_stay = simulate_monty_hall(switch=False, num_trials=num_trials)
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print(f"坚持原选择（不换门）:")
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print(f" 获胜次数: {wins_stay}")
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print(f" 胜率: {rate_stay:.4f} ({rate_stay * 100:.2f}%)\n")
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# 情况2：总是换门
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wins_switch, rate_switch = simulate_monty_hall(switch=True, num_trials=num_trials)
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print(f"总是换门:")
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print(f" 获胜次数: {wins_switch}")
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print(f" 胜率: {rate_switch:.4f} ({rate_switch * 100:.2f}%)\n")
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print("理论值对比:")
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print(" 不换门胜率: 1/3 ≈ 33.33%")
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print(" 换门胜率: 2/3 ≈ 66.67%") |