昨天提到了三門問題
答案是應該要換門
我們可以用以下程式碼驗證

import numpy as np
import random
import matplotlib.pyplot as plt

# 設定實驗次數
play_times = 1000

# 門數
door_num = 3
doors = list(np.arange(door_num))

# 紀錄
change_win = 0
hold_win = 0
change_winrate_record = []
hold_winrate_record = []

for play in range(play_times):
    # 決定寶物位置
    treasure = random.sample(doors, 1)
    # 第一次猜測
    first_choice = random.sample(doors, 1)
    # 開一個不是寶物也不是第一次猜測的門
    open_door = random.sample([d for d in doors if d not in treasure + first_choice], 1)
    # 重新選擇
    change_choice = random.sample([d for d in doors if d not in open_door + first_choice], 1)
    
    
    if treasure[0] == first_choice[0]:
        hold_win = hold_win + 1
    
    elif treasure[0] == change_choice[0]:
        change_win = change_win + 1
    
    # 取成比例
    change_winrate_record.append(np.round(change_win/(play+1), 3))
    hold_winrate_record.append(np.round(hold_win/(play+1), 3))

fig = plt.figure()
plt.plot(change_winrate_record, color = 'black', label = 'change')
plt.plot(hold_winrate_record, color = 'blue', label = 'hold')
plt.title('door_num = '+str(door_num)+', change : '+str(change_winrate_record[-1]))
plt.legend()
plt.show()

結果如圖

36：感覺好奇怪唷

RN：的確這剛開始的時候也有許多人很不適應呢
　　不過數學就是這麼奇妙(不會就是不會)~XD