import random

doors = [1,2,3]
nb_simulations = 1000000
win_door1 = 0
win_door2 = 0

for i in range(nb_simulations):
    winning_door = random.choice(doors)
    player_door1 = random.choice(doors)

    # Open a door
    doors_openable = doors.copy()
    doors_openable.remove(player_door1)
    if player_door1 != winning_door:
        doors_openable.remove(winning_door)
    doors_opened = random.choice(doors_openable)

    # Change ?
    doors_selectable = doors.copy()
    doors_selectable.remove(doors_opened)
    doors_selectable.remove(player_door1)
    player_door2 = doors_selectable[0]

    if winning_door == player_door1:
        win_door1 += 1
    if winning_door == player_door2:
        win_door2 += 1


freq_win_door1 = win_door1 / nb_simulations
freq_win_door2 = win_door2 / nb_simulations

if 0.33 < freq_win_door1 < 0.34 and 0.66 < freq_win_door2 < 0.67:
    print(True)
else:
    print(False)