Monty Hall Problem Simulation

"""

This is a simulation of Monty Hall Problem.

https://en.wikipedia.org/wiki/Monty_Hall_problem

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats.

You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.

He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

"""

import random

NUM_DOORS = 3  # three doors in the game

MAX_ROUND = 10000  # number of rounds for statistics

change_win_count = 0

for _ in range(MAX_ROUND):

  # randomly to put a car behind a door

  car_door = random.randint(0, NUM_DOORS - 1)

  # the player firstly selects a door

  player_first_guess = random.randint(0, NUM_DOORS - 1)

  # the host opens another door without a car

  host_door = random.choice([

      x for x in range(NUM_DOORS) if x != player_first_guess and x != car_door

  ])

  # the option if the player changes his mind

  player_second_guess = random.choice([

      x for x in range(NUM_DOORS) if x != player_first_guess and x != host_door

  ])

  # count the win if the second guess is correct

  if player_second_guess == car_door:

    change_win_count += 1

# Print the statistics result

print("Win percentage if you switch the choice is {r:.2f}%".format(

    r=(change_win_count * 100) / MAX_ROUND))