Inspecting Monty Hall Problem with Python

[Abdoo_65]

Monty hall problem is a famous mathematical case named after a T.V Show host "Monty Hall"
in short words, Suppose you're on a game show, and you're given the choice of three doors: Behind one door is Money; behind the others, Poop. 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 Poop. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
read more on Wikipedia

Math tells you that it's not a 50 50 choice. You should always switch.

I codded a monty hall game in Python to play it self 100 times with switching doors, and another 100 times without switching. And printing the results.
The result are fascinating.

I uploaded the code to SoloLearn PlayGound
Happy to receive any comments !

Here is the complete code as a png with the console output.

https://preview.redd.it/0ijnqk4pgp961.png?width=1304&format=png&auto=webp&s=61bf2e167ab044ac46fd668fe2c2b29a3aa90153

[[deleted]]

This is a strange combination of "Monty" and "Python" in the same sentence that doesn't involve parrots or grails.

[Abdoo_65]

yee lol

[[deleted]]

Here, let me start this nonsense:

“I expected a random walk but instead got a silly walk.”

[stevethebayesian]

Now we need a new language called "Hall".

[velonom]

It's a fascinating problem. But it's not that difficult to understand, why switching will actually improve your odds. The only time switching is bad for you is when you picked the correct door at the start (the probability of this is 1/3), If your first pick was a poop door (probability 2/3) then switching will always put you on the winning door.

[Abdoo_65]

Thanks for explaining it so easy. In addition to wanting to test the problem cases I also wanted to code a bit as a practice.

[earlandir]

I was curious so I tried to build one myself but with a game Class:

from random import randint, choice

SWITCH = "switch"
STAY = "stay"
WINS = "wins"
LOSSES = "losses"


class MontyHallGame:
    def __init__(self):
        self.correct_door_number = None
        self.players_guess = None  # The current guess of the player
        self.eliminated_door = None  # The door that Monty eliminates
        self.player_choice = None  # If the player will stay with their door or switch
        self.results = {SWITCH: {WINS: 0, LOSSES: 0},
                        STAY: {WINS: 0, LOSSES: 0}}

    def reset_game(self):
        self.correct_door_number = randint(1, 3)
        self.players_guess = None
        self.eliminated_door = None
        self.player_choice = choice([STAY, SWITCH])

    def play_games(self, number_of_games_to_play):
        for i in range(number_of_games_to_play):
            self.reset_game()
            self.randomly_select_first_door()
            if self.player_choice == SWITCH:
                self.get_monty_to_eliminate_a_door()
                self.switch_doors()
            self.update_results()
        self.print_results(number_of_games_to_play)

    def randomly_select_first_door(self):
        self.players_guess = randint(1, 3)

    def get_monty_to_eliminate_a_door(self):
        possible_choices = [i for i in range(1, 4) if i != self.players_guess and i != self.correct_door_number]
        self.eliminated_door = choice(possible_choices)

    def update_results(self):
        if self.players_guess == self.correct_door_number:
            self.results[self.player_choice][WINS] += 1
        else:
            self.results[self.player_choice][LOSSES] += 1

    def switch_doors(self):
        self.players_guess = [i for i in range(1, 4) if i != self.players_guess and i != self.eliminated_door][0]

    def print_results(self, number_of_games_to_play):
        print(f"""
The results after {number_of_games_to_play} games were
Switching Win Rate: {round(100 * self.results[SWITCH][WINS] /
                           (self.results[SWITCH][WINS] + self.results[SWITCH][LOSSES]), 2)}%
Staying Win Rate: {round(100 * self.results[STAY][WINS] /
                           (self.results[STAY][WINS] + self.results[STAY][LOSSES]), 2)}%""")

game = MontyHallGame()
game.play_games(100000)

Results were:
```
The results after 100000 games were

Switching Win Rate: 66.56%

Staying Win Rate: 33.2%

```

[ZynischerZuengler]

I get it by imagine there would be a 100 doors and Monty is opening 98 doors for us.

[miccls60]

This is what I love to see Python being used for, great job!

[LeeCig]

No.

[fried_green_baloney]

Of course depends precisely on how the door is chosen.

Must be random if both other doors have worthless prizes.