Monte Carlo'ing a modified monty python variant

modified_monty.py

"""Monte Carlo'ing Hillogram's Monty Hall Variant

Hillelogram on twitter came up with a surprising Monty Hall Variant: https://twitter.com/hillelogram/status/1175125663247998978

[BEGIN EDIT]

@hillelogram gives credit to this paper https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.33.3.144

/u/edderiofer on reddit pointed out that this is in fact the "Monty Crawl" variant from here: http://www.probability.ca/jeff/writing/montyfall.pdf

[END EDIT]

This source code is modified from its original version here: https://blog.teamtreehouse.com/modeling-monty-hall-problem-python
"""
from collections import namedtuple
import random

# Create an easy-to-return and easy-to-inspect data
# structure for Game results.
Results = namedtuple('Results', ['won', 'initial_door', 'monty_door'])


class Door:

    def __init__(self, location):
        self.location = location
        self.prize = False
        self.opened = False


class Game:
    """Monty Hall, always switch"""

    def __init__(self, monty_selection_func):
        self.monty_selection_func = monty_selection_func
        self.chosen_door = None
        self.initial_door = None
        self.monty_door = None
        self.doors = [
            Door(i) for i in range(1, 4)
        ]
        # Pick a random door and give it a prize
        random.choice(self.doors).prize = True

    def pick_door(self):
        self.initial_door = random.choice(self.doors)

    def open_false_door(self):
        # Get the non-chosen doors
        available_doors = [door for door in self.doors
                           if door is not self.initial_door
                           and not door.prize]
        self.monty_door = self.monty_selection_func(available_doors)
        self.monty_door.opened = True


    def switch_doors(self):
        # Always Switch
        available_door = [door for door in self.doors
                          if door is not self.initial_door
                          and not door.opened][0]
        self.chosen_door = available_door

    @classmethod
    def play(cls, monty_selection_func):
        game = cls(monty_selection_func)
        game.pick_door()
        game.open_false_door()
        game.switch_doors()

        won = game.chosen_door.prize
        initial_door = game.initial_door.location
        monty_door = game.monty_door.location
        return Results(won, initial_door, monty_door)


def monty_chooses_lowest(doors):
    return doors[0]


def monty_chooses_random(doors):
    return random.choice(doors)

# Play play 1e6 runs of the game to get significant numbers
num_simulations = int(1e6)
games = [Game.play(monty_chooses_lowest) for _ in range(num_simulations)]

# Find Games where we select 2 and monty selects 1
scenario_games = [game for game in games if game.initial_door == 2 and game.monty_door == 1]
wins = sum(x.won for x in scenario_games)
num_scenario_games = len(scenario_games)
win_percentage = 100 * wins / num_scenario_games
print("Won {:.2f}% when monty chose the lowest non-prize door: {:,} out of {:,}".format(win_percentage, wins, num_scenario_games))


# Play play 1e6 runs of the game to get significant numbers
num_simulations = int(1e6)
games = [Game.play(monty_chooses_random) for _ in range(num_simulations)]

# Find Games where we select 2 and monty selects 1
scenario_games = [game for game in games if game.initial_door == 2 and game.monty_door == 1]
wins = sum(x.won for x in scenario_games)
num_scenario_games = len(scenario_games)
win_percentage = 100 * wins / num_scenario_games
print("Won {:.2f}% when monty chooses random non-prize door: {:,} out of {:,}".format(win_percentage, wins, num_scenario_games))