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Monty Hall Problem Simulation in Python
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#!/usr/bin/env python | |
# coding: utf-8 | |
# Monty Hall Paradox Simulation in Python | |
from random import randint | |
import matplotlib.pyplot as plt | |
import matplotlib.ticker as ticker | |
# This function will generate random rounds for our game. Each round consists of 3 doors. Only one of the doors is correct, other two are wrong. | |
def generate_game(n: int): | |
game = [] | |
for _ in range(n): | |
doors = [False] * 3 | |
winner = randint(0, 2) # Choose winning door by random | |
doors[winner] = True | |
game.append(doors) | |
return game | |
# This is a helper function that takes a list of 3 doors, looks at the second and third door, and then opens the one with goat (i.e. wrong door). This simulates a host with knowledge of what is behind the doors. | |
def reveal_goat(doors): | |
# Get from doors 2 and 3 the one which contains goat. | |
for i in range(1, 3): | |
if doors[i] == False: | |
return i | |
# **Simulate random choice** | |
# | |
# Simulate situation where the player randomly chooses whether to keep his initial choice or switch his choice. | |
def simulate_random_choice(game: list): | |
wins = 0 | |
attempts = 0 | |
history = [] | |
for doors in game: | |
attempts += 1 | |
# Host reveals a door with goat. | |
goat = reveal_goat(doors) | |
# Player randomly chooses whether to keep initial choice or switch. | |
new_choice = randint(0, 1) | |
final_choice = 0 if new_choice == 0 else 2 if goat == 1 else 1 | |
if (doors[final_choice] == True): | |
wins += 1 | |
history.append(wins / attempts) | |
return wins, history | |
# **Simulate initial choice** | |
# | |
# Simulate situation where the player *only* keeps his initial choice and never switches. | |
def simulate_keep_choice(game: list): | |
wins = 0 | |
attempts = 0 | |
history = [] | |
for doors in game: | |
attempts += 1 | |
# User does not switch game. | |
if (doors[0] == True): | |
wins += 1 | |
history.append(wins / attempts) | |
return wins, history | |
# **Simulate switch choice** | |
# | |
# Simulate situation where the player switches his choice everytime. | |
def simulate_switch_choice(game: list): | |
wins = 0 | |
attempts = 0 | |
history = [] | |
for doors in game: | |
attempts += 1 | |
# Host reveals a door with goat. | |
goat = reveal_goat(doors) | |
# Player switches his doors (here he chooses the non-opened doors). | |
new_choice = 1 if goat == 2 else 2 | |
if (doors[new_choice] == True): | |
wins += 1 | |
history.append(wins / attempts) | |
return wins, history | |
# Now the computing begins. This generates $n$ random games for simulation. | |
game = generate_game(1000) | |
# Run the three simulations defined above for the generated game. | |
wins_random, history_random = simulate_random_choice(game) | |
wins_keep, history_keep = simulate_keep_choice(game) | |
wins_switch, history_switch = simulate_switch_choice(game) | |
# And finally, create some fancy graph so we can actually see the result. | |
plt.figure(figsize=(12,8)) | |
plt.plot(history_random, 'r', label="Random switch") | |
plt.plot(history_keep, 'g', label="Keep initial") | |
plt.plot(history_switch, 'b', label="Only switch") | |
plt.legend(loc='upper right') | |
plt.ylim(0, 1.0) | |
plt.xlim(0, 1000) | |
plt.ylabel("Chance", fontsize=16) | |
plt.gca().yaxis.set_major_formatter(ticker.PercentFormatter(xmax=1.0)) | |
plt.xlabel("Iterations", fontsize=16) | |
plt.grid(True) | |
plt.show() | |
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