montyhall_pandas.py

import random
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import pandas as pd

# Monty Hall simulation function
def monty_hall_simulation(trials=1000, switch=True):
    results = []
    for _ in range(trials):
        prize_door = random.randint(0, 2)  # Randomly place the car behind one of the doors
        chosen_door = random.randint(0, 2)  # Player's initial choice
        doors = [0, 1, 2]

        # Doors available for Monty to open (excluding player's choice and prize door)
        available_doors = [door for door in doors if door != chosen_door and door != prize_door]
        monty_door = random.choice(available_doors)

        # If the player chooses to switch, select the remaining door
        if switch:
            chosen_door = [door for door in doors if door != chosen_door and door != monty_door][0]

        win = (chosen_door == prize_door)  # Determine if the player won
        results.append((chosen_door, prize_door, monty_door, win))

    return pd.DataFrame(results, columns=['chosen_door', 'prize_door', 'monty_door', 'win'])

# Generate data
trials = 1000

df_switch = monty_hall_simulation(trials=trials, switch=True)  # Data for switching strategy
df_stay = monty_hall_simulation(trials=trials, switch=False)  # Data for staying strategy

# 1. Analyze the pattern of doors opened by Monty
plt.figure(figsize=(8, 5))
sns.countplot(x=df_switch["monty_door"], palette="coolwarm")
plt.xticks([0, 1, 2], labels=["Door 1", "Door 2", "Door 3"])
plt.xlabel("Door Opened by Monty")
plt.ylabel("Frequency")
plt.title("Monty's Door Choice Distribution")
plt.show()

# 2. Compare player's choice vs car location (Switching strategy)
plt.figure(figsize=(8, 5))
sns.heatmap(pd.crosstab(df_switch["chosen_door"], df_switch["prize_door"]),
            annot=True, fmt="d", cmap="YlGnBu")
plt.xlabel("Car Location")
plt.ylabel("Player's Final Choice")
plt.title("Player's Choice vs Car Location (Switch Strategy)")
plt.show()

# 3. Compare player's choice vs car location (Staying strategy)
plt.figure(figsize=(8, 5))
sns.heatmap(pd.crosstab(df_stay["chosen_door"], df_stay["prize_door"]),
            annot=True, fmt="d", cmap="OrRd")
plt.xlabel("Car Location")
plt.ylabel("Player's Final Choice")
plt.title("Player's Choice vs Car Location (Stay Strategy)")
plt.show()