ultraspeed_montyhall_numpy.py

import numpy as np
import time

def monty_hall_numpy(trials=100000000, switch=True):
    """
    Fully vectorized Monty Hall simulation using NumPy for maximum performance.

    Parameters:
        trials (int): Number of games to simulate.
        switch (bool): If True, the player switches doors; otherwise, they stay.

    Returns:
        float: Probability of winning when switching/staying.
    """
    # Step 1: Randomly place the car behind one of the three doors
    prize_doors = np.random.randint(0, 3, trials)  # NumPy generates all at once

    # Step 2: Players make initial random choices
    chosen_doors = np.random.randint(0, 3, trials)

    # Step 3: The host opens a door that is neither the chosen door nor the prize door
    # Create a mask for available doors
    all_doors = np.array([0, 1, 2])  # Three possible doors

    # Vectorized way to choose host door
    host_doors = np.zeros(trials, dtype=int)
    for i in range(3):  # Loop over door numbers (0, 1, 2)
        mask = (chosen_doors != i) & (prize_doors != i)  # Find valid doors for the host to open
        host_doors[mask] = i  # Assign a valid door for the host

    # Step 4: Player switches (if switch=True)
    if switch:
        # The remaining door (not chosen, not opened by the host)
        new_choices = 3 - chosen_doors - host_doors
        chosen_doors = new_choices  # Player switches

    # Step 5: Calculate wins (where chosen door == prize door)
    wins = (chosen_doors == prize_doors)

    return np.mean(wins)  # Probability of winning

# Measure execution time
tic = time.time()

# Run the fully vectorized Monty Hall simulation
win_probability = monty_hall_numpy(trials=100000000, switch=True)

toc = time.time()

# Print results
print(f"Winning probability when switching: {win_probability:.6f}")
print(f"Execution time: {toc - tic:.2f} seconds")