simulate_game.py

import numpy as np
import matplotlib.pyplot as plt

def simulate_game():
    tosses = 0
    while np.random.choice(['H', 'T']) == 'T':
        tosses += 1
    return 2**(tosses + 1)

# Simulate the game 10,000 times to approximate the expected payoff
simulations = [simulate_game() for _ in range(10000)]
expected_payoff = np.mean(simulations)

print(f'Approximate Expected Payoff: {expected_payoff}')