The famous Bayes table game. Computes the probability that Bob wins knowing the score is 5-3 for Alice.

bayesTableGame.py

import numpy as np
import time

def estimate_prob_bob_win(n_situations, seed=None, timeout=10):
    rng = np.random.default_rng(seed)

    bob_wins = 0
    n_games = 0

    t_start = time.time()
    while(True):
        p = rng.random()
        score_alice = rng.binomial(8, p)
        if score_alice == 5:
            n_games += 1
            score_alice_restant = rng.binomial(3, p)
            if score_alice_restant == 0:
                bob_wins += 1
        if n_games == n_situations:
            break
        if time.time() - t_start > timeout:
            print(f"Warning ! Timeout after {n_games} games")
            break
    return bob_wins / n_games


if __name__ == "__main__":
    probas = [estimate_prob_bob_win(1000) for _ in range(100)]
    probas = np.array(probas)
    print(f"P(Bob gagne | A = 5, B = 3) = {probas.mean()}")