dice.py

import random

def simulate_game():
    """Simulate a single game where A and B throw the die alternately."""
    while True:
        # Player A's turn
        if random.randint(1, 6) == 6:
            return "A"
        
        # Player B's turn
        if random.randint(1, 6) == 6:
            return "B"

def estimate_probability(num_trials):
    """Estimate the probability of the first player (A) winning."""
    a_wins = 0
    
    for _ in range(num_trials):
        if simulate_game() == "A":
            a_wins += 1
    
    return a_wins / num_trials

# Number of trials to run the simulation
num_trials = 1000000  # 1 million trials for better accuracy

# Estimate the probability
probability_A_wins = estimate_probability(num_trials)

print(f"Estimated probability that A wins: {probability_A_wins:.5f}")