Does this not simulate the problem in python?

    import random
    coin = ["heads", "tails"]
    guess = "heads"
    guesses_correct = 0
    wakings = 0

    n = 1_000_000
    for _ in range(n):
        actual = random.choice(coin)
        if actual == guess:
            wakings += 1
            guesses_correct += 1
        else:
            wakings += 2

    print(f"guessed correctly: {guesses_correct/wakings:0.2f}%")