Simulation that shows that with a fair roulette wheel Martingale betting system still has a 50% probability of doubling initial amount of money

double-bet-on-fail-strategy-sim.py

import random

N = 50
p_win = 0.5
num_experiments = 100000

def play_game(N):
    assert N >= 0
    target_N = 2 * N

    # Keep playing until you either lost all of your money or doubled your initial amount
    while 0 < N < target_N:
        assert N >= 0
        next_bet = 1  # always bet 1 at the beggining
        start_N = N

        while next_bet <= N:  # Check if we have enough money to make a bet
            current_bet = next_bet
            N -= current_bet
            assert N >= 0

            # Spin the roulette wheel and observe the outcome (in terms of win or lose)
            won = random.random() <= p_win

            if won:
                N += 2 * current_bet
                assert N == (start_N + 1)  # we always win +1
                break
            else:
                # Follow the strategy. When we lose, double the amount of money and try again
                next_bet *= 2

    assert N in (0, target_N)
    return N != 0

outcomes = [play_game(N) for _ in range(num_experiments)]
print(sum(outcomes) / num_experiments)  # observed average success rate
print((1 - 1/N) ** N)  # invalid prediction