Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose. Whenever q > 1/2, the expression 1 − (2 q ) n n > 0. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round. Increasing the size of wager for each round per the martingale system only serves to increase the average loss. In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19) 6 = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19) 6 = 97.8744%.
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