Let "bankroll" be the amount of money a gambler has at his disposal at any moment, and let "N" be any positive integer. Suppose that he raises his stake to formula_1 when he wins, but does not reduce his stake when he loses. This general pattern is not uncommon among real gamblers, and casinos encourage it by "chipping up" winners (giving them higher denomination chips). Under this betting scheme, it will take at most "N" losing bets in a row to bankrupt him. If his probability of winning each bet is less than 1 (if it is 1, then he is no gambler), he is virtually certain to eventually lose "N" bets in a row, however big "N" is. It is not necessary that he follow the precise rule, just that he increase his bet fast enough as he wins. This is true even if the expected value of each bet is positive.