But you can make money with his second Martingale which does not contradict Doob's theorem becouse the Martingale is not bounded. +The Father of Martingales Joe Doob proved that If S(0), (1), (2),.. is a bounded martingale and T is a stopping time then the expected value of S(T) = S(0) so you can not expect to make money with a bounded Martingale.