As the single bets are independent from each other (and from the gambler's expectations), the concept of winning ”streaks” is merely an example of gambler's fallacy, and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated (for instance due to economic cycles and delayed reaction to news of larger market participants), ”streaks” of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems (as trend-following or ”doubling up”). Mathematics portal Escalation of commitment St. Petersburg paradox. ^ a b Michael Mitzenmacher; Eli Upfal (2005), Probability and computing: randomized algorithms and probabilistic analysis , Cambridge University Press, p. 298, ISBN978-0-521-83540-4 , archived from the original on October 13, 2015 ^ Lester E. Dubins; Leonard J. Savage (1965), How to gamble if you must: inequalities for stochastic processes , McGraw Hill ^ Larry Shepp (2006), Bold play and the optimal policy for Vardi's casino, pp 150–156 in: Random Walk, Sequential Analysis and Related Topics , World Scientific ^ Martin, Frank A.
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