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A generalized martingale betting strategy. (English) Zbl 1183.60017

Summary: A generalized martingale betting strategy is analyzed for which bets are increased by a factor of \(m>1\) after each loss, but return to the initial bet amount after each win. The average amount bet and the average final fortune are derived for sequences of \(n\) bets, for the number of bets \(T\) that results in the first win, and for \(\min(T,n)\).

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60D05 Geometric probability and stochastic geometry