How to gamble if you’re in a hurry. (English) Zbl 1269.91026

Summary: The beautiful theory of statistical gambling, started by L. E. Dubins and L. J. Savage [How to gamble if you must. Inequalities for stochastic processes. New York etc.: McGraw-Hill Book Company (1965; Zbl 0133.41402); 2nd ed. New York: Dover Publications, Inc. (1976; Zbl 0359.60002)] (for subfair games) and continued by J. L. Kelly [“A new interpretation of information rate”, Bell Syst. Tech. J. 35, 917–926 (1956)] and L. Breiman [in: Proc. 4th Berkeley Symp. Math. Stat. Probab. 1, 65–78 (1961; Zbl 0109.36803)] (for superfair games), has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible and that our life is indefinitely long. Here, we study these fascinating problems from a purely discrete, finitistic and computational viewpoint, using both symbol-crunching and number-crunching (and simulation just for checking purposes).


91A60 Probabilistic games; gambling


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