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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).

MSC:

91A60 Probabilistic games; gambling

Software:

HIMURIM; PURIM
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References:

[1] Breiman L., Fourth Berkley Symp. Math. Stat. Prob. 1 pp 65– (1961)
[2] Chen R.W., J. Appl. Prob. 42 pp 121– (2005) · Zbl 1137.60323
[3] Kulldorff M., Siam J. Control Optim. 31 (1) pp 52– (1993) · Zbl 0770.90099
[4] Dubins, L.E. and Savage, L.J. 1976. ”Inequalities for Stochastic Processes (How to Gamble If You Must)”. New York: Dover. · Zbl 0359.60002
[5] Feller W., An Introduction to Probability Theory and Its Application 1, 3. ed. (1968) · Zbl 0155.23101
[6] Kelly J.L., Bell Syst. Tech. J. 35 pp 917– (1956)
[7] Maitra A.P., Discrete Gambling and Stochastic Games (1996) · Zbl 0864.90148
[8] Thorp E.O., Beat the Dealer, 2. ed. (1966)
[9] Thorp E.O., J. Am. Statist. Assoc. 61 pp 313– (1966)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.