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Dynamic programming and gambling models

1974
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Advances in Applied Probability
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Dynamic programming is used to solve some simple gambling models. In particular we consider the situation where an individual may bet any integral amount not greater than his fortune and he will win this amount with probability p or lose it with probability 1 — p. It is shown that if p ≧ ½ then the timid strategy (always bet one dollar) both maximizes the probability of ever reaching any preassigned fortune, and also stochastically maximizes the time until the bettor becomes broke. Also, if p ≦

doi:10.1017/s0001867800040027
fatcat:gp3fk26ggvdblpl3e5etan7cga