Prophet compared to gambler: additive inequalities for transforms of sequences of random variables

Frans A. Boshuizen

Statistics & Probability Letters, 1996, vol. 29, issue 1, 23-32

Abstract: Additive comparisons are given between optimal expected gains of a prophet and a gambler. A gambler knows only the past and the present and a prophet is a player with complete foresight. The optimal expected gains are obtained by betting on differences of consecutive uniformly bounded random variables. For example, if the random variables are i.i.d. and [0,1]-valued, then the difference between the prophet and the gambler is at most n/16 for a game of length n, and the bound n/16 is the best possible.

Date: 1996
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