Bavly, Gilad and Peretz, Ron
(2013)
How to gamble against all odds.
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The London School of Economics and Political Science, London, UK.
Abstract
We compare the prediction power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an Amartingale.A set of reals B anticipates a set A, if for every Amartingale there is a countable set of Bmartingales, such that on every binary sequence on which the Amartingale gains an infinite amount at least one of the Bmartingales gains an infinite amount, too. We show that for a wide class of pairs of sets A and B, B anticipates A if and only if A is a subset of the closure of rB, for some r > 0, e.g., when B is well ordered (has no leftaccumulation points). Our results answer a question posed by Chalcraft et al. (2012).
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