Bavly, Gilad and Peretz, Ron
How to gamble against all odds.
The London School of Economics and Political Science, London, UK.
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 A-martingale.A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales 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 left-accumulation points). Our results answer a question posed by Chalcraft et al. (2012).
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