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How to gamble against all odds

Bavly, Gilad and Peretz, Ron (2013) How to gamble against all odds. The London School of Economics and Political Science, London, UK.

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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 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).

Item Type: Monograph (Working Paper)
Official URL: http://www.lse.ac.uk/maths/home.aspx
Additional Information: © 2013 The Author
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 21 Nov 2013 11:17
URL: http://eprints.lse.ac.uk/54506/

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