Monotonous betting strategies in warped casinos

Barmapalias, George, Fang, Nan and Lewis-Pye, Andrew (2020) Monotonous betting strategies in warped casinos. Information and Computation, 271. ISSN 0890-5401

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Abstract

Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on red in order to bet on black, and vice-versa? We study this question from an algorithmic point of view and observe that every strategy M can be replaced by a separable strategy which is computable from M and successful on any outcome-sequence where M is successful. We then consider the case of mixtures and show: (a) there exists an effective mixture of separable strategies which succeeds on every casino sequence with effective Hausdorff dimension less than 1/2; (b) there exists a casino sequence of effective Hausdorff dimension 1/2 on which no effective mixture of separable strategies succeeds. Finally we extend (b) to a more general class of strategies.

Item Type:	Article
Official URL:	https://www.journals.elsevier.com/information-and-...
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	14 Oct 2019 09:54
Last Modified:	12 Dec 2024 01:55
URI:	http://eprints.lse.ac.uk/id/eprint/102082

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