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Monotonous betting strategies in warped casinos

Barmapalias, George, Fang, Nan and Lewis-Pye, Andrew (2019) Monotonous betting strategies in warped casinos. Information and Computation. ISSN 0890-5401 (In Press)

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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:
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 14 Oct 2019 09:54
Last Modified: 28 Jan 2020 00:13

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