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

Monotonous betting strategies in warped casinos