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.