  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.
