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.

在存在成功的投注策略的情况下，假设轮盘赌的结果并非完全随机。是否存在一种成功的“可分离”策略，即该策略不使用投注红色赢得的收益来投注黑色，反之亦然？我们从算法的角度研究这个问题，并观察到每个策略M都可以由一个可分离的策略替代，该策略可以从M计算并在M的任何结果序列上都是成功的是成功的。然后，我们考虑混合情况，并显示：（a）存在可分离策略的有效混合，该混合成功地在每个有效Hausdorff尺寸小于1/2的赌场序列中成功；（b）存在有效Hausdorff尺寸1/2的娱乐场序列，在该序列上没有有效的可分离策略组合。最后，我们将（b）扩展到更通用的策略类别。