Back to Search
Start Over
Monotonous betting strategies in warped casinos
- Publication Year :
- 2018
-
Abstract
- 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.
- Subjects :
- Mathematics - Logic
Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1807.04635
- Document Type :
- Working Paper