Betting strategies with bounded splits
Information Theory
2023-01-02 v1 math.IT
Abstract
We show that a pair of Kolmogorov-Loveland betting strategies cannot win on every non-Martin-L\"of random sequence if either of the two following conditions is true: (I) There is an unbounded computable function such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all , bet on at most positions among the first positions of the sequence. (II) There is a sublinear function such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all , bet on at least positions among the first positions of the sequence.
Cite
@article{arxiv.2212.14279,
title = {Betting strategies with bounded splits},
author = {Tomislav Petrović},
journal= {arXiv preprint arXiv:2212.14279},
year = {2023}
}