Betting strategies with bounded splits

Tomislav Petrović

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arXiv · 2212.14279

Betting strategies with bounded splits

Tomislav Petrović

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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 $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at most $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence. (II) There is a sublinear function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at least $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence.

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Tomislav Petrović. 2022-12-29. Betting strategies with bounded splits. https://arxiv.org/abs/2212.14279

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