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arXiv · 1210.5968

A pair of universal sequence-set betting strategies

Tomislav Petrović
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Abstract

We introduce the sequence-set betting game, a generalization of An. A. Muchnik's non-monotonic betting game. Instead of successively partitioning the infinite binary strings by their value of a bit at a chosen position, as in the non-monotonic game, the player is allowed to partition the strings into any two clopen sets with equal measure. We show that, while there is no single computable sequence-set betting strategy that predicts all non-Martin-Löf random strings, we can construct two strategies such that every non-Martin-Löf random string is predicted by at least one of them.

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Tomislav Petrović. 2015-12-22. A pair of universal sequence-set betting strategies. https://arxiv.org/abs/1210.5968

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