Probabilistic vs deterministic gamblers
Logic
2021-12-09 v1
Abstract
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence is a.e.\ computably random if there is no probabilistic computable strategy which is total and succeeds on for positive measure of oracles. Using the fireworks technique we construct a sequence which is partial computably random but not a.e.\ computably random. We also prove the separation between a.e.\ computable randomness and partial computable randomness, which happens exactly in the uniformly almost everywhere dominating Turing degrees.
Cite
@article{arxiv.2112.04460,
title = {Probabilistic vs deterministic gamblers},
author = {Laurent Bienvenu and Valentino Delle Rose and Tomasz Steifer},
journal= {arXiv preprint arXiv:2112.04460},
year = {2021}
}