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Probabilistic vs Deterministic Gamblers Bienvenu, Laurent Delle Rose, Valentino Steifer, Tomasz Algorithmic randomness Martingales Probabilistic computation Almost everywhere domination 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 X is a.e. computably random if there is no probabilistic computable strategy which is total and succeeds on X 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Laurent Bienvenu and Valentino Delle Rose and Tomasz Steifer 2022 Is Part Of LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2022.11 urn:nbn:de:0030-drops-158210 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.11 eng https://creativecommons.org/licenses/by/4.0/legalcode