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Probabilistic vs Deterministic Gamblers

Authors Laurent Bienvenu , Valentino Delle Rose , Tomasz Steifer

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Author Details

Laurent Bienvenu
  • LaBRI, CNRS & Université de Bordeaux, France
Valentino Delle Rose
  • Dipartimento di Ingegneria Informatica e Scienze Matematiche, University of Siena, Italy
Tomasz Steifer
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Warszawa, Poland

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Laurent Bienvenu, Valentino Delle Rose, and Tomasz Steifer. Probabilistic vs Deterministic Gamblers. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 11:1-11:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computability
  • Algorithmic randomness
  • Martingales
  • Probabilistic computation
  • Almost everywhere domination


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