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Dicey Games: Shared Sources of Randomness in Distributed Systems

Authors Léonard Brice , Thomas A. Henzinger , K. S. Thejaswini

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ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Mathematics of computing → Distribution functions
  • Theory of computation → Random network models
Keywords
  • Concurrent games
  • Shared randomness
  • Topology
  • Algebraic Geometry

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Abstract

Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team players randomise independently, they win with probability 1/8; if all players share a common source of randomness, they win with probability 1/2. What happens when each pair of team players shares a source of randomness? Can the team do better than win with probability 1/4? The surprising (and nontrivial) answer is yes!
We introduce Dicey Games, a formal framework motivated by the study of distributed systems with shared sources of randomness (of which the above example is a specific instance). We characterise the existence, representation and computational complexity of optimal strategies in Dicey Games, and we study the problem of allocating limited sources of randomness optimally within a team.

Cite As Get BibTex

Léonard Brice, Thomas A. Henzinger, and K. S. Thejaswini. Dicey Games: Shared Sources of Randomness in Distributed Systems. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 23:1-23:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.LICS.2026.23

Author Details

Léonard Brice
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
Thomas A. Henzinger
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
K. S. Thejaswini
  • Université libre de Bruxelles, Belgium

Funding

This work was supported in part by the ERC-2020-AdG 101020093 (VAMOS).
  • Brice, Léonard: Part of this work was realised when this author was an FNRS aspirant at Université libre de Bruxelles.
  • Thejaswini, K. S.: Part of this work was realised when this author was a post-doctoral researcher at IST Austria.

Acknowledgements

We thank all our colleagues who took the time to hear our puzzle and wasted several hours of their research time in pursuit of the optimal bounds for the 3-player matching pennies problem.

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