Dicey Games: Shared Sources of Randomness in Distributed Systems
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.
Keywords
Cite
@article{arxiv.2601.18303,
title = {Dicey Games: Shared Sources of Randomness in Distributed Systems},
author = {Léonard Brice and Thomas A. Henzinger and K. S. Thejaswini},
journal= {arXiv preprint arXiv:2601.18303},
year = {2026}
}
Comments
16 pages, 9 figures. To be published at LICS 2026