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arXiv · 2601.18303

Dicey Games: Shared Sources of Randomness in Distributed Systems

Léonard Brice·Thomas A. Henzinger·K. S. Thejaswini
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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.

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Léonard Brice, Thomas A. Henzinger, K. S. Thejaswini. 2026-01-26. Dicey Games: Shared Sources of Randomness in Distributed Systems. https://arxiv.org/abs/2601.18303

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