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.

翻译：考虑一个三人团队与魔鬼对抗的四人版“匹配硬币”游戏。每位玩家同时说出“正面”或“反面”。若四人的选择完全一致，则团队获胜；否则魔鬼获胜。若所有团队成员独立随机选择，其获胜概率为1/8；若所有玩家共享同一随机源，则获胜概率可达1/2。那么当每对团队成员共享一个随机源时会发生什么？团队能否获得高于1/4的胜率？令人惊讶（且非平凡）的答案是肯定的！本文提出“骰子博弈”这一形式化框架，其研究动机源于对具有共享随机源的分布式系统的分析（前述示例即为具体案例）。我们刻画了骰子博弈中最优策略的存在性、表示形式与计算复杂度，并深入研究了在团队内优化分配有限随机源的问题。