{"paper":{"title":"Dicey Games: Shared Sources of Randomness in Distributed Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In the four-player Matching Pennies game, a team using only pairwise shared randomness sources can win with probability strictly above one quarter.","cross_cats":["cs.LO","cs.MA"],"primary_cat":"cs.GT","authors_text":"K. S. Thejaswini, L\\'eonard Brice, Thomas A. Henzinger","submitted_at":"2026-01-26T09:33:28Z","abstract_excerpt":"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 frame"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"When each pair of team players shares a source of randomness, the team can win with probability higher than 1/4 in the 4-player Matching Pennies game against the Devil.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The model assumes that the only coordination mechanism available to the team is the allocation of shared randomness sources and that all choices occur simultaneously with no additional communication channels.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Dicey Games characterize optimal strategies and complexity for teams using pairwise or limited shared randomness, proving they can exceed 1/4 win probability in a 4-player matching-pennies game against an adversary.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In the four-player Matching Pennies game, a team using only pairwise shared randomness sources can win with probability strictly above one quarter.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e59624939da874efc7432adf1e850a11c48d504315db805010a2b7f782038166"},"source":{"id":"2601.18303","kind":"arxiv","version":2},"verdict":{"id":"d4098411-93aa-4ace-9013-df35168719a5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:19:30.183099Z","strongest_claim":"When each pair of team players shares a source of randomness, the team can win with probability higher than 1/4 in the 4-player Matching Pennies game against the Devil.","one_line_summary":"Dicey Games characterize optimal strategies and complexity for teams using pairwise or limited shared randomness, proving they can exceed 1/4 win probability in a 4-player matching-pennies game against an adversary.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The model assumes that the only coordination mechanism available to the team is the allocation of shared randomness sources and that all choices occur simultaneously with no additional communication channels.","pith_extraction_headline":"In the four-player Matching Pennies game, a team using only pairwise shared randomness sources can win with probability strictly above one quarter."},"references":{"count":47,"sample":[{"doi":"10.1007/s10489-","year":2021,"title":"LExCI: A framework for reinforcement learning with embedded sys- tems","work_id":"ed1decee-4659-47d2-ad8f-ffb5e7cd9194","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Ricardo Alonso and Odilon Câmara. 2016. 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Game Theory3, 4 (Dec. 1974), 217–237. doi:10.1007/BF01766876","work_id":"3b332ee3-af18-46be-aadd-056d3d8354df","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":47,"snapshot_sha256":"e14e88517168afc8a09b57075b3bc88aaf585b599fd2659326cc689bee0d10fe","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"299f11893d956988c1953433bbda177e59198b20fc04fa171c174bca358a0edc"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}