Pith Number

pith:JJ7C4AL5

pith:2026:JJ7C4AL5NIGWIUPC75DVEPW2YB

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Dicey Games: Shared Sources of Randomness in Distributed Systems

K. S. Thejaswini, L\'eonard Brice, Thomas A. Henzinger

In the four-player Matching Pennies game, a team using only pairwise shared randomness sources can win with probability strictly above one quarter.

arxiv:2601.18303 v2 · 2026-01-26 · cs.GT · cs.LO · cs.MA

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

47 extracted · 47 resolved · 0 Pith anchors

[1] LExCI: A framework for reinforcement learning with embedded sys- tems 2021 · doi:10.1007/s10489-

[2] Ricardo Alonso and Odilon Câmara. 2016. Persuading voters.American Economic Review106, 11 (2016), 3590–3605 2016

[3] Robert J. Aumann. 1974. Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics1, 1 (1974), 67–96. doi:10.1016/0304-4068(74) 90037-8 1974 · doi:10.1016/0304-4068(74

[4] Robert J Aumann. 1974. Subjectivity and correlation in randomized strategies. Journal of mathematical economics1, 1 (1974), 67–96 1974

[5] R. J. Aumann and J. H. Dreze. 1974. Cooperative games with coalition structures. Int. J. Game Theory3, 4 (Dec. 1974), 217–237. doi:10.1007/BF01766876 1974 · doi:10.1007/bf01766876

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Randomise Alone, Reach as a Team

Receipt and verification

First computed	2026-05-18T03:09:24.295906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a7e2e017d6a0d6451e2ff47523edac06dcb047f7b15d6ba61d0da6328c4fce0

Aliases

arxiv: 2601.18303 · arxiv_version: 2601.18303v2 · doi: 10.48550/arxiv.2601.18303 · pith_short_12: JJ7C4AL5NIGW · pith_short_16: JJ7C4AL5NIGWIUPC · pith_short_8: JJ7C4AL5

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JJ7C4AL5NIGWIUPC75DVEPW2YB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4a7e2e017d6a0d6451e2ff47523edac06dcb047f7b15d6ba61d0da6328c4fce0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d36a237c5fd29b8efa1eca74f1636261daf7e70c7c9f5a1c75d5142cd2ee7e7",
    "cross_cats_sorted": [
      "cs.LO",
      "cs.MA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-01-26T09:33:28Z",
    "title_canon_sha256": "f53620497ab05eb2c772a011e04a9b92c6fc749f8adb4d85e86a84d7710344df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.18303",
    "kind": "arxiv",
    "version": 2
  }
}