bibkey: easlick2026minimaldice
authors: Terry Easlick
year: 2026
title: "Computer-assisted results for n-sided non-transitive dice taking face values in [n]"
doi: null
url: https://arxiv.org/abs/2610.40321v1
claim: "Conjecture 1 asks whether six is the largest n at least three for which the global maximum length of a simple cycle at the least attainable unconditional strict winning probability above one half equals n."
strata_touched:
  - D5/S3/Combinatorics/Dice/EaslickMinimalAdvantage
  - D5/S3/Combinatorics/Dice/EaslickCycleSeeds
  - D5/S3/Combinatorics/Dice/EaslickPaddedCycles
  - D5/S3/Combinatorics/Dice/EaslickSixBound
license: CC-BY-4.0
triage: anchor

Easlick, minimal-advantage dice cycles

Definitions 1 and 2 use fair independent rolls of nondecreasing n-tuples of labels in [n], allow repeated labels, and identify a die by its sorted tuple. The standard tuple is included in Example 1. Strict wins are unconditional: ties contribute zero and are not removed from the sample space. Cycles have distinct vertices and include their closing edge.

Conjecture 1 is the conjunction S(6) and, for all integers n at least seven, not S(n), where S(n) says the global maximum simple-cycle length is exactly n.

The source cycle data in Appendices G, H, I and J are by Terry Easlick, arXiv:2610.40321v1, licensed under Creative Commons Attribution 4.0 International. The eleven-face and uniformly padded cycles are derived constructions.

Verified locator

URL: https://arxiv.org/abs/2610.40321v1

Pinned source: Terry Easlick, arXiv:2610.40321v1, Definitions 1 and 2, Example 1, Conjecture 1 and Appendices G–J. No DOI is declared.