PreprintCC BY 4.0arXiv
Computer-Assisted Results for n-Sided Non-Transitive Dice Taking Face Values in [n]
Abstract
We consider non-transitivity among dice with n sides restricted to taking face values in the set {1,…,n}. We give a computer-assisted proof that n=6 is the smallest n≥3 which admits a non-transitive cycle of maximum length n with uniform and minimal winning advantage. For n=6, we identify the two unique non-transitive cycles of length 6. We present computational evidence supporting a conjecture that n=6 is the largest n≥3 which admits a non-transitive cycle of maximum length n with uniform and minimal winning advantage.
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BibTeX
@misc{easlick2026computerassisted,
title = {{Computer-Assisted Results for \(n\)-Sided Non-Transitive Dice Taking Face Values in \([n]\)}},
author = {Terry Easlick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40321},
eprint = {2610.40321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40321},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Computer-Assisted Results for n-Sided Non-Transitive Dice Taking Face Values in [n]
AU - Terry Easlick
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40321
UR - https://arxiv.org/abs/2610.40321
AB - We consider non-transitivity among dice with n sides restricted to taking face values in the set {1,…,n}. We give a computer-assisted proof that n=6 is the smallest n≥3 which admits a non-transitive cycle of maximum length n with uniform and minimal winning advantage. For n=6, we identify the two unique non-transitive cycles of length 6. We present computational evidence supporting a conjecture that n=6 is the largest n≥3 which admits a non-transitive cycle of maximum length n with uniform and minimal winning advantage.
ER -