The Topology of Poker
Algebraic Topology
2025-10-14 v3 Computer Science and Game Theory
Abstract
We examine the complexity of the ``Texas Hold'em'' variant of poker from a topological perspective. We show that there exists a natural simplicial complex governing the multi-way winning probabilities between various hands, and that this simplicial complex contains -dimensional spheres as induced subcomplexes. We deduce that evaluating the strength of a pair of cards in Texas Hold'em is an intricate problem, and that even the notion of who is bluffing against whom is ill-defined in some situations.
Cite
@article{arxiv.2305.02023,
title = {The Topology of Poker},
author = {Laurent Bartholdi and Roman Mikhailov},
journal= {arXiv preprint arXiv:2305.02023},
year = {2025}
}
Comments
Added URL of data; corrected remark about contractibility