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arXiv · 2305.02023

The Topology of Poker

Laurent Bartholdi·Roman Mikhailov
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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 $4$-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.

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BibTeXRIS

Laurent Bartholdi, Roman Mikhailov. 2023-05-03. The Topology of Poker. https://doi.org/10.1016/j.geb.2025.09.013

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