# The Topology of Poker

arXiv: https://arxiv.org/abs/2305.02023 · HTML: https://mlsanity.com/paper/2305.02023/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2023.

## Built on by (most cited first, 1 of 1)

- [A mathematical theory of balancing relational generalization and memorization](https://mlsanity.com/paper/2605.22972/) (2026)

## Abstract (arXiv)

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.