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.

翻译：我们从拓扑视角审视“德州扑克”变种的复杂性。研究表明，存在一个天然的单复形结构，用以刻画不同手牌之间的多向胜率关系，且该单复形包含作为诱导子复形的$4$维球面。由此推断，评估德州扑克中底牌牌力是复杂问题，甚至在部分情境下“谁对谁诈唬”这一概念本身也缺乏明确定义。