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：我们从拓扑学视角审视“德州扑克”变体的复杂性。我们证明存在一个自然的单纯复形，它制约着不同手牌之间的多方获胜概率，并且该单纯复形包含作为诱导子复形的4维球面。由此推论，评估德州扑克中一手牌的实力是一个复杂问题，甚至在某些情况下，“谁在诈唬谁”这一概念本身都缺乏明确定义。