2023/05/03 by Bartholdi, Laurent, Mikhailov, Roman · 1 citation
#Algebraic Topology (math.AT) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.02023
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.