The topology of poker

Abstract

We introduce a topological invariant of games, based on homotopy theory, that measures their complexity. We examine it in the context of the ``Texas Hold’em'' variant of poker, and show that the invariant’s value is at least 4. 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. The use of higher topological methods to study intransitivity of multi-player games seems new.