Work

The topology of poker

Year: 2025

Type: article

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.

Source: Games and Economic Behavior

DOI: 10.1016/j.geb.2025.09.013

Authors: Laurent Bartholdi, Roman Mikhailov

Institutions: Institut Camille Jordan, St Petersburg University

Language: English

Topic: Game Theory and Applications

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funder: FP7 Ideas: European Research Council