TY - JOUR

T1 - The topology of poker

AU - Bartholdi, L

AU - Mikhailov, R

PY - 2026/1

Y1 - 2026/1

N2 - 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.

AB - 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.

KW - Poker

KW - Texas Hold'em

KW - Simplicial homology

KW - Homological dimension

UR - https://www.mendeley.com/catalogue/09bc2f95-8925-3552-a2f2-7e06f9bbc04e/

U2 - 10.1016/j.geb.2025.09.013

DO - 10.1016/j.geb.2025.09.013

M3 - Article

VL - 155

SP - 1

EP - 9

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

ER -