A Non-Terminating Game of Beggar-My-Neighbor
Combinatorics
2025-10-28 v1
Abstract
We demonstrate the existence of a non-terminating game of Beggar-My-Neighbor, discovered by lead author Brayden Casella. We detail the method for constructing this game and identify a cyclical structure of 62 tricks that is reached by 30 distinct starting hands. We further present a short history of the search for this solution since the problem was posed, and a record of previously found longest terminating games. The existence of this non-terminating game provides a solution to a long-standing question which John H. Conway called an `anti-Hilbert problem.'
Keywords
Cite
@article{arxiv.2403.13855,
title = {A Non-Terminating Game of Beggar-My-Neighbor},
author = {Brayden Casella and Philip M. Anderson and Michael Kleber and Richard P. Mann and Reed Nessler and William Rucklidge and Samuel G. Williams and Nicolas Wu},
journal= {arXiv preprint arXiv:2403.13855},
year = {2025}
}