A non-terminating game of beggar-my-neighbor
File(s)BMN_accepted.pdf (362.69 KB)
Accepted version
Author(s)
Type
Journal Article
Abstract
We demonstrate the existence of a non-terminating game of Beggar-My-Neighbor.
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.’
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.’
Date Acceptance
2024-11-25
Citation
American Mathematical Monthly
ISSN
0002-9890
Publisher
Taylor and Francis Group
Journal / Book Title
American Mathematical Monthly
Copyright Statement
Subject to copyright. This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
Rights Embargo Date
10000-01-01