A non-terminating game of beggar-my-neighbor
File(s)
Published 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 Issued
2025-10-01
Date Acceptance
2024-11-25
Citation
American Mathematical Monthly, 2025, 132 (10), pp.978-994
ISSN
0002-9890
Publisher
Taylor and Francis Group
Start Page
978
End Page
994
Journal / Book Title
American Mathematical Monthly
Volume
132
Issue
10
Copyright Statement
© 2025 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
License URL
Identifier
10.1080/00029890.2025.2558484
Publication Status
Published
Rights Embargo Date
10000-01-01
Date Publish Online
2025-10-20