A Non-Terminating Game of Beggar-My-Neighbor

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...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Casella, Brayden, Anderson, Philip M, Kleber, Michael, Mann, Richard P, Reed Nessler, Rucklidge, William, Williams, Samuel G, Wu, Nicolas
Format: Article
Language:English
Subjects:
Games
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Summary: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.'
ISSN:2331-8422