Transfinite game values in infinite draughts
Abstract
Infinite draughts, or checkers, is played just like the finite game, but on an infinite checkerboard extending without bound in all four directions. We prove that every countable ordinal arises as the game value of a position in infinite draughts. Thus, there are positions from which Red has a winning strategy enabling her to win always in finitely many moves, but the length of play can be completely controlled by Black in a manner as though counting down from a given countable ordinal.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.02053
 arXiv:
 arXiv:2111.02053
 Bibcode:
 2021arXiv211102053H
 Keywords:

 Mathematics  Logic;
 Computer Science  Computer Science and Game Theory;
 Mathematics  Combinatorics;
 03E60;
 91Axx
 EPrint:
 15 pages, 12 figures. Adapted from chapter 3 of the second author's MSc dissertation arXiv:2111.01630, for which he earned a distinction at the University of Oxford in September 2021. Commentary can be made about this article on the first author's blog at http://jdh.hamkins.org/transfinitegamevaluesininfinitedraughts