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.
Keywords
Cite
@article{arxiv.2111.02053,
title = {Transfinite game values in infinite draughts},
author = {Joel David Hamkins and Davide Leonessi},
journal= {arXiv preprint arXiv:2111.02053},
year = {2021}
}
Comments
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/transfinite-game-values-in-infinite-draughts