Transfinite game values in infinite draughts

In this joint paper with Prof. Joel David Hamkins, we prove that every countable ordinal is realised as the game value of a position in infinite draughts, simplifying further the constructions in chapter 3 of my MSc dissertation.

You can read this article at arXiv:2111.02053.

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.

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