Transfinite game values in infinite draughts

Autor:	Hamkins, Joel David, Leonessi, Davide
Rok vydání:	2021
Předmět:	Mathematics - Logic Computer Science - Computer Science and Game Theory Mathematics - Combinatorics 03E60 91Axx
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.02053 Zobrazit plný text záznamu View this record from Arxiv