2022/01/17 by Hamkins, Joel David, Leonessi, Davide
#03E60 #91A44 #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2201.06475
We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both players have drawing strategies. Meanwhile, the transfinite game-value phenomenon, now abundantly exhibited in infinite chess and infinite draughts, regrettably does not arise in infinite Hex; only finite game values occur. Indeed, every game-valued position in infinite Hex is intrinsically local, meaning that winning play depends only on a fixed finite region of the board. This latter fact is proved under very general hypotheses, establishing the conclusion for all simple stone-placing games.