无限Hex是平局
Infinite Hex is a draw
AI总结：
本文引入无限六边形格上的无限Hex游戏，证明其与先手获胜的有限游戏不同，双方均有平局策略，且仅存在有限游戏值，该局部性结论适用于所有简单落子游戏。
摘要：
我们引入了无限Hex游戏，将熟悉的有限游戏扩展到无限六边形格上的自然对弈。有限游戏是先手玩家的胜利，相比之下，我们证明无限Hex是平局——双方玩家都有平局策略。同时，在无限国际象棋和无限跳棋中大量展现的超限游戏值现象，遗憾地不会在无限Hex中出现；仅出现有限游戏值。实际上，无限Hex中每个具有游戏值的位置本质上是局部的，意味着获胜对弈仅依赖于棋盘上固定的有限区域。后一事实在非常一般的假设下得到证明，为所有简单的落子游戏确立了该结论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
