论文标题
无限十六进制是吸引人
Infinite Hex is a draw
论文作者
论文摘要
我们介绍了无限六角形的游戏，将熟悉的有限游戏扩展到了无限六角形晶格上的自然游戏。尽管有限的游戏是第一位球员的胜利，但我们证明了Infinite Hex是一场吸引力 - 两个玩家都有绘画策略。同时，现在在无限的国际象棋和无限草稿中表现出的跨越游戏价值现象，遗憾的是，无限的十六进制并没有出现。仅发生有限的游戏值。确实，无限十六进制中每个游戏值的位置都是本质上的，这意味着赢得比赛仅取决于董事会的固定有限区域。后一个事实在非常普遍的假设下证明了这一点，为所有简单的石材隔板游戏提供了结论。
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.
