论文标题

最多43个动作,至少29个:最佳策略和界限

At Most 43 Moves, At Least 29: Optimal Strategies and Bounds for Ultimate Tic-Tac-Toe

论文作者

Bertholon, Guillaume, Géraud-Stewart, Rémi, Kugelmann, Axel, Lenoir, Théo, Naccache, David

论文摘要

Ultimate Tic-Tac-toe是著名的TIC-TAC-TOE(NOUDGHS和CROSSES)棋盘游戏的变体。两名球员竞争赢得了三个结盟的“田野”,每个球员都是TIC-TAC-TOE游戏。每个举动都确定下一个球员必须参加哪个领域。 我们表明,对于第一个球员来说,有一个获胜的策略,因此最多有43次动作有最佳的获胜策略。第二名球员至少可以保持29轮;并确定任何最佳策略的前两个动作。

Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and crosses) board game. Two players compete to win three aligned "fields", each of them being a tic-tac-toe game. Each move determines which field the next player must play in. We show that there exist a winning strategy for the first player, and therefore that there exist an optimal winning strategy taking at most 43 moves; that the second player can hold on at least 29 rounds; and identify any optimal strategy's first two moves.

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