如何用重复位置解决游戏（Teeko）
我一直在尝试找到一种算法来强烈解决游戏 teeko 。该游戏是在每个玩家有4件的5x5板上玩的，并尝试朝任何方向对齐或从中创建一个正方形。 （假设没有下降阶段）
我尝试通过使用alpha beta修剪和其他优化（如换位表）使用negamax来解决游戏，但似乎没有起作用，因为求解器通常会陷入困境偏离那里的策略，因为这会导致他们失去。从我的研究中，我发现了nash equilibium 作为潜在的解决方案，但我不知道如何知道实施它。此外，我发现该游戏已经解决，并发现与佩特特（Perfect）玩耍的游戏先前会导致抽奖： https://pcarrier.com/teeko/text/teeko.results.txt
是否有任何算法可以给出与minimax和hanlde重复位置相同的结果，以及我如何实现我它是否还有其他算法与minimax相同的结果？
I have been trying to find a algorithm to strongly solve the game Teeko. The game is played on a 5x5 board were each player has 4 pieces and attempts align them in any direction or create a square out of them. (assume there is no drop phase)
I have tried solving the game by using a negamax with alpha beta pruning and other optimizations like a transposition table but that has not seemed to have worked because the solver would usually get stuck in loops were neither player wants to deviate from there strategy as it would result in them loosing. From my research I have found stuff like Nash Equilibrium as a potential solution but I cant figure out how to implement it. Furthermore, I have found that the game has been solved and found that the with prefect play it result in a draw previously: https://pcarrier.com/teeko/text/teeko.results.txt
Are there any algorithms that might be able to give the same result as minimax and hanlde repeating positions and how could I implement it and are there any other algorithms that give the same result as minimax?
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Minimax（或Negamax）能够使用换位表处理重复位置，正如您在问题中提到的那样。换位表的实施很复杂，所以也许您有一个错误？
minimax的问题是您要么：
需要解决它，直到游戏完成才能获得分数为止。对于Tic-Tac-toe等简单游戏，这是可能的，但对于诸如国际象棋等更复杂的游戏。
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使用一些启发式函数对每个节点进行评分，例如国际象棋。
我不确定Teeko，是否可以使用minimax和alpha beta修剪到所有叶子节点？您能做其他事情来减少搜索树，例如换盘表或其他切割途径吗？如果是这样，那么minimax是一个不错的选择。
是否可以为此游戏创建某种评估功能？对我来说似乎很难，但这也许是因为我对游戏的了解很少。拥有中央正方形更好吗？连续获得2比散布碎片要好吗？如果您是游戏的好玩家，或者在线找到好的来源，则评估功能是您可能会看到的。
Minimax (or Negamax) is well capable of handling repeating positions using transposition tables, as you mention in your question. Transposition tables are complicated to implement though so maybe you have a bug?
The problem with minimax is that you either:
NEed to solve it until the game is completed to get a score. This is possible for simple games like tic-tac-toe, but not for more complicated games like chess.
Score each node using some heuristic function, which is the case for e.g. chess.
I am not sure about Teeko, is it possible to get to all leaf nodes with minimax and alpha beta pruning? Could you do other things to reduce the search tree, like transpotision tables or other cut offs? If so then minimax is a great option.
Is it possible to create some kind of evaluation function for this game? It seems hard to me, but maybe that is because I know too little about the game. Is it better to have central squares? Better to get 2 in a row than to spread out pieces? Evaluation function is something you could have a look at if you are a good player of the game, or find good sources online.