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Metrics that relate mating nets to the lattice of accessibility are a very common and powerful approach to "solving" games where computation looks nothing like enumeration.
![is there an 8 piece chess endgame tablebase is there an 8 piece chess endgame tablebase](https://i.imgur.com/DC2C9rr.jpg)
By simple applications of game-theoretic partitioning lemmas, this implies that there is a lattice of metrics identifying position accessibility. Every such monotonic metric provides a partitioning of solution space, excluding not only end positions but intermediates. For instance, "total pawn distance to backrank" only decreases over a game, starting at 48 on each side. There are numerous metrics we know the behavior of. And any such solution is purely constant time. The difficulty is in finding metrics that capture more complicated netting patterns - but note, although this is "hard", this is purely algebraic. We can do this for a number of easy endgames. This can be done until mate, simply using basic metrics of the position. With these three metrics - which you can read off of a board without any enumeration - you can prove a mate length and make a winning move for that mate length to bring it to a mate length -1 away. Black king and rook versus white king, for instance, has the obvious mathematical signatures of "white king distances from edge opposite black king", "black rook perpendicular distance from white king" (or shortest approach distance on one translation), and "black king perpendicular distance from white king". Just as a simple example - we already have numerous endgames we can prove a winning sequence without enumeration. The result on the computational complexity of a game's position is orthogonal to solving the game - you are completely misunderstanding what is going on with that result. Please continue to give us your feedback and suggestions on how we can help make /r/chess better for everyone.
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