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With all 7-man endgame tablebases completed years ago, and the 8-mean endgame tablebases in the works now, why have we not seen new strategies outlined for, say, how to win with rook and two knights against rook and bishop, or any of the other many combinations of endgames?

After all, we do have the full solutions to checkmate in many of these positions. But where are the new endgame theories and strategies?

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    Tim Krabbé about tablebase truth : "Playing over these moves is an eerie experience. They are not human; a grandmaster does not understand them any better than someone who has learned chess yesterday. The knights jump, the kings orbit, the sun goes down, and every move is the truth. It's like being revealed the Meaning of Life, but it's in Estonian."
    – Evargalo
    Feb 12 at 14:27
  • Relevant wiki page : en.wikipedia.org/wiki/…
    – Evargalo
    Feb 12 at 14:30

2 Answers 2

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Endgame complexity scales super-exponentially with the number of pieces. This is why each successive N+1-piece tablebase takes so much more computing power than N-piece tablebase.

This isn't merely a huge numbers issue (mating with KR/K on a googol x googol board is still trivial - in principle) but rather the inability of human to understand a (mating) algorithm that can't be broken down to chunks. For example, try to replay the longest 6-man mate on Syzygy and see if any of the moves make any sense to you. Even much simpler endgames are already hard for humans to understand:

John Nunn wrote an entire book on the winning/drawing procedures for R+1 vs R. RNNvRB replaces a single pawn with two knights and a bishop.

Fabiano Caruana failed to convert a winning RBvR ending - hundreds or thousands of times less complex than RNNvRB - with a World Championship spot on the line. He probably could've won with more time, but the point is - even a player as strong as him hasn't completely mastered every part of the ending.

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  • Could you expand a bit? The main point isn't the scaling (I can mate with a rook on a googol*googol board, it might take some time :-) but the complexity of the win itself which is near completely irreducible, I.e. the only viable strategy is (say) memorizing 239 moves (times subvariants if needed). Feb 9 at 8:17
  • That's what I was trying to get at with "Endgame complexity scales super-exponentially with the number of pieces". Feel free to edit if you can make it clearer.
    – Cleveland
    Feb 9 at 18:48
  • I try tomorrow, you can always revert if you are not convinced. Feb 10 at 15:52
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I think it's because the tablebase solutions are not based on theory, but on exhaustive search. And they have passed the limits of human memory, even the memory of someone like Carlsen, who remember thousands and thousands of positions.

It's hard to come up with the exact number of possibilities for each set of pieces, because some positions are illegal or impossible, but we can make rough guides.

The first king can be on any of 64 squares. The second kind on any of 57 squares (if the first king is somewhere in the middle). Then one rook can be on (roughly) 62 squares, another rook on 61, and the knights on 60 and 59. (Again, this will be a slight overestimate, but not too much, I think).

That's 48,840,445,440 positions! Of course, some are symmetric to others, but even figuring those exactly is going to be hard. And the solution to each of those 50 billion solutions would have to be memorized, because, again, the computer doesn't base the solutions on logic or "chess thinking".

This is happening now much earlier in the game. The computer will recommend moves that "no human would play" (or so many grandmaster commentators say).

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