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You can measure the sharpness of the position, as in this paper section 2.3 "Complexity of a position". They find their metric correlates with human performance.

https://en.chessbase.com/news/2006/world_champions2006.pdf




I think this is something a bit different. That sort of assessment is going to find humans perform poorly in extremely sharp positions with lots of complicated lines that are difficult to evaluate. And that is certainly true. A tactical position that a computer can 'solve' in a few seconds can easily be missed by even very strong humans.

But the position Ding was in was neither sharp nor complex. A good analog to the position there is the rook + bishop v rook endgame. With perfect play that is, in most cases, a draw - and there are even formalized drawing techniques in any endgame text. But in practice it's really quite difficult, to the point that even grandmasters regularly lose it.

In those positions, on most of every move - any move is a draw. But the side with the bishop does have ways to inch up the pressure, and so the difficulty is making sure you recognize when you finally enter one of those moves where you actually need to deal with a concrete threat. The position Ding forced was very similar.

Most of every move, on every move, led to a draw - until it didn't. Gukesh had all sorts of ways to try to prod at Ding's position and make progress - prodding Ding's bishop, penetrating with his king, maneuvering his bishop to a stronger diagonal, cutting off Ding's king, and of course eventually pushing one of the pawns. He was going to be able to play for hours just constantly prodding where Ding would have stay 100% alert to when a critical threat emerges.

And this is all why Ding lost. His final mistake looks (and was) elementary, and he noticed it immediately after moving - but the reason he made that mistake is that he was thinking about how to parry the other countless dangerous threats, and he simply missed one. This is why most of everybody was shocked about Ding going for this endgame. It's just so dangerous in practical play, even if the computer can easily show you a zillion ways to draw it.


Nice paper. I’d like if someone re-ran the numbers using modern chess engines… the engine they used is exceedingly weak by modern standards.


Actually is is so weak, that it would be stomped out 1000:0 by modern engines. I like the methodology too, but the conclusions are not defendable.




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