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Analysis by Houdini 4: d 25 dpa

1. = (-0.15): 19.h5 Qf5 20.g4 Qd7 21.Ng3 Nc5 22.b4 Nd3 23.Re3 Re8 24.Rxd3 Bxd3 25.Qxd3 Qxg4 26.b5 a6 27.bxc6 Nxc6 28.Bb2 Rad8 29.Qxa6 Qb4 30.Rb1 Ne5 31.a3 Qb3 32.Qf1 Nf3+ 33.Bxf3 Qxf3 34.Bd4 Ra8 35.h6 gxh6 36.Rxb6 Ra4 37.Bb2 h5 38.Rf6 Qb3 39.Qc1

You can't say that. Well, of course you can, but it wouldn't be correct. All that you can truthfully say is that at d = 53 plies Stockfish 9 is still deficient in its grasp of the position. But at d = 54 and subsequent searches it might have found 19.Bg5 for good, or at least for the additional search levels used. And, as soon as everyone has agreed that at d=N Stockfish has found 19.Bg5 "for good", Stockfish might decide at d=N+1 that 19.b4 (or even perhaps a different move) is better. You just never know until you get there.

For this reason I have egotistically defined AylerKupp's Corollary to Murphy's Law (AK2CL) which states "If you use your engine to analyze a position to a search depth=N, your opponent's killer move (the move that will refute your entire analysis) will be found at search depth=N+1, regardless of the value you choose for N."

Sure, that has been known for almost 70 years and was mentioned in Claude Shannon's seminal paper on computer chess playing, https://vision.unipv.it/IA1/Program..., "A very important point about the simple type of evaluation function given above (and general principles of chess) is that they can only be applied in relatively quiescent positions." And pretty much all top chess engines do this and have been doing it for some time.

But all this can do is mitigate the horizon effect in obvious situations. The impact of the horizon effect can be drastic such as missing a mate in 1 because the move is beyond the last ply searched or more subtle such as lowering the confidence level in the later moves of <every> to be much lower than the confidence level in the early moves of the same computer line since these later moves don't the benefit of a deep search. I personally don't think that <any> approach that relies on forward searching can completely eliminate the horizon effect, although it can also be mitigated by (obviously) searching deeper and forward sliding.

<Using a hash table helps here by extending the depths of searches.>

It depends on what you mean by "searches". When searching a chess engine keeps track of the number of pieces remaining on its board and, once the number reaches 6, it can find the final (and perfect) evaluation of that position using 6-piece tablebases and therefore stop searching. So, within this narrow definition of "search", using tablebases actually <reduces> the depths of searches since they become no longer necessary. Of course, the tablebases provide an implicit extension of the moves needed to achieve the reported result, but these cannot be considered as "searches" performed by the chess engine. And the Syzygy tablebases used by Stockfish do not have distance-to-mate information so Stockfish would not know either the number of moves required to reach that result nor the best line in the sense of reaching that result in the minimum number of moves.

For Black's 20th, around depth 35/52 (2 billion boards examined), SF version 9 decides that maybe the plausible alternative 20 ... f5 21 Qf4 is slightly better for Black than the game line.

But even so it never sees 21 Bg5 as the main line after 20 ... Kh8, or at least I didn't wait long enough (3 billion boards, or about 75% of the compute that SF was allowed for each move in the actual game).

When allowed to grind on 20 ... Kh8, it "soon" (0.5 billion board positions) decides that 21 Bg5 is best for white. And by the time it's looked at 1 billion positions, it has decided it's probably going to lose a pawn or so.

So it's plausible to guess that SF would have "seen" Bg5 if it had been given compute time to explore each 1-ply-away move to a depth of more than 0.5 billion boards.

I counted and it looks like Alpha has about 30 possible moves in this position. Assuming 10 can quickly be eliminated as "very weak", that leaves about 20 branches to explore to depth of 0.5 billion or more, or about 10 billion positions total. This is about two and half times as much compute as SF was actually being granted for each move in the match.

So the procedure might settle into a "solution" that is still far from the best. Then maybe it will pop out of that less-optimal solution with more training and find a better one. Or maybe it won't.

Like this: imagine you've been asked to find the highest nearby hill. But it's really foggy and always will be. So you wander around in hilly terrain in the fog for while, and eventually you find a hilltop. It might be the highest one for miles, or you might be surrounded higher, more optimal peaks. But you can only guess. At some point you just say, this is probably the best I'm going to do. And stop.

<Without humans, what is earth “worth” and why would it be worth saving?>

That's the anthropocentric perspective that we're naturally programmed to adopt but Big Paunch could ask what the world would be worth without cockroaches. A computer would not necessarily adopt the human perspective. I might look at the sum total of suffering in the world and try to find a way to minimize it and quickly figure out that the primates who are busy poisoning and polluting and bombing and torturing every thing that moves are just a little too rambunctious for the common welfare of the planet.