It is not true to say he dismisses 15...Nh5, just that he thinks that the rook capture after 16 Be3 Nf4 17 Bxf4 Rxf4 is the only logical continuation.

I decided to investigate the 17...exf4 capture, for the reasons you indicate. If Black can keep the position closed, the f4 pawn can lead to an advantage on the Kside, and the heavy pieces can lift behind a pawn rush.

I set Stockfish for 33 depth, and it showed that White can open the position, and get a substantial edge.

15...Nh5 16 Be3 Nf4 17 Bxf4 exf4

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22...exd5 23 exd6 Bxd6 24 Qxd5 Rb5 25 Qc6 Ng5 26 Nxg5 Rxg5 27 Qf3 h6 28 Rcd1 +0.81/33

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28...Bc5 with the idea of 29...Rg3 doesn't work because of 29 Ne5, but the toughest defence makes use of the same idea.

28...Bb4 29 Qb3 Rxg2+ 30 Kh1 Rg3! 31 fxg3 Qc6+ 32 Kg1 Bc5+ 33 Ne3 disc + Kh8 34 Qd5 Bxe3+ 35 Kh1

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<But to shoot for a position where you have to play like a wizard just to get a probable loss is not a recommendation for 15...exf4>

Used to be out of this world, now just another top 5 player."

[0.00] to [+0.49]: Equal

[+0.50] to [+0.99]: White is slightly better but probably not enough to win.

[+1.00] to [+1.99]: White is definitely better and possibly good enough to win.

[+2.00] and up: White is winning. Most GUIs consider a White advantage of [+1.50] and up as winning for White but I prefer to be more conservative.

And starting the analysis from your final position

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Stockfish 8 evaluates the resulting position at [+0.52], d=39, after 28...Bb4 29.Qb3 Rxg2+ 30.Kh1 Rg3 31.fxg3 Qc6+ 32.Kg1 Bc5+ 33.Ne3+ Kh8 34.Qd5 Bxe3+ 35.Kh1 Qc2 36.Qg2 Qc5 37.Qf3 Bd4 38.gxf4 Bxb2 39.Qd5 Qc3 40.Qg2 Qf6 41.Rd7 Bc3 42.Ree7 Rg8 43.Rf7 Qe6 44.Rxc7 Bf6 45.Rfd7 Qf5 46.Qf3 Qxa5 47.Qe4 Qh5 48.Kg2 Re8 49.Rd5 Qxh3+ 50.Kxh3 Rxe4 51.Kg4 Bg5 52.Rf5 Bf6 53.Rfc5 Bg5 54.Rc4 Rxc4 55.Rxc4 Be7 56.Rc8+ Kh7 57.Kf5 Bb4, so the evaluation of [+0.81] by Stockfish after 28.Rcd1 seems reasonable. And, with R vs. B+2P but with White having the more active king, this evaluation of [+0.52] after 57...Bb4 also seems reasonable.

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So if in the position I gave, Stockfish trends downward at higher depths, as you say it does down to +0.52, a +.81 could be said to be only a slight advantage. But that just means the eval is really +0.52.

So an evaluation standing alone like +0.81 could mean almost anything, and in another position could be trending toward a win.

I agree. But for convenience (or, I suppose, laziness) we all typically cite an evaluation and a search depth in supporting "our" assessment of a position. What we should probably do, as you indicate, is look at the evaluation trends and continue to run the analysis until the trends flatten out and stabilize.

Another possible indicator is the evaluation difference between the engine's best move and its second best move. If the evaluation difference is increasing, it's likely (but not guaranteed!) that the engine's top move is indeed the top move and it's probably reasonably safe to stop the analysis. But if the evaluation difference is decreasing, the engine's current second best move might overtake the engines current best move, and we should probably let the engine analysis continue running.

But in either case we must always keep in mind AylerKupp's Corollary to Murphy's Law (AKC2ML). See my forum's header for details.

And I agree, anything between [+0.50] and [+0.99] results in the same human assessment, so the evaluations [+0.81] and [+0.51] are effectively the same, at least as far as humans are concerned. Which is probably another way of saying that the resolution of humans as far as classifying any advantage for one side or the other in a particular position is ± 0.5 pawns.

And yes, in all engine vs. engine games, not just TCEC matches, I've noticed that engines sometimes engage in seemingless endless shuffling, what I call "engine dithering". I suppose that's not that different than some players, particularly a stronger player playing a weaker player, do something similar, marking time until their opponents make a mistake or at least an inaccuracy. Then they pounce and take advantage of it.

I take your point. Examining the proximity of the candidate moves would have indicated I should have let the analysis run.

In the case at hand, here is a snapshot of a midpoint of the analysis showing at 33 depth three moves were within hailing distance of each other.

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1. ± (0.75): 22.e5 exd5 23.exd6 Bxd6 24.Qxd5 Rb5 25.Qc6 Ng5 26.Nxg5 Rxg5 27.Qf3 Rb5 28.Re4 Qf6 29.Rd1 h6 30.Nxd6 cxd6 31.b4 d5 32.Red4 Qd6 33.Qd3 Kh8 34.Rxd5 Rxd5 35.Qxd5 Qxb4 36.Qd6 Qxd6 37.Rxd6 Rf6 38.Rxf6 gxf6 39.Kf1 f3 40.gxf3 Kg7 41.Ke2 Kf7 42.Kd3 Ke6 43.Kd4 Kd6 44.Kc4 h5 45.Kb4 Kc6

2. ± (0.72): 22.Qd2 Rbb8 23.e5 exd5 24.exd6 Bxd6 25.Qxd5 Rb5 26.Qc6 Ng5 27.Nxg5 Rxg5 28.Qf3 Rb5 29.Re4 Qf6 30.Rd1 h6 31.Nxd6 cxd6 32.b4 d5 33.Red4 Qe7 34.Qd3 f3 35.gxf3 Kh8 36.Rb1 Qf6 37.Kg2 Rd8 38.Rd1 Qd6 39.Qf5 Rf8 40.Rxd5 Qxb4 41.Rxb5 axb5

3. ⩲ (0.63): 22.Kh1 Ng5 23.e5 Nxf3 24.Qxf3 exd5 25.exd6 Bxd6 26.Qxd5+ Qf7 27.Qxf7+ Kxf7 28.Red1 f3 29.g3 Kg6 30.Nxd6 cxd6 31.Rxd6+ Rf6 32.Rd2 h5 33.Kg1 Rb5 34.Rc7 Kh6 35.Rdd7 Re6 36.Rxg7 Re1+ 37.Kh2 Re2 38.Rh7+ Kg6 39.Rcg7+ Kf6 40.Rf7+ Kg6 41.Rhg7+ Kh6 42.g4 hxg4 43.Rxg4 Rxf2+ 44.Kg3 Rfxb2 45.Rf6+ Kh5 46.Rxa6

From a practical point of view though, a super GM like Aronian would shut down the analysis once this point is reached in his prep, and that is probably the reason he ditched the 15...Nh5 plan entirely. Not because it loses, but because the unbalancing capture with the pawn on f4 is risky with little or no chance of Black advantage.

"When he got these rooks on f8 and b2, it looked like he had something, but just looking at the position, optically it looks like there is something, but with the pawn structure with the way it was, it seemed kind of suspect."

That seemed to me to be a very telling comment, because to get the Rook to b2, Levon had to exchange on c3, which the engines flag as starting White's big advantage. Levon saw the chance to get all his pieces working, and went into to it thinking he would find a resource.

After the key moves, 21 Rf1 and 24 Rae1 leading to the b2 rook exchange, Nakamura commented again.

"It just feels like in this position

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even though you have these pieces kind of near White's King, they are not really creating threats.

I think that is one thing Magnus is very good at actually, ...if there there really is no concrete threats, he is very good at pushing you back."

21 Rf1 stands out as the turniing point. Levon might have thought he was forcing this move, but in this case, it is the only move to grab a big edge for White +.72 at 33 depth, while all the other moves allow near equality.

What's interesting about Nakamura's analysis (apart from the point about Rf1) is how impressionistic he is. His approach seems much more intuitive than mechanistic/scientific:

"but just looking at the position, optically it looks like there is something, but with the pawn structure with the way it was, it seemed kind of suspect"

"It just feels like in this position..."