Its seems to me nowadays computers simply play better, i.e. they consistently choose better moves. Where does human factor come into play, how can a human help engine to beat another engine?
Or was Kasparov simply wrong?
Edit: here's the podcast, most of it is politics, chess part is near the very end https://www.samharris.org/podcast/item/the-putin-question
Experienced human correspondence chess players with a strong chess engine definitely play better chess than just the engine itself.
If you think about it, the human player could always simply follow the engine moves without any thinking. However, you're not going to win the world correspondence title if you don't do your own analysis. You have an engine, but your opponent also have an engine! You just can't win a game unless you guide the engine.
A strong International Correspondence Chess Grandmaster know how to analyze a chess position with a chess engine. They can make a move on a board, and evaluate the new positions again with the engine. There is no way the engine by itself can beat this human+engine perfect combination - tactics + long-term strategic thinking.
This has been tested in 2014. A strong version of Stockfish (ELO 3200) was pitted against Nakamura (2800) with an early version of Rybka (3000) to help him. The Rybkamura team lost.
https://www.chess.com/news/view/stockfish-outlasts-nakamura-3634
This is evidence against Kasparov's claim.
The general thought is that computers still have problems with calculating long-term plans and positional considerations correctly.
There are many examples of modern computers getting "confused" in closed positions where long-term planning is worth more than brute force thinking. Many have a contempt factor which forces them to make a poor move rather than accept a draw against a weaker opponent. Nakamura has exploited this algorithm in many famous games.
For positional considerations, the reason for this weakness is the rarity of possibilities. Except for some lines in the Ruy Lopez, Alekhine, and the Caro-Kann, capturing toward the center is the norm. There are exceptions where capturing away from the center is better, mostly for attacking purposes. Programming in the exceptions would cause an increase in the size of the program and slow down the speed. However the computer does search far enough ahead the this is becoming less of a concern.
If you follow engine tournaments, you'll find that although computers are very strong, there are still times when they do the most stupid of things. Here's an example from the most recent TCEC superfinal between Stockfish and AllieStein.
[FEN "2b1r3/6r1/p2p1k1p/Pp1PpP1P/1Pp2pP1/2P2P2/1K2R1B1/3R4 w - - 23 149"]
[White "Stockfish"]
[Black "AllieStein"]
Try analyzing the position yourself before looking at what the engines say. What would you give this position?
If you said 0.00, I completely agree with you. After all, White can't make progress - all the pawns are firmly wedged. The only thing White can do is play g5, but that's just going to lose several pawns. Meanwhile Black is just as stuck. White can easily defend the pawn on d5. The only pawn break Black has is ...e4, but that will actually lose the game by not just throwing a pawn, but also opening lines for White to make inroads.
However, if you look at the engine evals, Stockfish gave +0.90, and AllieStein gave -0.50. If you look at the charts of how the evals vary, you'll see they're straight horizontal lines (at least Stockfish's is - AllieStein, being a neural network engine, has a less consistent but still mostly horizontal eval). This is what computer chess viewers derogatorily call "horizone". The engines aren't smart enough to realize they're not making progress. They will happily shuffle until the 50-move rule helps them realize that it's a draw. This kind of fortress situation is quite common, but can be avoided. If you're a human piloting Stockfish, you can see this fortress come up several moves before, realize that Stockfish is heading into a horizone, and choose a different move that keeps some winning chances in the position.
But that's not all humans can contribute! As it turns out, AllieStein spotted an ingenious way to make progress. Check out what happened 15 moves later. By this time, Stockfish had realized it wasn't making progress, and its eval had dropped to +0.38. Meanwhile AllieStein's eval had increased to -0.79. And then there happened ...
[FEN "2b3r1/8/p2p3p/Pp1PpPrP/1Pp1RpP1/2P2Pk1/2K5/3R1B2 w - - 53 164"]
[White "Stockfish"]
[Black "AllieStein"]
1. Ree1 Kxf3
What kind of fanatic plays 164...Kxf3? Is AllieStein insane? Who the hell ventures into enemy territory with a lone king to grab pawns anyway? Black can't even back off through g5 because the square is currently blocked.
If you're a human piloting AllieStein, you'd immediately realize this is a pivotal moment. Either AllieStein is seeing something profound, or it's making a huge blunder. Before actually making the move, you'd try out variations to see what might happen. You might not be strong enough to tell yourself, but AllieStein is sufficiently powerful to tell that within a few moves Black's so-called advantage has cratered. After 164...Kxf3 165. Be2+, Black is dangerously close to being checkmated. 165...Ke3 166. Rf1 threatens Rf3+, Re1 and Bd1 checkmate. Black is forced to take desperate measures like ...Bxf5, after which his position collapses. AllieStein on its own didn't see this, and lost this game. But human + AllieStein is likely to have avoided this.
This is just an example of the more obvious ways a human can contribute. Correspondence players will be able to say more, since they get familiar with their engine's strengths & weaknesses, and feed their engine ideas on how to get to their strongest positions while avoiding the opponent's. From what I've gathered talking to correspondence players, the odds are that they will draw against someone playing only engine moves (since chess is a draw after all), but they won't lose either, and they will score wins. That's where humans can contribute.
