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Are there any moves from real, preferably reasonably well known games which humans agree are great moves, but which engines cannot see, or, at least, think are weak/average?

Here is an example that I know of (although probably not a great example) from a Kasparov-Topalov game called "Kasparov's Immortal" on chessgames.com. After Topalov played Qd6, Kasparov sacrificed the rook on d4, which Stockfish depth 71, as said in a video by the Chess Club and Scholastic Center of Atlanta, still thinks to be just an acceptable move. But it is a move which human players may consider to be extremely creative and very strong.

[Title "Kasparov-Topalov, Wijk aan Zee NED, 1/16/1999"]
[FEN ""]
[startply "46"]

1. e4 d6 2. d4 Nf6 3. Nc3 g6 4. Be3 Bg7 5. Qd2 c6 6. f3 b5 7. Nge2 Nbd7 8. Bh6 Bxh6 9. Qxh6 Bb7 10. a3 e5 11. O-O-O Qe7 12. Kb1 a6 13. Nc1 O-O-O 14. Nb3 exd4 15. Rxd4 c5 16. Rd1 Nb6 17. g3 Kb8 18. Na5 Ba8 19. Bh3 d5 20. Qf4+ Ka7 21. Rhe1 d4 22. Nd5 Nbxd5 23. exd5 Qd6 24. Rxd4 cxd4 25. Re7+ Kb6 26. Qxd4+ Kxa5 27. b4+ Ka4 28. Qc3 Qxd5 29. Ra7 Bb7 30. Rxb7 Qc4 31. Qxf6 Kxa3 32. Qxa6+ Kxb4 33. c3+ Kxc3 34. Qa1+ Kd2 35. Qb2+ Kd1 36. Bf1 Rd2 37. Rd7 Rxd7 38. Bxc4 bxc4 39. Qxh8 Rd3 40. Qa8 c3 41. Qa4+ Ke1 42. f4 f5 43. Kc1 Rd2 44. Qa7

Are there any moves in well known games which engines don't recommend, but which the best human players would prefer?

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    Actually for that specific position, SF 13 figures out that 24.Rxd4 is the best move at roughly depth 28-29. SF just doesn't say Rxd4 is winning, as 24...cxd4 allows Black to draw with perfect play, while 24...Kb6 even gives him a slight advantage. But SF still gives 24.Rxd4 as the best move since everything else is bad for White. – Inertial Ignorance Jun 19 at 16:30
  • @InertialIgnorance interesting. In the video it says the engine (SF13) says Rxd4 is not the best move at depth 71. Are you able to test at greater depth (perhaps SF finds a better move between depth 29 and 71?) – stevec Jun 19 at 16:44
  • On our sister site Puzzling.SE: Why isn't this chess puzzle trivial? – I wrote an answer there. – Glorfindel Jun 19 at 20:09
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    @stevec On chessbase's cloud evaluations, I can see someone let their SF 13 think to depth 53 on this position today (likely because of your question). Not sure if that was actually me unless I left my engine running for a while, but it looks like 1.Rxd4 is given as the top move (with a -0.13 evaluation). Earlier today I saw 1.Rxd4 given with a 0.00 evaluation at depth 71 on the cloud (someone generated it in april), but I no longer see it listed at the moment since chessbase only shows three evals. – Inertial Ignorance Jun 19 at 23:05
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    @stevec I'm guessing Finegold saw this same depth 71 evaluation that said 1.Rxd4 was "only" equal, and that's why he made the comments he did. But he's likely inaccurate in saying that the engine saw a better move. – Inertial Ignorance Jun 19 at 23:06
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You may be interested in the chess.com article 10 Positions Chess Engines Just Don't Understand, by NM Sam Copeland. If you don't like reading, there's a video by the author and another video of Hikaru reading through and giving his thoughts.

A frequent theme in these positions are setups with long-term factors that engines are not aware of, in particular closed positions where a human can see it is impossible to make progress, and lengthy maneuvering plans.

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I recall an amazing move made by Peter Leko against Vladimir Kramnik, as told by the YouTuber agadmator in a video, published on June 10th 2018, entitled "Invisible to Engines | One Of The Greatest Moves Ever Played". The game can be relayed chessgames.com with notes provided by Raymond Keene.

[Title "Vladimir Kramnik-Peter Leko, Classical World Championship Match, Brissago Switzerland, 10/7/2004"]
[FEN ""]
[startply "49"]

1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 O-O 8. c3 d5 9. exd5 Nxd5 10. Nxe5 Nxe5 11. Rxe5 c6 12. d4 Bd6 13. Re1 Qh4 14. g3 Qh3 15. Re4 g5 16. Qf1 Qh5 17. Nd2 Bf5 18. f3 Nf6 19. Re1 Rae8 20. Rxe8 Rxe8 21. a4 Qg6 22. axb5 Bd3 23. Qf2 Re2 24. Qxe2 Bxe2 25. bxa6 Qd3! 26.Kf2 Bxf3 27. Nxf3 Ne4+ 28. Ke1 Nxc3 29. bxc3 Qxc3+ 30. Kf2 Qxa1 31. a7 h6 32. h4 g4

The move in question is Leko's 25... Qd3! Keene's notes summarize it neatly: "The key move which Kramnik and his team had underestimated before the game."

I believe that agadmator's narration, starting at 7:13 on Kramnik's move 24th move, gives enough context for an answer. I have written a transcript.

"Kramnic immediately played queen captures on e2 and it seems like a winning move and in fact Kramnic had this position on the board before the game. He and his team decided that this was of course winning for White. It's okay, bishop captures on e2 and now b captures on a6. It seems that for the queen the only compensation Kramnic has is this rook, a rook and a nice passed pawn that is ready to go to a7 and a8. So you kind of don't want to allow pawn to a7 and a8 and this is the position I've been talking about. So here bishop captures on a6 is the idea and every engine I've tried give bishop captures on a6. But this is why this game is so famous and this is why this move by Peter Leko is so famous. It's one of the legendary moves played in chess history and I really do want you to pause the video here and try to find this move. Give it a minute or two and if you can afford more give it more. But even if you don't find it or don't really know what to find it then I also invite you to try out your engines. Maybe your engine can help you here because I haven't actually found an engine that can solve this position."

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    To be fair, Stockfish 13 does see the move in a couple of seconds, although engines at the time did not. – Nihar Karve Jun 19 at 5:23
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    Another position Agadmator covered which engines (still?) cannot see: youtube.com/watch?v=8wCJalNkTEI. It's a puzzle rather than a real game though – mowwwalker Jun 20 at 20:54

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