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Initially, I was interested in the question "what are the longest sacrificial middlegame attacks?" ([Kasparov's Immortal] is one of the most famous sacrificial middlegame attacks). But this question is pretty vague, so I decided to specify it.

What are the longest known "golden sequences" in chess? A golden sequence is defined as...

  • A variation which allows the protagonist side (White or Black) to win or draw or gain an advantage. Depending on the protagonist's goal. Variation starts when the protagonist is at least down a piece / without a piece.
  • While the variation happens, the protagonist has to stay down material (at least down 1 point); most of the variation the protagonist should be at least without a piece; at least 2 queens should remain on the board; at least 3 heavy pieces (queens or rooks) overall should remain on the board.
  • The variation shouldn't be based on an obvious repeating idea OR all of the protagonist's moves can't be checks. (one of those conditions is probably excessive)

Position with the golden sequence doesn't have to be legal. Correctness of the sequence doesn't have to be 100% proven. Moreover, subtle mistakes in the sequence are allowed (because it's just that hard to find longer golden sequences). In principle, even violations of the conditions above are allowed if the sequence follows "the spirit" of the idea.

Here are some examples of golden sequences:

  • [Kasparov's Immortal] has a golden sequence of 14 moves: 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. Both sides make subtle mistakes, so the sequence is half-sound.

  • A position from Dubov vs R Svane, 2019 has a golden sequence of 21 moves, if Black makes a couple of subtle mistakes: 21. Rh7+ Kg8 22. Rxf7 Rxf7 23. Qxg6+ Kf8 24. Qh6+ Rg7 25. Bxd5 Ke8? 26. Qh5+ Kd7 27. Qh3+ Ke8 28. Qh5+ Kd7 29. Be6+ Kc6? 30. Qf3+ Kb5 31. Bxc4+ Ka5 32. Qd5+ Bc5 33. b4+ Ka4 34. Qg2 Bxb4 35. Qc6+ Kxa3 36. Bb3 Bf5+ 37. e4 Bxe4+ 38. Nxe4 b5 39. Qc1+ Kxb3 40. Qc2+ Ka3 41. Qa2#. (The actual game was slightly shorter.) It's half-sound. By the way, the entirety of Andersen's [Immortal Game] lasted no longer than 23 moves, with a golden sequence of 10-11 moves.

  • Stoofvlees vs. Igel is one of the most sacrificial engine games I've seen, it has a golden sequence of 21 moves: 1. Nb5!! axb5 2. axb5 b6 3. Ra6 Kb7 4. Bd4 Nc8 5. c3 Ba5 6. c4 g4 7. Rxa5!! bxa5 8. b6 Qd6 9. c5 Qc6 10. Nd2 a4 11. Nb3!! axb3 12. Ra1 Nd6 13. Ra7+ Kb8 14. cxd6 Qc1+ 15. Bf1 Nh6 16. Qe2 Qc6 17. Qa6 b2 18. Qa2 b1=Q 19. Qxb1 Nf5 20. b7 Nxd6 21. Ra6 Nxb7 22. Rxc6. It's sound enough, given that it was played by two engines. (I do realize that engines make mistakes too.) Also, it's the most silent golden sequence I know, Black King received only a single check. Torch played against Leela without a rook for 21 moves: 1. fxe6!! Nxd6 (...) 20. Rh4+ Kb5 21. Qxd5. Meanwhile AlphaZero's [famous knight sacrifice] in the opening produced a golden sequence of only 18 moves: 20. h4 f6 (...) 37. Rd1 Nc5 38. Rxd8.

  • This composition (Shinkman, William Anthony, American Chess Bulletin, Jan 1910) has a checkmate in 36 moves. It's not a golden sequence only because all moves are checks / the length is achieved through an obvious repeating idea.

  • [E Diemer vs F Trommsdorf] — out of all crazy games I know, this is the longest and the most correct one (contrast it with C van de Loo vs M Hesseling). 28 crazy moves starting with 13. Rxh7, even though it doesn't fit the exact definition of a golden sequence. Grigory Serper's [endless array of sacrifices] was just 22 moves long: 17.Nd5 cxd5 (...) 40.Qd6+ Kf7 41.Qxe7+ (there was an unnecessary repetition) with a golden sequence of only 15 moves.

  • I Khairullin vs V Bologan has a golden sequence of 41 moves with little mistakes. [Morozevich vs Vachier-Lagrave] has a golden sequence of 33 moves, except it contains too many mistakes and the protagonist fails at his goals: 15. Nxe6 Qa5 (...) 48. Kc4 Qxd5+. Both of those outliers have the theme of a trapped rook.

  • This grotesque position (by me) seems to have a completely sound golden sequence of 33 moves: 1. Qhxh4 Qxh4 2. Rxh4+ Kxg6 3. Qxg5+ Kxg5 4. Nxf3+ Kg6 5. Rh6+ Kg7 6. Rh7+ Kxh7 7. Qxf7+ Rg7 8. Ng5+ Kh6 9. Ne4+ Kh7 10. Qh5+ Kg8 11. Qe8+ Kh7 12. Kf2 Rxg2+ 13. Kxg2 Nf8 14. Rh1+ Kg8 15. Rxh8+ Kxh8 16. Qxf8+ Kh7 17. Ng5+ Kg6 18. Qf6+ Kh5 19. Ne6 Qg7+ 20. Nxg7+ Qxg7+ 21. Qxg7 f4 22. Qf7+ Kg5 23. Qxf4+ Kg6 24. Qh6+ Kf7 25. Qh7+ Ke6 26. Qg6+ Ke7 27. Bg5+ Kd7 28. e6+ Kc8 29. e7 Qd5+ 30. Kf2 Qc7 31. e8=Q+ Kb7 32. Qe7 and on the next move the sequence ends (not enough heavy pieces on the board). It's possible to have ~36 moves; 40 moves should be possible if you jumble the pieces on the side in a right way (or not).

[White "My grandma"]
[Black "My grandpa"]
[FEN "6rb/qq1n1b2/pqp3Bk/pq2Pppq/p2pR2b/pQpP1rQ1/P1PN2P1/2BRK2Q w - - 1 1"]

1. Qhxh4 Qxh4 2. Rxh4+ Kxg6 3. Qxg5+ Kxg5 4. Nxf3+ Kg6 5. Rh6+ Kg7 6. Rh7+ Kxh7 7. Qxf7+ Rg7 8. Ng5+ Kh6 9. Ne4+ Kh7 10. Qh5+ Kg8 11. Qe8+ Kh7 12. Kf2  Rxg2+ 13. Kxg2 Nf8 14. Rh1+ Kg8 15. Rxh8+ Kxh8 16. Qxf8+ Kh7 17. Ng5+ Kg6 18. Qf6+ Kh5 19. Ne6 Qg7+ 20. Nxg7+ Qxg7+ 21. Qxg7 f4 22. Qf7+ Kg5 23. Qxf4+ Kg6 24. Qh6+ Kf7 25. Qh7+ Ke6 26. Qg6+ Ke7 27. Bg5+ Kd7 28. e6+ Kc8 29. e7  Qd5+ 30. Kf2 Qc7 31. e8=Q+ Kb7 32. Qe7 

So, it seems like ~25 moves is a pretty hard limit, even for engine games. (Not counting games with trapped rooks.) Not hard to see why. Anything that approaches the limit is a deep brilliancy; anything that goes beyond 25 moves is a wild anomaly. I think golden sequences reveal a limited, but a pretty good way to estimate chess' potential for complexity.

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  • (Sorry, I don't have enough reputation to include all the relevant links. ) Feb 4 at 11:03

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