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The bishop has no targets on h3 and this move allows black to break at the center. It would have been better to recentralize with Qf4.
19...d5 20. Qf4+ Ka7 21. Rhe1 d4 22. Nd5!
If Black plays 22…Nfxd5?, White responds with 23. exd5 Qd6 24. Qxf7+ which leads to White being up a piece, e.g. 24…Kb8 25. Re6 Qc7 26. Re7 Nd7 27. Nc6 Bxc6 28. dxc6 Qxc6 29. Bxd7.
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The position after 23…Qd6
22...Nbxd5 23. exd5 Qd6 24. Rxd4!!
Now the fireworks start.
24...cxd4?
While Black would have been better off declining the rook sacrifice with Kb6!, the game would have been largely forgotten.
Black can not reply with Nxd5 because White could have then played Qxf7+.
25. Re7+!! Kb6
If Black played 25…Qxe7??, White plays 26. Qxd4+ to start one of the three forced mating sequences:
26…Kb8 27. Qb6+ Bb7 28. Nc6+ Ka8 29. Qa7#
26…Kb8 27. Qb6+ Qb7 28. Nc6#
26…Qc5 27. Qxc5+ Kb8 28. Qb6+ Bb7 29. Qxb7#
26. Qxd4+!
This sacrifices a knight to continue the attack.
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Position after 27… Ka4
26...Kxa5 27. b4+ Ka4 28. Qc3?!
Lubomir Kavalek, writing for The Washington Post, was the first one to observe that Ra7!! is a better attack for White in this position.
28...Qxd5
28...Bxd5?? is refuted with 29. Kb2 followed by Qb3+ and cxb3#.
29. Ra7 Bb7 30. Rxb7 Qc4!
This move forces the white queen to move away temporarily.
After the game, Topalov analyzed the position with his second Silvio Danailov for hours and told the press at the tournament that Black had drawing chances after 30…Rhe8 31. Rb6 Ra8 32. Be6. However, Black is in trouble if White instead plays 32. Bf1!!.
If Black played 30…Qxb7??, 31. Qb3# follows.
31. Qxf6 Kxa3?!
Black takes the pawn to prevent checkmate from 32. Qxa6#.
However, Black had much better drawing chances with 31…Rd1+! During the game, Kasparov visualizing this line saw White having a stronger endgame after 32. Kb2 Ra8 33. Qb6 Qd4+ 34. Qxd4 Rxd4 35. Rxf7 a5 36. Be6 axb4 37. Bb3+ Ka5 38. axb4+ Kb6 39. Rxh7 but realized, after the game was over, that Black could have fought for a draw with 39…Rf8. Computer analysis shows no clear win for White after 39…Rf8, but also shows White had better fighting chances after 35. Bd7 Rd6 36. g4 in a line very hard for humans to visualize.
As the game ended, Kasparov remembers the audience in the hall applauding.
References
Kaehler, Arne (10 November 2021). "Svitlana's Smart Moves - Kasparov's immortal". ChessBase. Retrieved 27 August 2022. ... one of the greatest chess games ever played is the one between Garry Kasparov and Veselin Topalov from 1999 in Wijk aan Zee.
"The Best Chess Games Of All Time". Chess.com. 18 August 2018. Retrieved 27 August 2022. Kasparov has a long list of brilliancies to his credit, but this game is his virtually undisputed masterpiece.
^ Kasparov, Garry (2014). Garry Kasparov on Garry Kasparov: Part III. Everyman Chess (Gloucester Publishers Limited).