Kasparov's Immortal Game. Flawed? 24...Kb6! Suggest an improvement for White Kasparov's immortal game vs Topalov is often regarded as one of the best games in chess history. 

However, after analyzing it, I find that objectively speaking, Kasparov played some bad moves and got into a slightly worse position. Here, in this position below, Kasparov sacrificed his rook on d4 and Topalov made a mistake by capturing it. 

    [White "Garry Kasparov"]
    [Black "Veselin Topalov"]
    [FEN "b2r3r/k4p1p/p2q1np1/NppP4/3p1Q2/P4PPB/1PP4P/1K1RR3 w - - 0 24"]

    1. Rxd4 cxd4 2. Re7+ Kb6 3. Qxd4+ Kxa5 4. b4+ Ka4 5. Qc3 Qxd5 6. Ra7 Bb7 
    7. Rxb7 Qc4 8. Qxf6 Kxa3 9. Qxa6+ Kxb4 10. c3+ Kxc3 11. Qa1+ Kd2 12. Qb2+ Kd1 
    13. Bf1 Rd2 14. Rd7 Rxd7 15. Bxc4 bxc4 16. Qxh8 Rd3 17. Qa8 c3 18. Qa4+ Ke1 
    19. f4 f5 20. Kc1 Rd2 21. Qa7 1-0


However, if Topalov had played 24...Kb6! then Kasparov's initiative would have come to nothing. 

    [White "Garry Kasparov"]
    [Black "Veselin Topalov"]
    [FEN "b2r3r/k4p1p/p2q1np1/NppP4/3p1Q2/P4PPB/1PP4P/1K1RR3 w - - 0 24"]

    1. Rxd4 Kb6! 2. b4 Qxf4 3. Rxf4 Nxd5 4. Rxf7 cxb4 5. axb4 Nxb4 6. Nb3 Bd5 7. Rf6+ 
    Nc6 8. f4 Rhf8 9. Rxf8 Rxf8 


and Black is slightly better. 

If we compare this position to the position after move 16, White does seem slightly better. 

   [White "Garry Kasparov"]
   [Black "Veselin Topalov"]
   [FEN "r3k2r/1b1nqp1p/p1pp1npQ/1p2p3/3PP3/P1N2P2/1PP1N1PP/1K1R1B1R w kq - 0 13"]


The question therefore is, where did Kasparov misplay the position? How did he lose his small positional advantage. Where is the improvement for White? Or is White's positional advantage an illusion? Is the position objectively equal or even better for Black?
The question therefore is, where did Kasparov misplay the position? 


No, he did not. All the lines give Black equal chances, no matter what move White chose to play.


  How did he lose his small positional advantage.


He did not lose advantage because there was none in the first place. White position just looks "prettier". He can not stop the freeing d5 break, which means that Black will eventually equalize.


  Where is the improvement for White?


At this point I see no improvement, but maybe some super computer or creative GM can find one. Time will tell.


  Or is White's positional advantage an illusion?


White has healthier pawn structure, but you do not consider Black's dynamic resources such as development advantage and active piece placement. They counterbalance White's healthier pawn structure.

After Black gets d5 break it all depends if White can punish Black for pushing too many pawns forward. To do that, he need an endgame with better pieces but that will never happen with proper play because Black has better posted and more active pieces.

White does not have an advantage, but his position is "prettier" due to the healthier pawn structure. Again I point out that black has better piece placement, and can liquidate the d6 backward pawn after which things are unclear.


  Is the position objectively equal or even better for Black? 


I will quote Mr.Kasparov himself from Chess Informant 74 :

[fen "2kr3r/1b2qp1p/pn1p1npQ/1pp5/4P3/PNN2P2/1PP3PP/1K1R1B1R w - - 2 16"]

1.Na5 ( 1.a4?! b4 2.a5 bxc3 3.axb6 Nd7=/+ ) 1...d5 2.Nxb7 ( 2.g3 b4∞ ) 2...Kxb7 3.exd5 Nbxd5 4.Nxd5 Nxd5 5.Bd3 f5 6.Rhe1 Qc7 7.Bf1 c4∞ 


Here is the zip file that holds almost every published analysis of this game, including Kasparov's comments after the game. It was also instructive to go through the comments of top GMs as well as other "lesser players" who used engines for the analysis. Just click on the spinning red box:



SUMMARY:

Although White has better pawn structure, he is behind in development and his queen is misplaced. 

Black does have a backward pawn on d6 and has compromised his pawn structure on both wings but that is not so bad for him since his pawns restrict the opposing light pieces. He has more space on the queenside and a chance to obtain initiative on that part of the board, while his holes on dark squares on the kingside can not be effectively exploited. He has wonderful piece coordination and activity and will achieve the freeing d5 break, eliminating the weakest piece in his setup, thus achieving full equality. 

I evaluate this position as sharp/unclear with equal chances for both sides.

As for Topalov losing this one, you must be aware that Kasparov tried a3 as a novelty, which probably threw Topalov out of balance a little, so he misplayed it in the end. He was probably in time pressure, or simply lost focus due to calculating all the possibilities in a new position which is always a difficult task. Up until cxd4? he played well, even Kasparov had to award exclamation points for some of his moves.

Hopefully this helps. If you have further questions leave a comment.

Best regards.