<INTRODUCTION>

Kasparov vs Kramnik, 2000 is the <first game of the Kasparov-Kramnik World Championship Match (2000)>, which was set up by the Braingames organization during the split from FIDE.

Quantitative mapping of this game between these players follows. Figures in brackets immediately after each move are the corrected engine evaluations generated on the forward slide that followed the initial reverse slide originating from the last move of the game after all moves had been inputted into the engine. Some evaluations are bolstered by analysis, while some are the result of further –occasionally multiple - slides in one or both directions. This smoothed out nearly all fluctuations in the engine’s evaluations, apart from in the opening.

General methods used are described in the bio of the User: bridgeburner (at the top of this page).

Engine preferences are included throughout the game where they differ from players preferences except in the well trodden opening, where evaluation values are included for completeness rather than in the interests of complete accuracy which is not knowable in the opening.

Some analysis is included to provide some idea of the reason for the engine preferences where they didn’t coincide with the moves played. In this game, despite it having theoretical importance, the variations were not explored in depth (ie: move by move deep slide), and therefore the variations posted next to the engine preferences are a cut and paste of engine analysis, albeit an extremely deep ply cumulative result of sliding back and forth along the main line.

<Summary>

THE GAME

Commentary for this game is extracted from Karsten Mueller ’s online publication <Kasparov-Kramnik 2000).

GAME MOVES 1-2:

<1. e4> (0.21) <1…e5> (0.21)

<2. Nf3> (0.21) <2. ..Nc6> (0.26)

Müller: <A bit of a surprise, since normally the Petroff with 2...Nf6 is Kramnik’s main weapon against 1.e4.>

GAME MOVE 3:

<3. Bb5> (0.22)

Müller: <!? Kasparov is not to be outdone and plays the Ruy Lopez instead of the Scotch. It is apparent that both players have worked out some unusual openings strategies for this match.>

GAME MOVE 3:

<3…Nf6> (0.22)

Müller: <The Berlin Defense is not encountered as often as the main variation with 3...a6, but it doesn’t have a bad reputation. Initially both players follow well-known paths to the endgame.>

GAME MOVES 4-5:

<4. 0-0> (0.13) <4…Nxe4> (0.14)

<5. d4> (0.13) <5…Nd6> (0.13)

This appears to have been first played by James Innes Minchin against George Alcock MacDonnell in 1866, a novelty that allowed him to draw against the famous player.

GAME MOVES 6-7:

<6. Bxc6> (0.13) <6…dxc6> (0.13)

<7. dxe5> (0.13) <7…Nf5> (0.13)

Minchin played <7…Ne4> and drew. While the stats show it is a reasonable defense, this move has been superceded by the now universally played text move, successfully introduced by Fritz Riemann in 1880 in his Berlin match against Emil Schallopp. Schallop’s response was <8. Qe2> which was met by <8…Nd5>, soon winning a pawn and eventually, the game.

GAME MOVE 8:

<8. Qxd8+> () <8…Kxd8> (0.13)

Müller: <This is an interesting and often discussed position. White has a vital extra pawn on the kingside, and Black cannot castle. In return, Black has the bishop-pair and no easily exploitable weaknesses. Opinions about the evaluation of the position are inconclusive. We will see if the discussion is taken up again in the course of this match.>

GAME MOVE 9:

<9. Nc3> (0.13)

Lasker experimented with 9. g4 in a 1901 simul and was soundly beaten: Lasker vs A Y Hesse, 1901. Unsurprisingly, it never caught on and there is no record in the database of this move being played again.

GAME MOVE 9:

<9…Bd7> (0.13)

According to the database, this move debuted in this game. The earliest response to 9. Nc3 was 9…h6 in Wemmers vs F Riemann, 1880, a move which was played almost universally until it was gradually supplanted in late 20th century theory.

GAME MOVE 10:

<10. b3> (0.03)

10. h3 has since become more popular, and if results are any indication, is a better move.

GAME MOVES 10-12:

<10…h6> (0.19)

<11.Bb2 > (0.21) <11…Kc8> (0.54)

<12. h3> (0.41)

Müller: <This is Garry’s novelty. Kramnik now responds in a way that makes it difficult for White to achieve g4, because it can be attacked with h7-h5. 12.Rad1 a5 13.h3 b6 14.a4 Bb4 15.Ne2 Re8 16.Nf4 g6 17.g4 Ng7 18.Rd3 Ne6 19.Nxe6 Bxe6 20.Nd4 Bd7 21.Ne2 Bd6 22.f4 f5 23.exd6 Rxe2 24.dxc7 Kxc7 25.Be5+ Kc8 26.Rfd1 Be6 27.Rd6 1–0, Shirov vs Krasenkow, 2000>.

GAME MOVE 12:

<12…b6> (0.46)

GAME MOVES 13:

<13. Rad1> (0.44)

Müller: <Kasparov has 1:13 remaining vs. 1:48 for Kramnik, which tells us who stayed in the main line of his preparation longest. The position is a bit better for White, but the black bishops are not easy to overcome.>

Engine preference: <13. a4> (+0.54) <13…a5 14.Rad1 Be7 15.Rd3 Nh4 16.Nxh4 Bxh4 17.Ne2 Bf5 18.Rf3 Bxc2 19.Rxf7 Bxb3 20.Rxg7 Re8 21.Nd4 Bxa4 22.Nf5 Bd8 23.Nxh6 Be7 24.f4 Bf8 25.Rh7>

GAME MOVE 13:

<13…Ne7> (0.47)

Engine preference: <13…Be7> (+0.44): <14.Rd2 a5 15.a4 Rd8 16.Rfd1 Nh4 17.Nxh4 Bxh4 18.Ne2 Bf5 19.Rxd8+ Bxd8 20.Nd4 Bd7 21.Re1 g6 22.e6 fxe6 23.Nxe6 Kb7 24.Nf8 Bf5 25.Re2 h5>

GAME MOVE 14:

<14. Ne2> (0.41)

Engine preferences:

1. <14. Rd2> (+0.47) <14…Bf5 15.Ne2 Kb7 16.Ng3 Be6 17.Rfd1 Ng6 18.Nh5 Rg8 19.Nd4 Bd7 20.f4 Bb4 21.Rd3 Be7 22.c4 Raf8 23.a4>

2. <14.Rfe1> (+0.43) <14… c5 15.Ne2 Ng6 16.h4 h5 17.Ng5 Be7 18.Nxf7 Rf8 19.Ng3 Bg4 20.e6 Bxh4 21.Bxg7 Re8 22.Rd3 Rxe6 23.Rxe6 Bxe6 24.Ne5 Nxe5 25.Bxe5>

3. <14. Ne4> (+0.41)

GAME MOVES 14-16:

<14…Ng6> (0.41)

<15. Ne1> (0.41) <15…h5> (0.41)

<16.Nd3 > (+0.24)

Müller: < Kasparov has only 39 minutes left, which indicates that he has had problems finding a plan that would bring serious danger to his opponent. 16.Nf3!? 16 Ng5 was also possible, and takes advantage of the fact that 15...h5 has weakened the g5-square.>

Engine preferences:

1. <16. Kh2> (+0.41): <16…h4 17.f4 c5 18.Nc3 Ne7 19.Nf3 Nf5 20.Rfe1 Be7 21.Rd2 Be6 22.Nd5 Kb7 23.c4 Rae8 24.Kg1 c6 25.Nxe7>

2. <16. c4> (+0.40): <16…h4 17.Kh2 c5 18.Nc2 Be6 19.Ne3 Rh5 20.f4 Ne7 21.Nc3 Kb7 22.Ncd5 Re8 23.Ng4 Rd8 24.Nde3 Rxd1 25.Rxd1 g6 26.Nf6 Rh8 27.Neg4>

3. <16. f4> (+0.32): <16…Nh4 17.c4 Bc5+ 18.Bd4 Bxd4+ 19.Nxd4 c5 20.Ndf3 Nf5 21.Kf2 Bc6 22.Nc2 Kb7 23.Ne3 Nxe3 24.Kxe3 Rhe8 25.Rfe1 Rad8 26.Rxd8 Rxd8 27.f5 a5 28.h4>

GAME MOVE 16:

<16…c5> (+0.40)

Engine preference:

1. <16…Kb7> (+0.24): <17.Nc5+ Bxc5 18.Rxd7 Rae8 19.Rxf7 Nxe5 20.Bxe5 Rxe5 21.Nf4 Rf8 22.Rxf8 Bxf8 23.Ng6 Re8 24.Nxf8 Rxf8 25.Rd1 g6 26.Rd7 b5 27.Kf1 Rf5 28.Ke2 Kb6

2. <16…a5> (+0.30): <17.Rfe1 Bb4 18.c3 Be7 19.c4 a4 20.Nd4 Nf8 21.Bc3 Kb7 22.Nf4 axb3 23.axb3 Ra2 24.e6 fxe6 25.Ndxe6 Bxe6 26.Nxe6 Nxe6 27.Rxe6 Bc5>

GAME MOVE 17:

<17. c4> (+0.19)

Müller: < Closing up the position is advantageous for White. Black’s bishop-pair is better in open positions.>

GAME MOVE 17:

<17…a5> (+0.20)

Müller: <Kramnik wants to open the a-file for his rook with an eventual a5-a4.>

GAME MOVE 18:

<18. a4> (+0.00)

Müller: <Kasparov nails down the queenside in typical fashion. Black can no longer mobilize his pawn majority because of the doubled pawn (after ...c6 and ...b5, White simply stays put), while at the same time Kasparov is able to get a passed pawn on the kingside in the long run. Kasparov has 37 minutes left and strolls across the stage looking confident, while Kramnik, who has much more time on his clock, seems quite uncomfortable in his seat.>

Engine preferences:

1. <18. f3> (+0.20)

2. <18. Ne1> (+0.17) <18…Be7>

3. <18. Nc3> (+0.16): <18…Be6>

GAME MOVE 18:

<18…h4> (0.14)

Müller: <!? Kramnik 49:00. 18...Be7?! 19.Ndf4 Nxf4 20.Nxf4 Bf5 21.Nd5 Bd8 22.Ne3± (Fritz).>

GAME MOVE 19:

<19. Nc3> (+0.00)

<Engine preference> <19. Ndf4> (+0.14): <19…Bf5 20.Nxg6 Bxg6 21.Rd2 Bf5 22.Nf4>

GAME MOVE 19:

<19…Be6> (+0.13)

<Engine preferences>: <19…c6> (0.00)

GAME MOVE 20:

<20. Nd5> (0.13)

Müller: <Even after 20.f4 Rh5 21.Nd5 Kb7 22.Ne3 Ne7 Black can stop f2-f4-f5.>

GAME MOVE 20-21:

<20…Kb7> (0.13)

<21. Ne3> (+0.13) <21…Rh5> (+0.13)

Müller: <This unusual development of the rook is directed against f2-f4-f5.>

GAME MOVE 22-23:

<22. Bc3> (+0.13) <22…Re8> (+0.13)

<23. Rd2> (+0.10)

<Engine preference> <23. Bb2> (+0.13): <23…Bc8 24.Rfe1 Rh8 25.Rd2 Rh5>

GAME MOVE 23:

<23…Kc8> (+0.36)

<Engine preferences>

1. <23…Be7> (+0.10): <24.f4 Bc8 25.Rfd1 c6>

2. <23…Bc8> (+0.10): <24.Rfd1>

3. <23…Rg5> (+0.18): <24.Kh1 Bc8 25.Kh2 Be6 26.Bb2>

GAME MOVES 24-25:

<24. f4> (+0.36) <24…Ne7> (+0.36)

<25. Nf2> (+0.36) <25…Nf5 > (+0.36)

Müller: <Black has achieved a solid blockade; neither side can make any progress>

Draw agreed.

Final position:

click for larger view

<CONCLUSION> The biggest jump in engine evaluations came with Kramnik’s innovation at <11…Kc8> (+0.33), which lead to a well-analyzed position that he was able to hold without apparent difficulty. In fact, Kasparov used up far more time in the opening.

According to the database, this move debuted in this game.]

seems to be incompatible with

[<12. h3> (0.41)

The psychological hit on Kasparov must be understood in the context that Kasparov's greatest weapon in his career was his unsurpassed opening preparation. His repertoire as white nearly always got him into at least equal middlegames wherein he had room to use his considerable native skills to beat his opponents. Suddenly he realized that Kramnik had neutralized this white advantage, that winning with white would be a real problem. This game was drawish with little room for struggle right out of the opening.

On the other hand, Kramnik's morale must have been tremendously boosted by this game. He realized that he he might just have deprived Kasparov of his biggest weapon.

Now both players understood that Kasparov could not rely on any opening surprise anymore to get into the kind of middlegames that he liked. Kasparov would have to work hard over the board to obtain a winning advantage with white for the rest of the match.

In contrast, in the 1995 WC match Kasparov crushed Anand when he repeatedly obtained advantageous middle games right out of openings that Anand mishandled. Kramnik, who was Kasparov's second in that match, understood this completely; and knew that depriving Kasparov of any opening advantage would double his chances for a possible match victory.

<INTRODUCTION>

Kramnik vs Kasparov, 2000 is the second game of the Kasparov-Kramnik World Championship Match (2000).

Quantitative mapping of this game between these players follows. Figures in brackets immediately after each move are the corrected engine evaluations generated on the forward slide that followed the initial reverse slide originating from the last move of the game after all moves had been inputted into the engine. Some evaluations are bolstered by analysis, while some are the result of further –occasionally multiple - slides in one or both directions. This smoothed out nearly all fluctuations in the engine’s evaluations, apart from in the opening.

General methods used are described in the bio at the top of this page.

Engine preferences are included throughout the game where they differ from players preferences except in the well trodden opening, where evaluation values are included for completeness rather than in the interests of complete accuracy which is not knowable in the opening.

Some analysis is included to provide some idea of the reason for the engine preferences where they didn’t coincide with the moves played.

<Important Note>: All evaluations outside the opening are subject to at least two 20 ply engine evaluations. Where engine evaluations do not correlate in consecutive moves where the later move played is the engine’s first preference, the evaluation process is “goosed” to enable the moves in question to be subject to additional and sometimes repeated sliding analysis in both directions, and to have their evaluations augmented by deep ply variation analysis.

The entire mapping process occurs with the engine running non-stop to preserve all the hash files that add information to the engine’s evaluation process.

<Summary>

THE GAME

Commentary for this game is extracted from Karsten Müller’s online publication <Kasparov-Kramnik 2000): http://www.chesscafe.com/text/kvsk2....

GAME MOVE 1:

<1. d4> (+0.20)

Müller: <”!? Kramnik wants to go for it. He has prepared a plan against Kasparov’s Grünfeld!”>

GAME MOVES 1-3:

<1…Nf6> (+0.20)

<2. c4> (+0.16) <2. ..g6> (+0.24)

<3. Nc3> (+0.22) <3…d5> (+0.24)

Müller: <” Kasparov accepts the challenge.”>

GAME MOVEs: 4-9

<4. cxd5> (+0.24) <4…Nxd5> (+0.24)

<5. e4> (+0.24) <5…Nxc3> (+0.24)

<6. bxc3> (+0.15) <6…Bg7> (+0.29)

<7. Nf3> (+0.15) <7…c5> (+0.13)

<8. Be3> (+0.00) <8…Qa5> (+0.15)

<9. Qd2> (0.00) <9…Bg4> (0.50)

Engine preferences:

1. <9…0-0> (0.00): <10.Rb1>

2. <9…Nc6> (+0.08): <10.Rb1 a6 11.Bc4 O-O 12.O-O cxd4 13.Nxd4 Ne5 14.Be2 Qc7 15.f4 Nc4 16.Bxc4 Qxc4 17.e5 Qc7 18.Qc2 b5 19.a4 bxa4 20.Qxa4 Bb7>

3. <9…b6> (+0.24): <10.Bc4 Nc6 11.Rc1 Ba6 12.Qd3 b5 13.Bd5 Rc8 14.Qd2 O-O 15.Bh6 cxd4 16.Bxg7 Kxg7 17.cxd4 Qxd2+ 18.Kxd2>

GAME MOVES 10-11:

<10. Rb1> (0.50) <10…a6> (0.50)

<11. Rxb7 > (0.50)

Müller:<”Ivanchuk and Levin give this natural move a “?!” in Chess Informant. Kramnik apparently sees it differently. 11.Rb3?! b5 with counterplay, as in [ Timman vs Ivanchuk, 1992 Linares ] (Informant 54/42).”>

GAME MOVES 11-12:

<11…Bxf3> (0.63)

<12. gxf3> (0.63) <12…Nc6> (0.63)

Müller: <” Ivanchuk and Levin give this variation in Informant without an evaluation.”>

GAME MOVE 13:

<13. Bc4> (0.58)

<Engine preference>: <13. Bg2> (+0.63): <13…Rd8 14.O-O cxd4 15.cxd4 Qxd2 16.Bxd2 Nxd4 17.Bb4 Bf6 18.e5 Bg5 19.Re1 Nc2 20.f4 Bh4 21.Ba5 Nxe1 22.Bxd8 O-O 23.Bxe7 Bxe7 24.Rxe7 Nd3>

GAME MOVE 13:

<13…0-0> (0.79)

Müller: <” 13...e6 14.Bxe6 (Skripchenko) (14.0-0!?) 14...Nd8 15.Bd5 Nxb7 16.Bxb7 Rb8 17.Bc6+–; 13...cxd4 14.cxd4 Qxd2+ 15.Kxd2 Nxd4 16.f4 .”>

<Engine preference>: <13…Rc8> (+0.58): <14.Bd5 cxd4>

GAME MOVE 14:

<14. 0-0> (0.51)

Engine preferences:

1. <14. Bd5> (+0.79): <14…Rfb8 15.Bxc6 Rxb7 16.Bxb7 Rb8 17.O-O cxd4 18.cxd4 Qxd2 19.Bxd2 Rxb7 20.Be3 f5 21.Rc1 Rb2 22.Rc7 f4 23.Bxf4 Bxd4 24.Rxe7 Bxf2+ 25.Kh1>

2. <14. Ke2> (+0.56): <14…Rfd8 15.Rd1 cxd4 16.cxd4 Bxd4 17.Bd5 Rxd5 18.exd5 Qxd5 19.Rc1 Rd8 20.Rb3 f5 21.Ke1 Qxf3 22.Qc2 Qh1+ 23.Ke2 Bxe3 24.Qc4+ Qd5 25.Qxd5+ Rxd5 26.Rxc6 Bf4 27.Rxa6>

GAME MOVE 14:

<14…cxd4> (0.51)

Müller: < (“14...Rfd8!?”)>

GAME MOVE 15:

<15. cxd4> (0.51) <15…Bxd4> (0.51)

Müller: <”After 15...Qxd2 16.Bxd2 Nxd4 17.Kg2, the pair of bishops gives White a small but permanent advantage. The weak a-pawn in particular may cause Black some headaches.”>

GAME MOVE 16:

<16. Bd5> (+0.51) <16…Bc3> (+0.62)

Müller: <”16...Qxd2 17.Bxd2 Rfc8 .”>

GAME MOVE 17:

<17. Qc1> (+0.+0.52)

Engine preference: <17.Qc2> (+0.62): <17…Rac8 18.Rc1 Ne5 19.Qb3 Nxf3+ 20.Kg2 e6 21.Kxf3 exd5 22.Qxd5 Qxd5 23.exd5 Be5 24.Rxc8 Rxc8 25.Rb6 Bxh2>

GAME MOVE 17:

<17…Nd4> (+0.93)

Müller: <”Kasparov gives up a pawn in order to get one of the white bishops off the board, going into an endgame with opposite-colored bishops.”>

Note: Kramnik has won the opening battle and the only winning chances would be with White. Kasparov acknowledges this and plays for the draw.

Engine preference: <17…Rac8> (+0.52): <18. Bb6 Qb4 19.a3 Qb2 20.Qxb2 Bxb2 21.a4 Ba3>

GAME MOVES 18-21:

<18. Bxd4> (+0.93) <18…Bxd4> (0.93)

<19. Rxe7> (+0.93) <19…Ra7> (+0.97)

<Engine preference>: <19...Bc5> (+0.93): <20.Rb7 Ra7 21.Rxa7 Bxa7>

<20. Rxa7> (0.97) <20…Bxa7> (0.97)

<21. f4> (+0.75)

Müller: <”Kramnik wants to contest the dark squares and start a kingside attack in the long run. 21.Qg5 allows 21...Qc3.”>

<Engine preferences>:

1. <21. Kg2> (+0.97): <21…Qb6 22.h4 Bb8 23.Rd1 Qf6 24.Qg5 Qxg5+ 25.hxg5 Bf4 26.Rd4 a5 27.Ra4 Bd2 28.Kg3 Rc8 29.f4 Rc1 30.Rd4 Bc3 31.Rd3>

2. <21. h4> (+0.90): < 21…Qd8 22.Qg5 Qd6 23.h5 Bb8 24.Qh4 Qf4 25.Qxf4 Bxf4 26.hxg6 hxg6 27.Bb7 a5 28.Rd1 Kg7 29.Rd7 Kh6 30.Bd5>

3. <21. Qg5> (+0.88): <21.Qg5>

GAME MOVES 21-22:

<21…Qd8> (+0.75)

<22. Qc3> (+0.75)

Müller: <”Kramnik maintains his strategy not to leave the dark squares to Kasparov’s queen and bishop.”>

GAME MOVES 22-25:

<22…Bb8> (+0.75)

<23. Qf3> (+0.75) <23…Qh4> (+0.75)

<24. e5> (+0.75) <24…g5> (+0.75)

<25. Re1> (+0.75)

Müller: <”Kramnik goes into an endgame with rooks, opposite-colored bishops, and an extra pawn. 25.e6!? (Skripchenko).”>

GAME MOVES 25-29:

<25…Qxf4> (+0.75)

<26. Qxf4> (+0.75) <26…gxf4> (+0.75)

<27. e6> (+0.75) <27…fxe6> (+0.75)

<28. Rxe6> (+0.75) <28…Kg7> (+0.75)

<29. Rxa6> (+0.75) <29…Rf5> (+0.88)

<Engine preferences>:

1. <29…Rd8> (+0.75): <30.Ra5 Bc7 31.Rc5 Bd6 32.Rb5>

2. <29…Rf6> (+0.80)

GAME MOVE 30:

<30. Be4> (+0.83)

<Engine preference>: <30. Bf3> (+0.88): < 30…Rc5 31.Kg2 Rc2 32.Be4 Rd2 33.Ra5 h6 34.a4 Ra2 35.Kf3 Kf6 36.Bd5 Rc2 37.h4 Bd6 38.Bb7 Rc5>

GAME MOVES 30-31:

<30…Re5> (+0.83)

<31. f3> (+0.75)

<Engine preference>: <31. Bf3> (+0.83): <31…Re7 32.Ra8 Bd6 33.Kg2 Kf6 34.Ra6 Ke5 35.Ra5+ Kf6 36.Bd5>

GAME MOVES 31-34:

<31…Re7> (+0.75)

<32. a4> (+0.75) <32…Ra7> (+0.75)

<33. Rb6> (+0.75) <33…Be5> (+0.75)

<34. Rb4> (+0.75)

Müller: <”This endgame is very unpleasant for Kasparov because the rooks are still on the board. And, in time trouble, all problems are compounded.”>

GAME MOVE 34:

<34…Rd7> (+0.98)

Müller: <”? Allowing the a-pawn to advance farther. But activating the rook also weakens the h-pawn considerably.”>

<Engine preferences>:

1. <34…Bc3> (+0.75): <35.Rc4 Bd2 36.Kg2 Be3 37.Bc2 h5 38.Rc6 Ra5 39.h4 Kf7 40.Bb3+ Kg7 41.Kf1 Re5 42.Bc2 Rd5>

2. <34…Bd6> (+0.80): <34...Bd6 35.Rc4 Ra5 36.Kg2 Rg5+ 37.Kh3 Kf7 38.Rc6 Ke7 39.Kh4 h6 40.Bd3 Kd7 41.Bb5 Ke6 42.Rc2 Bb4 43.Be8 Ke7 44.Bb5 Be1+ 45.Kh3 Kf6>

3. <24…Ra5> (+0.80): <35.Rc4 Bd6 36.Kg2 Rg5+ 37.Kh3 Kf7 38.Rc6 Ke7 39.Kh4 h6 40.Bd3 Kd7 41.Bb5 Ke6 42.Rc2 Bb4 43.Be8 Ke7 44.Bb5 Be1+ 45.Kh3 Kf6>

GAME MOVE 35:

<35. Kg2> (+0.98) <35…Rd2+> (+1.11)

GAME MOVE 36:

<36. Kh3> (+1.11) <36…h5> (+1.67)

The losing move, weakening the h-pawn fatally, and leading inexorably to the loss of the game, and ultimately the match and the crown, creating chess history. This move is classified as a <blunder> under project methodology, after which the game is a loss in all variations.

<Engine preferences>:

1. <36…Ra2> (+1.11): <37.Bd5 Rd2 (if 37…Rb2 38. Rxb2 Bxb2 39. Kg4 wins, eg: 39…Bc1 40. a5 Be3 41. Kf5 Bg1 42. a6 Kf8 43. Ke6 Ke8 44. Kd6 Kd8 45. Be6 ) 38. Rb7+ Kf6 39. Rf7+ Kg6 40. Rd7 Kg5 41. a5 Bc7 42. a6 Bb6 seems to hold>

This analysis was tested to 20-28 ply on each move through to the last move displayed here and beyond.

2. <36…h6> (+1.35)

GAME MOVES 37-38:

<37. Rb5> (+1.67) <37…Kf6> (+1.67)

<38. a5> (+1.67)

Müller: <”38.Rb6+!? was an alternative (Fritz 6).”>

GAME MOVES 38-39:

<38…Ra2> (+1.67)

<39. Rb6+> (+1.64)

<Engine preference>: <39. Rc5> (+1.67)

GAME MOVE 39:

<39…Ke7> (+9.14)

As the game was already lost, this does not count as a blunder under Project methodology, even though it leads to an immediate rather than gradual loss. The Project is unconcerned about evaluation jumps that maintain a game within the won/lost zone. The engine’s preference is as per Müller’s analysis.

Müller: <”?? In time trouble Kasparov gives the game away to a two-mover. With 39...Kg7 he could have defended quite tenaciously, but White wins nevertheless as Kramnik demonstrated. I had found this plan as well, and published it in my Endgame Corner column #3 at ChessCafe.com:

40.a6 Bd4 41.Rg6+ Kf8 42.Bb7 Ra5 43.Rd6 Be3 44.Rd5 normally it is not such a good winning idea to trade rooks in this kind of endgame, but here it works because of the weak black h-pawn and White’s far advanced a-pawn: 44...Rxd5 45.Bxd5 Kg7 (45...Ke7 46.Kh4+–) 46.Kg2 Kf6 47.h4! fixing the weak h-pawn on a dark square is very important! 47...Ba7 (47...Ke7 48.Kh3 Kd6 49.Bf7 Kc7 50.Bxh5 Kb6 51.Kg4 Kxa6 52.Bf7 Kb6 53.Kf5 Kc7 54.Ke6 Bd4 55.h5 Bg7 56.Be8 Kd8 57.Ba4 Bh6 58.Kf6 Bf8 59.Kf7 Bh6 60.Kg6 Bf8 61.h6 Bb4 62.h7 Bc3 63.Kf7+–) 48.Be4 Be3 49.Kf1 Ba7 50.Ke2 Bg1 51.Kd3 Bf2 52.Bh7 Kg7 (52...Ke5 53.Ke2 Bg1 54.Bg6+– ) 53.Bf5 Kf6 54.Ke4 Be3 55.Bh3+–.>

GAME MOVE 40:

<40. Bd5> (+9.14) Black resigns

Müller: <”The pawn endgame after 40.Bd5 Rxa5 41.Re6+ Kd7 42.Rxe5 Kd6 43.Rxh5 Rxd5 44.Rxd5+ Kxd5 45.Kg4 is of course hopeless.”>

Final position:

click for larger view

<CONCLUSION>

Kasparov played true to his active style. The engine was screaming for him to defend against the passed a-pawn by maintaining his Rook in front of it. However, in accordance with his aggressive style <34…Rd7> was the start of a plan to place his Rook on his 7th rank (Kramnik's second rank) and swing it behind the passed a-pawn. This plan severely compromised his defense, as it allowed Kramnik to march his pawn to the 5th rank unimpeded.

Note that in the final position

click for larger view

Kasparov has attained a pseudo-aggressive position, with his Rook behind the passed a-pawn and on Kramnik's second rank, his Bishop and King centralized, and the White king seemingly cornered on the edge of the board. Yet it is also a totally lost position for Black as he does not have enough material to force a direct mate, and he is forced to enter a lost King and pawn ending a pawn down. It is possible that Kasparov was betrayed by his own aggressive style in this game.

This game, following right after the drawish first, must have greatly sapped Kasparov's morale. This can be understood in the context that Kasparov's greatest weapon throughout his career was his unrivaled opening prep. In the 1995 World Championship match with Anand, time and time again Kasparov managed to enter advantageous middle-games out of openings that Anand mishandled. Kramnik, being Kasparov's second in that match, completely understood this and had devised a strategy that would neutralize Kasparov's White opening advantage; and give him chances to win with his own White games.

The first game demonstrated that Kramnik had successfully neutralized Kasparov's opening White advantage with the Berlin, and that Kasparov now had to rely entirely on over the board play to win every White game that could be won, without the opening advantage that he enjoyed in the 1995 match. This second game was won by Kramnik in a Karpovian style that he probably knew was particularly effective against Kasparov. Kasparov went for pseudo-aggressive play when the real essence of the position called for him to hunker down on defense. Yet the skilled Kasparov somehow still managed to avoid committing a decisive mistake. When he did, just a single one, Kramnik immediately KO'd him.

One can just imagine the demoralizing effect of this game on Kasparov. Kramnik on the other hand knew that he had his former mentor teetering on a seat at the edge of a building. Kramnik mercilessly kept him there for the rest of the match, never giving him a single clearly won position; and finally another bad opening in the closing stage of the match allowed the former student to poke the tottering King right off the high chess throne.

<I could see excluding the first 12 moves, say, if one was analyzing an average player whose score might be artificially inflated if he happened to have good book knowledge.>

True, although to be frank I'm not sure I'd have any reason to be interested in anyone below the level of the absolute elite, historical and current.

For a consistent methodology in this respect, exclusion of opening moves applied in any of these move-by-move methodologies should commence when one player leaves "the book", and not before. The depth of theory obviously varies between openings. A fixed number of excluded moves would allow measurement inaccuracies to creep in and affect the result.

It occurred to me that all the top players will have home prep derived from computers, so it's clear that many post-book moves are preps, which clearly does not measure OTB thinking as such, apart from the effort of having to remember that home prep.

I'm not sure there's any real solution to this conundrum, as home prep may not even be the product of the player in the modern day, but of his seconds.

So your DNA research has lead you to the earth-shattering discovery that some individuals are more talented for certain things than others. Few people knew that, including brain surgeons. Everybody was under the impression that we are clones of one another.

<The last 6 players you mentioned were all drawn to chess in the pre-WWI era when the number of people was smaller and thus the number of mentally gifted ones must be proportionally fewer.> <Based on this logic I claim that it's very improbabale that Steinitz, Lasker, Pillsbury, Rubinstein, Capablanca and Alekhine had as able brains as players of the late 20th century.>

The pool from which chess players is derived being smaller will have some effect on the average innate talent of a group of players, say the top 20 for example. A smaller pool means essentially that the distance between one and 20 will be larger than with a bigger pool.

But from that you can draw no conclusions about individual players. If the pool is sufficiently large (and by the 1920s it was) the chances of finding specimens that are at or near the natural limits are good enough. In other words, doubling or tripling the size of the pool will have only a marginal effect in differences between top players. And sometimes no effect at all.

If your conclusions were true, then a country like Uruguay, with a population 60 times smaller than Brazil, could never produce 11 soccer players able to outperform the best 11 Brazilians. But they did. And a country like Cuba with a comparatively minuscule chess pool and tradition could not produce anyone who could outperform all the best players from an astronomically larger pool elsewhere. And Jamaica could never produce so many elite runners... examples can be given endlessly.

What applies to spacial selection also aplies to temporal selection.

I also think that's the best approach. It's also what was done in the Ferreira study, which I consider one of the most straightforward and fog-free approaches to these knds of measurements. He says he included all the moves because:

"With respect to opening theory/preparation, we consider it to be an integral part of strength of play."

Totally unfeasable for many reasons. Lack of enough data being first. There is also no reason whatsoever to assume a linear increase in performance with time. You would expect the increase to be larger when doubling a short time control than a long one. Which means you would need enough data to analyze increases starting from many different initial controls. This will further vary enormously between one player and another, and even in the same player at different ages.

If you have that kind of data and have worked on it, show it. Otherwise any attempt at making adjustments from the relatively minor variations in classic time controls at different periods are certain to do much more damage than good to these kinds of studies.

Same thing applies to the complexity/difficulty issue. First you have to decide how to quantify it in each position. Then you have to decide how to quantify the adjustments you will make based on the quantified difficulty. How you propose to avoid the inherent arbitrariness of it all remains a mystery.

Your faith-based assertion that it is a <self-evident fact> that Lasker could not have played at the same level as Kramnik, and that it would be <utterly unconceivable> if they played at the same level, just because of a larger chess pool today, makes it completely clear you are starting out from your pre-conceived conclusions and trying to work your way to them by introducing totally unquantifiable fudge factors that according to you need to be introduced in order to... reach the appropriate conclusions that you already found self-evident before you started.

Thanks for the comments, all of which I agree with, including those to <nimh>.

I’ve been tracking down discussions on computer analysis of level or accuracy of play, a subject I find very interesting. Your work strikes me as very valuable and different in the sense that it is kind of an artisanal variety in this new field of study. Obviously for analysis of large amounts of games it would be unfeasable, but it is great for comparison of specific matches.

In the more "industrial" type of studies where this level of fine analysis is impossible, I like Regan’s a lot. A few days ago I ranked the IPRs above 2800 in his analysis of a large number of matches – I think he analyzed all the significant matches in the last 120 years or so. All the usual suspects are there. But look at Hou Yifan!

http://www.cse.buffalo.edu/~regan/p...

The ranking I obtained from that study is as follows:

Kasparov WC 1984 (vs Karpov) (games 10-29): 3042
Capablanca 1919 (vs Kostic): 3001
Hou Yifan 2011 (vs Humpy Koneru): 2971
Kramnik WC 2000 (vs Kasparov): 2969
Fischer 1971 (vs Petrosian): 2969
Karpov WC 1984 (vs Kasparov) (games 10-29): 2957
Kramnik WC 2004 (vs Leko): 2945
Fischer 1971 (vs Taimanov): 2923
Fischer 1971 (all matches): 2921
Kasparov WC 1986: 2907
Lasker WC 1907 (vs Marshall) 2869
Kasparov WC 1984 (vs Karpov) (games 30-48): 2863
Kasparov WC 1984 (vs Karpov) all games: 2859
Kasparov WC 2000 (vs Kramnik) 2851
Karpov WC 1987 (vs Kasparov): 2838
Topalov WC 2006 (vs Kramnik): 2832
Fischer 1971 (vs Larsen): 2830
Alekhine WC 1927 (vs Capablanca) 2812
Lasker WC 1909 (vs Janowski) 2811
Spassky 1974 (vs Karpov): 2810
Capablanca WC 1921 (vs Lasker) 2808
Karpov WC 1986 (vs Kasparov): 2807
Kasparov WC 1995 (vs Anand) 2807
Kasparov WC 1993 (vs Short): 2805
Kasparov WC 1990 (vs Karpov): 2800

I also like the approach in the Ferreira analysis:
http://web.ist.utl.pt/diogo.ferreir...

One thing I find very remarkable in the Ferreira method of "average gain per move" from which he calculates "strength" as if it were an elo figure, is the close agreement his “strength” figures usually have with the ELO of the players at the time of the match. Also, in the WC matches between Karpov and Kasparov, the strength figure shows astonishing stability from one match to the next in both players (much more than their ELO) and the distance separating them is ridiculously small.

1984...............ELO..........Strength
Kasparov...........2715..........2754
Karpov.............2705..........2754

1985...............ELO..........Strength
Kasparov...........2700..........2760
Karpov.............2720..........2749

1986...............ELO..........Strength
Kasparov...........2740..........2758
Karpov............ 2705..........2758

1987...............ELO..........Strength
Kasparov...........2740..........2748
Karpov.............2700..........2755

Thanks for your comments and very useful information, including the links.

It's certainly intriguing about Hou. Is she a genuine world beater who for one reason or another is playing well below her best, or is she playing not far below her best and just had a few purple patches, such as her match against Koneru, and her wonderful efforts in Gibraltar and Reykjavik where she was scything through the 2700s, including Polgar and almost including Caruana.

Ferreira, Diogo R. Determining the Strength of Chess Players Based on Actual Play http://web.ist.utl.pt/diogo.ferreir...

Regan, K. (2012). Intrinsic Ratings Compendium
http://www.cse.buffalo.edu/~regan/p...

Regan, K. and Haworth, G. (2011). Intrinsic Chess Ratings. Proceedings of the Twenty-Fifth AAAI Conferenceon Artificial Intelligence http://www.aaai.org/ocs/index.php/A...

Regan, K., Macieja, B., and Haworth, G. (2011). Understanding Distributions of Chess Performances http://www.cse.buffalo.edu/~regan/p...

I find the method of the Ferreira study intriguing. He sums up the differences with Bratko and Guid as follows:

<In connection with the work by Guid and Bratko (2006) , we highlight the following differences to our own work.

• We used HOUDINI 1.5a which is one of the strongest engines currently available (only superseded by H OUDINI 2.0c at the time of this writing), with a search depth of 20 plies.

• We carried out the analysis from move 1 (actually, analysis begun with the starting position, so that the gain of the first move could be determined). With respect to opening theory/preparation, we consider it to be an integral part of strength of play.

• With regard to suboptimal play in won/lost positions, we considered that playing strength should be de- termined based on whatever a player brings about on the board. If a player plays suboptimally, and this changes the position evaluation, then it should have an effect on the perceived strength of play.

• Our method for comparing players is based on the distribution of gain expressed as a histogram with the maximum possible resolution (in this work, we used intervals 1 centipawn). This is in contrast with other approaches that consider only one or two parameters (e.g., mean loss, or mean and standard deviation).

• Rather than an expected error or best move percentage, our method provides an expected score between players that can be directly translated into an estimated rating difference. To the best of our knowledge, this is the first time that computer analysis can be translated directly into the Elo-rating scale.

Thanks. From the little I've looked at so far I'm inclined toward Ferreira also as the whole notion of measuring complexity seems to me to be overrated and a little absurd.

He analyses the full series of Karpov-Kasparov games in their five World Championship matches, a total of 144 games.

When quantifying the “average complexity per position” for each player, the value he comes up with is 25.88 for Kasparov and 16.98 for Karpov.

How on earth is it possible that two players playing each other, and therefore dealing with the same games and nearly the same positions (differentiated only by one move) are said to be facing such a big difference in the average complexity of the positions they deal with?

This implies that after Kasparov makes a move, the complexity of the position is greatly <reduced> so that Karpov faces a much simpler position. And when Karpov moves, he tends to complicate the position for Kasparov.

Not only does it make no sense to me, but it seems to be the exact opposite to what these two players are supposed to do.

One of the complexity measurement advocates would have to opine about whether you're missing anything there. To me, your line of reasoning sounds self evident.