Karpov - Kasparov: 144 match games, 104 draws. The final evaluation was beyond 0.75 in only 5 of the 104 draws. (Rybka, 16+plies)

2 dead draws from Sevilla (1987), two games from the last quarter of the first match (probably wina by Kasparov), and the final game from 1990 -- winning position (+2,14/17) for Kasparov, but he only needed a draw to take the money and the crown, so...

Median eval (modulus, final positions, 104 draws): 0,08

Mean eval (modulus, final positions, 104 draws): 0,21

[0.00 - 0.10] : 57 games

[0.11 - 0.30] : 25 games

[0.31 - 0.50] : 11 games

[0.51 - 0.74] : 6 games

The 5 [0.75+] games above mentioned:

Karpov vs Kasparov, 1984

Karpov vs Kasparov, 1985

Karpov vs Kasparov, 1987

Karpov vs Kasparov, 1987

<12...Nc5 13. Bb5> <DarthStapler> is correct.

12. c6 Nc5 13. Bb5 bxc6 14. Bxc6+ ---rook and K is forked

or

if white plays 13. Bb5 after 12...Nc5 it will be good to play 13... 0-0!

12... Nc5 13. Bb5 0-0! 14. e5 Nfe4! 15. Nf3? Rxf3! 16. gxf3 Qh4+ 17. Kf1 Ng4 wins the rook

<INTRODUCTION>

Anand vs Kramnik, 2008 is the <second game of the 2008 title match>. Quantitative mapping of this game between these players is below. Figures in brackets immediately after each move are the corrected engine evaluations generated on the return slide. The reverse slide smoothed out many, but not all fluctuation in the engine’s evaluations. The complexity of some variations was very likely too great to enable a fuller reconciliation from the forward slide. <General methods used are described in the bio.> The evaluation values in the opening come at the end of a full forward slide to the last move of the game and a full return slide back to the starting position. Engine preferences, with evaluations, are included where they differ from players preferences.

<Summary>

After the cautious preliminaries in game 1, this was a colossal struggle. The game was extremely complex and will repay deep study. Black had a small advantage in a complex Sämisch Nimzo-Indian, but White equalized by move 8. White took advantage of the dubious <21…Ndf6> before dissipating that advantage with <31.Bc2>. A couple of inaccuracies at moves 31 and 32 by Black could have cost the game in a long and complex ending, but due to time trouble, the soon to be World Champion (and one time Blitz and Rapid Play Champion of the world) was unable to penetrate the thicket of possibilities in time and accepted a draw when he was in a position of strong and potentially winning advantage.

Although there were some inaccuracies, there were no blunders or bad moves as such, as defined in the methods used. However, a combination of a couple of the aforementioned dubious moves 31 and 32 could have lead to a lost game for Black, and accordingly they have together been treated as one bad move, especially as sliding analysis revealed continually increasing advantage that could have extended the combined error of these two moves into an evaluation shift exceeding the nominal 0.96 that has been deemed a bad move for the purposes of weighting the game.

<THE GAME>

<1. d4> (=0.16) <1…Nf6> (=0.16)

<2. c4> (=0.14) <2…e6> (=0.14)

<3. Nc3> (=0.14) <3…Bb4> (=0.14)

<4. f3> (=-0.23) <4…d5> (=-0.23)

<5. a3> ( -0.29) <5…Bxc3+> ( 0.29)

<6. bxc3> (=-0.23) <6…c5> (=-0.23)

<7. cxd5> ( -0.45) <7…Nxd5> (=0.06)

<8. dxc5> (=0.06) <8…f5> (=0.06)

<9. Qc2> (=0.03) <9…Nd7> (=0.14)

<10. e4> (=0.14) <10…fxe4> (=0.14)

<11. fxe4> (=0.14) <11…N5f6> (=0.14)

<12. c6> (=0.03)

<Engine’s preferences>: <12. Nf3> (=0.14); <12. Bc4> (=0.14)

<12…bxc6> (=0.03)

<13. Nf3> (=0.03)

<13…Qa5> (=0.06)

<Engine preference:: <13…Ng4> (=0.03)

<14. Bd2> (=0.00)

<Engine preference>: <14. Be2> (=0.06)

<14…Ba6> (=0.00)

<15. c4> (=0.00) <15…Qc5> (=0.00)

<16. Bd3> (=-0.02 )

<Engine preference>: <16.Qd3> (=0.00), a line given as a draw by repetition. Thankfully, White chose the fighting option.

<16…Ng4> (=-0.02)

<17. Bb4> (=-0.02) <17…Qe3+> (=0.19)

<Engine preference>: <17…Qb6> (=-0.02)

<18. Qe2> ( 0.28)

First preference of both engine and Anand. The engine’s evaluation of this move did not stabilize following forward and reverse slides and re-slides, a prima facie indication of a very complex variation. Most evaluations tend to settle down on the reverse slide. When it doesn’t, it’s indicative of more significant moves within the engine’s horizon than is usual.

<18…0-0-0> ( 0.50)

<Engine preferences>: <18…c5> ( 0.28); and <18…Rd8> ( 0.29)

<19. Qxe3> ( 0.39) <19…Nxe3> ( 0.39)

<20. Kf2> (=0.10)

<Engine preferences>: <19…Rg1> ( 0.39); <19…Be7> (=0.21)

<20…Ng4+> (=0.10)

<21. Kg3> (=0.10) <21…Ndf6> ( 0.89)

<Top three engine preferences>: <21…Nge5> (=0.10); <21…h5> ( 0.36) and <21…Nde5> ( 0.44)

<22. Bb1> ( 0.89) <22…h5> ( 0.89)

<23. h3> ( 0.89) <23…h4+> ( 0.89)

<24. Nxh4> ( 0.89) <24…Ne5> ( 0.89)

<25. Nf3> ( 0.89) <25…Nh5+> ( 0.89)

<26. Kf2> ( 0.89) <26…Nxf3> ( 0.89)

<27. Kxf3> ( 0.88)

<Engine preference>: <26. gxf3> ( 0.89)

<27…e5> ( 0.88)

<28. Rc1> ( 0.87)

<Engine preference>: <28. Bc3> ( 0.88)

<28…Nf4> ( 0.87)

<29. Ra2> ( 0.87) <29…Nd3> ( 1.00)

<Engine preference>: <29…Rh6> ( 0.87)

<30. Rc3> ( 0.88)

<Engine preference>: <30. Bxd3> ( 1.00)

<30…Nf4> ( 0.88)

Forced: <30…Nxb4> ( 2.29) or <30…Ne1+> ( 2.37)

<31. Bc2> (=0.17)

An evaluation shift against White of 0.71, representing a <dubious move> under weighting method B. <Scores 0.5> <Cumulative weight = 1.0)

<First three engine preferences>: <31. Rf2> ( 0.88); <31. Rc1> ( 0.87); and <31. Rb2> and <31.Kg3> ( 0.65)

<31…Ne6> ( 0.60)

<Engine preference>: <31…Rh6> (=0.17)

<32. Kg3> ( 0.60) <32…Rd4> ( 1.13)

<Engine preferences>: <32…Rh6> ( 0.60); <32…c5> ( 0.77)

Black’s last two moves were inaccurate and resulted in a combined evaluation shift against his position of 0.96 that could have, on balance, lead to a lost position with best play on both sides. <Accordingly these two moves are deemed to constitute a bad move, and add a weighting of 1.> <Cumulative weighting = 2.0).

Draw agreed.

<ANALYSIS>

<Note> The fluctuations generated in the relatively low (16 minimum) ply forward slide were smoothed out in the equivalent return slide. The corrected evaluations extracted from the return slide are used in this analysis, as they are considered more reliable than the raw evaluations generated on the initial forward slide. All moves have been evaluated on forward and return slide for completeness.

<Evaluation range>:

Between <=/ 0.45> applying to <7. cxd5> - representing a small advantage for Black - and < 1.13> in respect of the move <32…Rd4> representing a significant/moderate advantage for White.

<The largest evaluation shifts>:

- for White was 0.71 between <30…Nf4> ( 0.88) and <31.Bc2> (=0.16).

- for Black

was 0.79 between <21. Kg3> (=0.10) and <21…Ndf6> ( 0.89)

<Computer statistics>:

• 93.8% of the ply in this game (50/64) coincided with engine preferences 1, 2 or 3

• 87.5% of the ply in the game (56/64) coincided with engine preferences 1 or 2

• 65.6% of the ply in the game (42/64) coincided with the engine’s first preference

• 96.9% of Kramnik’s moves (31/32) coincided with the engine preferences 1, 2 and 3

• 90.6% of Anand’s moves (29/32) coincided engine preferences 1, 2 and 3

• 87.5% of Kramnik’s moves (28/32) coincided with engine preferences 1 and 2

• 81.3% of Anand’s moves (26/32) coincided with engine preferences 1 and 2

• 71.9% of Kramnik’s moves (23/32) coincided with the engine’s first preference

• 53.1% (17/32) of Anand’s moves coincided with the engines first preference.

<The engine evaluation of the final position>:

was < 1.13> in a position agreed drawn.

<CONCLUSION>

<Using method A, the game is weighted at 2, representing 1 bad move and 0 blunders by Anand and 1 bad move and 0 blunders by Kramnik.