But IMO, removing games selectively makes the process less "scientific".>

We all agree on that point, at least. I think it was Charles Sullivan at truechess that may have been making these omissions, but I don't know first hand.

<i'm using a cap of 1.1 (i adjusted from 1.00), 1 error does not drastically reduce the accuracy value of a player.>

I guess I like to make a distinction between how serious an error is, which is why the basic division of errors in my method is between blunders, that change the status of a game from won or drawn, and other errors which don't.

After all, better 5 mistakes that don't lose a game than 1 that does (eg: Kramnik overlooking mate in one against Fritz 12). I tried to reflect this philosophy by weighting each error (blunders = 2, bad moves = 1, dubious moves =0.5), but the problem with doing that is that I may as well have labelled them red, yellow and blue, as such weightings cannot be added.

Now I simply count the errors in different categories of seriousness.

<Mathematics has to deal with inflation at the end of the spectrum or even "infinities" and must apply "renormalization", hence a "cap".>

I work on this principle when evaluating blunders. Most if not all engines have a "draw zone" from -1.40 to +1.40 within which a game is meant to be defensible.

The principle is that once a position evaluation moves outside that boundary, the game is won/lost, even with perfect defense...otherwise the game is drawn. A lost game inevitably leads to mate if the defender doesn't resign, and so the evaluations of moves in a won/lost game is essentially meaningless, as the value of mate is infinite on the scale.

Hence, the difference between a 1.30 position and a 1.50 position is not 0.20 but infinite, and I basically don't even bother noting the differences between moves outside the "draw zones" unless a player blunders the win back into the "draw zone" or even worse clear through to the other side of the "draw zone". The proviso of course is that the 1.30 evaluation is one that is stable (and this can take a lot of time to verify) and the 1.50 position is verified as lost (which can also take time to verify).

For this reason, any non-fatal errors I find I value simply according to their seriousness, and these can be up to 2.80. I also have a sneaking suspicion that because of the way values behave near the 1.40 boundary, that there may not be a strict mathematical relationship between the evaluation of errors even away from these boundaries that their numerical evaluation lead us to believe exist.

I'm personally refraining from using average error calculations for these reasons until I can figure this aspect out, although they may in fact be quite workable within the "draw zone".

It's an interesting fact that in my study of the 21 games of the 1910 and 2008 World championships, I did not find a single non-fatal error of more than 1.20 and very few above 1.00. At no stage did any of the four players lose a won game, or even lose a game in which they had a significant advantage.

Games between less skilful players will most likely feature more serious errors.

I mentioned before that I have taken weeks and even months to fully evaluate the mistakes in a world championship game. The reason for this is that an engine's evaluations are frequently only a first or second guess (or even a fourth, fifth or sixth guess!), and that further scrutiny by employing variation analysis or deeper ply evaluations or reverse sliding analysis can reveal a completely different picture.

Above all, I feel an engine's evaluations have to be <true> for them to be of any use at all.

Regarding your question, I have already answered it before. I did not realize that you had an unanswered question for me.

<what makes you so sure that humans already reached their limits in chess.>

This <visayanbraindoctor> hypothesis is exactly that- a hypothesis. The <Bridgeburner> Project is an experiment meant to test it.

<<visayanbraindoctor> hypothesis: humans already reached their limits in chess.>

Find out if the past World Champions beginning in the era when chess clocks started played with the same error rate as present-day World Champions, using the <Bridgeburner> Analysis - Project methodology.

If the <Bridgeburner> Analysis - Project shows that the past World Champions played with a much bigger error rate than present-day World Champions, then the hypothesis above is false.

If the <Bridgeburner> Analysis shows that the past World Champions played with approximately the same error rate as present-day World Champions, then the hypothesis above is strengthened.

You should not be obsessed by my posts. I noticed that you followed me to the Capablanca page, trying to show mistakes in my message, and then doing the calculations yourself. Frankly, since you have been following me around recently and posting several messages to each message I have been posting, I have tended to ignore your messages. I believe you yourself can answer most of your own questions if you put your mind to it; you're an intelligent fellow.

This is from the Nakamura page, which is not the appropriate page for it; so I am re-posting it in your forum if you don't mind.

<nimh> Quoting the above studies does not invalidate my statement:

As for <difficulty>, it is a subjective human perception or feeling that differs from individual to individual, and cannot be accurately quantified.

We have been through this before and you know my opinion: I find the accuracy part of the studies you mention credible, but not the <complexity/difficulty> part.

Just because a study has been published, it does not get to be immune from critique, and so can be cited like sacred dogma.

<I'm also quite sure that you have played chess yourself.>

I have played enough chess to know that different players have different perceptions as to the degree of the difficulty of any given position.

For example, given this position:

click for larger view

Get any 4 kibitzers at random, and have them rate the difficulty of the above position on a scale of 1 to 10, with 10 the most difficult. If difficulty is an objective phenomenon that can be accurately quantified, then all of the kibitzers would assign it with exactly the same number.

<f (expected error) = actual error/ difficulty> What is the definition of difficulty and how is it rigidly measured? How can the probability of a potential event in the future be computed from an event in the past divided by a vague ill-defined term such as difficulty? I cannot even make sense of this equation.

Perhaps we are talking off tangent. So let us start with the basics.

What is the scientific method?

Which of your statements conforms to the scientific method or does not?

(<Bridgeburner> has actually already pointed this out to you above.)

You do not have to answer me, but I suggest that you apply the above questions to your work. I think your work is on very shaky grounds, and you yourself do not even seem to be familiar, or have a lack of understanding, of the scientific method, which may be one reason why you do not realize that your work is on very shaky grounds. If you do not understand the scientific method, then it's not too late to study it and apply it to your own works.

I do not think Naka's page is the proper place for this discussion. I am going back to Bridgeburner's forum.

A very interesting finding, especially if the following is true

<Games between less skillful players will most likely feature more serious errors.>

You have analyzed the Zukertort vs Steinitz, 1886 from the Steinitz-Zukertort World Championship Match (1886), which is the first official WC match, and it showed a lot more errors than the 1910 and 2008 World Championship matches. Since analyzing only one game from the first official WC match cannot be used to infer if the 19th century WC matches had a higher error rate compared to 20th century WC matches, the implication is that some time in the far future, you might find it worth your effort to analyze a sample of these 19th century WC games. Perhaps a sample of 4 games from this match. Just a thought for the far future. (",)

But what's with my "strategy and patterns" argument? Better understanding of strategy may have not reduced the number of errors in terms of this project (as strategical errors are often microscopic) but they may have reduced the number of inaccuracies which are so small that even the strongest of the modern engines cannot give a final verdict on whether the move was accurate or not.

Same with (strategical) pattern recognition.

If it really were a subjective perception then how do you explain that accuracy in fact decreases in more difficult conditions, as the graps show?

<Just because a study has been published, it does not get to be immune from critique, and so can be cited like sacred dogma.>

Of course it isn't immune from critique as to methods to calculate it and which factors to use, but the existence of such phenomenon is axiomatic. It isn't limited to chess only - everywhere in life you can observe that the actualy performance always suffers whenever conditions worsen. And if in evaluating performance we don't take 5his into account, we'd easily come to a faulty conclusion that a person him/herself is responsible for the loss of performance.

You have also presented no scientific proof that difficulty is by nature immeasurable, merely repeated your subjective claims.

<I have played enough chess to know that different players have different perceptions as to the degree of the difficulty of any given position.>

Yes, of course, but my question was something else altogether.

<Get any 4 kibitzers at random, and have them rate the difficulty of the above position on a scale of 1 to 10, with 10 the most difficult. If difficulty is an objective phenomenon that can be accurately quantified, then all of the kibitzers would assign it with exactly the same number.>

What humans think is completely another matter has has no importance here.

3 difficulty parameters are based on engine outputs and the fourth one is simply the amount of material on board. They're applied rigidly on each position. There's nothing subjective there. But you know that, if you have read my paper, everything is explained there.

<<f (expected error) = actual error/ difficulty> What is the definition of difficulty and how is it rigidly measured?>

The difficulty in this case represents a hypothetical co-effect of all 4 difficulty parameters. The formula was meant to indicate how higher difficulty results in lesser average expected error.

<How can the probability of a potential event in the future be computed from an event in the past divided by a vague ill-defined term such as difficulty?>

It's not the probability that's calculated here, and expected error is not the same as future events.

<I cannot even make sense of this equation.>

Not my poroblem if you capabilities to understand are so low.

<What is the scientific method?
<Which of your statements conforms to the scientific method or does not?>

If the point of these questions was to cast doubt over my methodology, the you have no reason to worry at all. It is scientific and well documented and replicable.

But you both completely miss the point.

You're obviously right that a study has to adhere to scientific standard to be trustworthy, but it's no use if you do not understand and taske into account <basic groundings> of the subject under scrutiny.

In chess one has nothing to do with even TB-like accuracy if it's absolute strength analysis what's in question. The reason is that how moves appear on board in realtion to perfect play depends also on external conditions like thinking time and the difficulty of positions.

<We have had this discussion over and over again. I really have no wish to keep on repeating it. I do not wish to appear as to degrade your work out of pettiness;>

But this is perfectly what you've been doing. My impression of you is that you first create an idea etched in stone in your head and refuse to consider any evidence pointing otherwise, and you do everything to distort facts to support your ill-founded claims.

<that is not the case. You might feel very irritated at me at this point in time, but you might just thank me in the far future for being honest in my critique of your work.>

What humans think as the difficulty of chess positions has everything to do with this topic. Or at least I thought difficulty was the topic.

Given this position:

click for larger view

Have Stockfish evaluate its difficulty on a scale of 0.100 to 1.000.

Have 4 random kibitzers evaluate the same position's difficulty also on a scale of 0.100 to 1.000.

Lasker was one of the most dominant players in history. OK, that match against Schlechter was drawn, but that's because Schlechter played better than usually rather than because Lasker played worse than his normal. That Lasker was dominant, there is no doubt.

Kramnik in his match against Anand was dominated himself, by Anand. That is, he played as accurately as the player whose dominance at the beginning of the 20th century was overwhelming, yet this accuracy was only enough to go down in flames... Not that I think Kramnik would go down like this again, but I think the Kramnik we witnessed in Bonn is not the most accurate Kramnik there can be. And even that, he went down, like a stone, while playing as accurate as Lasker in what you considered one of the most accurate matches ever.

All the study has indicated based on two World Championship matches is that Lasker, Schlechter, and Kramnik were playing at a similar accuracy, while Anand was perhaps playing a tad more accurately than them.

Your <modern players <do> play better.> is just another way of phrasing my hypothesis, which the <Bridgeburner> experiment is still investigating.

You could phrase it this way:

Hypothesis: Modern players do play better.

Potential 1 Data/Observations generated by experiment:

Kramnik, Anand, Kasparov all played much more accurately that Lasker, Schlechter, and Capablanca.

Conclusion: Modern players do play better.

If one looks at Capablanca's notes, one would see that the endgame baffled him. Genius that he was, Capa usually was very quick in his evaluations of endgame positions as won, drawn, or lost, but this one is a case in which he sounds unsure of himself. And he must have given it much attention with all his awesome native skills, as it is the first game of his first World Championship Match.

I have read that many blindfold masters are not as impressed by Najdorf's blindfold performance, when compared to Alekhine's, considering the quality of the blindfold games they both produced and Alekhine's attitude of playing out every game into the ending without taking easy draws.

<FM Marc Lang (2303 FIDE-Elo, 2250 German rating) played on 35 boards, reached 19 wins, 13 draws and 3 losses against an average of 1403 German rating.>

Blindfold chess was more popular pre-WW2, away from Botvinnik's condemnation of it in the Soviet Union. Strong GM caliber players, even aside from Alekhine and Reti, such as Borislav Kostic would engage in it. For example:

http://en.wikipedia.org/wiki/Boris_...
<In 1910 he moved to Cologne and from there, traveled and toured extensively, mainly in the Americas, playing matches against local champions and exhibiting his legendary skills as a player of simultaneous blindfold chess. At New York in 1916, he once played twenty opponents without sight of a board and won nineteen games and drew one, while engaging in polite conversation with opponents and spectators.>

GM caliber players apparently would also engage each other in blindfold matches, as Alekhine and Bogolyubov did while interned by the Germans. While that could be argued as occurring in an informal situation, I have no doubt these two uncompromising players did their best to crush one another. A more formal blindfold mini-match was held between Schlechter and Mieses:

Jacques Mieses

http://www.karlonline.org/205_3.htm

This "Duel with bandaged eyes" is more impressive than the Melody Amber set-up wherein players play on an empty chess board; both Schlechter and Mieses were literally blindfolded and so had no sight of board or man. Any one who has tried to play blindfold will testify that playing without seeing the board is much harder than playing on an empty board. The games are highly tactical as apparently the combinative Mieses was able to dominate the match.

Schlechter vs Mieses, 1909

Mieses ends the game with a back rank combination that Schlechter overlooked.

Mieses vs Schlechter, 1909

Mieses fearlessly essays the Göring Gambit in the opening, but after a lot of fireworks galore, the game petered out to a draw.

Schlechter vs Mieses, 1909

Another tactical game wherein Mieses sacs his Queen for 3 pieces and wins the ending.

Many of the pre-WW1 masters (aside from Mieses) also regularly engaged in simultaneous blindfold exhibitions, upon which they significantly depended upon for their income, including WC Steinitz, Blackbune, and of course Pillsbury.

1. <Lecturing a neurologist and brain surgeon about the human brain:>

HHHHAHAHA I just saw that at the Memorable Quotes page.

2. Thanks for all of the detective work on the <Rubinstein> web resources- they've been an enormous help to me in the course of researching a video documentary I'm making about him.

<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>