Saturday, May 16, 2015

Random Thoughts on Studying Endgames

While waiting for pairings last Thursday night, I enjoyed conversing with local master and South Carolina's top rated player Sam Copeland. Among the topics we discussed was Jeremy Silman's book on the endgame, Silman's Complete Endgame Course: From Beginner to Master. There was apparently some discussion on Facebook about the book's quality, and I commented that in my opinion there really is no such thing as a bad endgame book. As long as the book contains diagrammed positions to consider, one can't go wrong by reading it. Did any surrounding text or possible wrong analysis to the position really matter? Last century the quality of the writing in an endgame book might have mattered. This century, with the tools now available to us, I really don't think so. That's because we can use those tools to help get to the heart of the truth about endgame positions.

Any twentieth century book about an endgame, however proficient and ingenious its author, is going to be riddled with errors, probably in almost every endgame position the book offers. That's because endgames are so rich and complex that the human brain can't possibly get a true handle on all the complexities, nuances, and possibilities of any but the simplest endgames, not even after spending hours and days in home study on positions. Even the simplest of endgames are no easy chore to grasp. However, a computer program can really, really help us to arrive at authoritative conclusions that eluded even the world's most advanced endgame specialists just thirty years ago.

Here is an endgame I want to offer for consideration, Black to move:

The position is from Breyer-Nyholm, Baden-Baden 1914.Reuben Fine discusses it in Basic Chess Endings, number 62a in his "White Has an Outside Passed Pawn Section". Fine states that White "should experience little difficulty in winning" positions like this. Indeed, all else being equal, an outside passed pawn normally wins, especially as the number of pawns each side holds increases. This is because Black has to divert his King to capture the outside passer, leaving White the better King position with which to gobble the pawns left unprotected on the other side of the board.

But what about this particular position? Black will at some point have to take his King offside to eat White's c-pawn. However, the c-pawn is not very outside. Also, once the c-pawn is gone there is not that much material left on the board. Another advantage Black has is that his King at present is in a beautiful position. Are these factors considerable enough for Black to hold the position to a draw against the static (i.e. virtually permanent) White advantage of the outside passer?

There are eight "pieces" on the board, counting Kings; therefore, this position exceeds the range of endgame tablebases at this time and is not subject to precise calculation today. We are therefore still left to our own resources. However, when supplemented by computer programs, these are sufficient for a definitive conclusion.

A) Fine quotes an early analyst, Marco (in Wiener Schachzeitung), who concluded that White's passer triumphs. Fine gives the line 1...h5 2.h4 e5 3.c3+ Ke4 4.Ke2 g6 5.Kd2 Kf4 6.Kd3 g5 7.hxg5 Kxg5 8.Ke4 Kf6 9.Kd5 (L. Steiner's suggestion) 9...Kf5 10.c4 e4 11.Kd4 Kf4 12.c5 e3 13.Kd3 Ke5 14.Kxe3 Kd5 15.Kf4 Kxc5 16.Kg5 and White wins. Fine added only that if 3...Kc4 4.Kc2 is still winning, and that White should avoid playing 9.c4 Ke6 10.c5 h4 11.c6 Kd6 12.c7 Kxc7 13.Kxe5 Kd7 14.Kf5 h3!! and Black draws because he can get his King to f8.

A British Grandmaster and world leading specialist on endgame theory Jon Speelman came along to reassess the position in his 1981 book (revised 1988) Analyzing the Endgame in the chapter titled "Two Less Complicated Endgames". Less complicated! Right! If you played through the above analysis without a computer program, I am sure you wondered at many points, why did he move there, and what about such and such move? This endgame is anything but simple.

Black's drawing strategy is to try to exchange pawns off on the kingside. He hopes to allow White a pawn on the h-file at a point when he can reach f8 with his King to achieve a drawn position. Speelman correctly points out that in the analysis given above, 9.c4 actually still wins for White. After 9...Ke6, White should play 10.g3! (rather than 10.c5?). After 10...Kd6 11.Kf5 Kc5 12.Kxe5 Kxc4 13.Kf5 White will be able to Queen his g-pawn.

B) Speelman then goes on to show that there were a lot of analytic mistakes made and that Black in fact with correct play should easily be able to secure a draw. The first mistake is back in the position reached after 1...h5 2.h4 e5 3.c3+ Fine stated that after 3...Kc4 4.Kc2 White is still winning. Kovacevik (in Sahovski Glasnik 9/74) showed that 4...e4! draws for Black. 5.Kd2 Kb3 6.Ke3 Kxc3 7.Kxe4 Kd2 8.Kf5 Ke3 9.Kg6 Kf4 10.Kxh5 Kg3 11.Kg5 Kxg2 12.Kg6 Kg3 13.h5 Kg4 draw.

C) Interestingly, after 1...h5 2.c3+ (instead of 2.h4) Kovacevik shows that 2...Kc4? would lose for Black because White has the surprising bolt 3.g4! 3...h4 (3...hxg4 4.hxg4 Kd5 5.Kd3 e5 6.c4+ Kc5 7.Ke4 Kxc4 8.Kxe5 Kd3 9.g5 Ke3 10.g6 wins) 4.g5 g6 5.Kc2 e5 6.Kd2 e4 7.Ke3 Kxc3 8.Kxe4 Kd2 9.Ke5 Ke3 10.Kf6 Kf3 11.Kxg6 Kg3 12.Kh5 Kxh3 13.g6 and White wins. Speelman mentions, and a computer program confirms, the way to the draw after 1...h5 2.c3+ is 2...Ke4 3.h4 and 3...Kd5 or 3...Ke5 draws, e.g.: 3...Kd5 4.Kd3 e5 5.c4+ Kc5 6.Ke4 Kxc4 and Black's King gets back in time to save the day as in B above. Speelman also finds the same draw for Black after 1...h5 2.c3+ Kd5. Interestingly enough, Speelman says that the line 3.g4? hxg4 4.hxg4 Ke4 "gives Black no problems." I'll say! Black actually wins according to the computer program, and in very interesting fashion. 5.g5 g6 6.Ke2 e5 7.Kd2 Kf4 8.c4 Kxg5 9.c5 Kf6 10.c6 Ke6 11.c7 Kd7 In this line we see how White's not "very" outside passed pawn cost him the game. White can maintain a draw with 3.h4, 3.Kd3, 3.Ke3, or 3.Ke2 instead of 3.g4? of course.

In conclusion, Speelman points out that Black's position is far from critical. Black does not need to play 1...h5 to draw. 1...g5 also draws perfectly well. Computer programs actually show that Black can draw with any of five moves in this position, 1...h5 among them, but least advisable (most risky). The four perfectly equalizing moves at Black's disposal are 1...g5, 1...g6, 1...e5, and 1...Ke4. Although barring an egregious error by White, Black has no winning chances in the above diagram, his King is well enough situated to deal easily with White's static advantage of the outside passer.

Arriving back to the opening point of my purpose for writing this column, with computer programs it is now possible to check the analysis of any endgame position given in any endgame book. Therefore, there is no bad endgame book so long as it provides endgame positions for consideration and independent checking. Perversely, I'll even go farther out on this limb by asserting that Fine's Basic Chess Endings and other twentieth century endgame books that were not computer checked may be even better books to study the endgame by. Not only is the cataloging of positions in logical order likely more thorough and comprehensive in these venerable tomes, but despite, perhaps even because of, their many errors they make the reader examine conclusions for himself. As always the computer can be used as a tool to check and show hidden, unconsidered paths, especially the intriguing hard-to-see finesses missed by earlier analysts. But it is the obligation of the player making the study to learn and understand the hidden facets of endgame positions and then remember them well enough to apply them in games when a position in which a similar principle arises.

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