24 August 2010

More R+P vs. B+P Magic

After writing the recent post on R+P vs. B+P (see R vs. B Plus Knight Pawns), I reviewed previous posts in my tablebase category and discovered one with the same material: Tablebase 1 - Polugaevsky/Kasparov ½. Starting from the position given in that post, three world class GMs -- Gligoric, Polugaevsky, and Kasparov -- all overlooked a moment in the game where a double blunder occurred; White threw away a theoretical draw and Black failed to capitalize on it.

I dragged out my copy of Averbakh's treatise on Rook & minor piece endings, which is one book of his five volume series on theoretical endgames, and looked for similar positions. His chapter on R+P vs. B+P splits the examples into two parts. The first part examines Pawns separated by at least one file, while the second deals with Pawns on the same or on adjacent files. Since my two previous posts both featured positions with Pawns on the same file, I compared Averbakh's second part to the tablebase results. How accurate is his analysis?

On the whole the analysis is extremely good, but not perfect. In the 17 positions I found two erroneous evaluations. The first stems from the following position.

Averbakh no.430
[FEN "8/8/8/8/4pk2/8/r3BP2/4K3 w - - 0 1"]

Averbakh gives 1.Kf1! Ra1+ 2.Kg2 Rb1 3.Bh5! Re1 4.Be8 Re2 5.Kf1 Rd2 6.Bh5 Draw. I don't understand the short comment in Russian here, but he apparently believes that White has a fortress making it impossible for Black to approach the Pawn. The tablebase disagrees, saying the position after 6.Bh5 is a win in 40 moves. One critical path goes as follows:

6...Rb2 7.Be8 Rb8 8.Ba4 Ke5 9.Bc6 Rb6 10.Ba4 Kd4 11.Ke2 Rb2+ 12.Kf1 Kd3 13.Bc6 Rb1+ 14.Kg2 Kd4 15.Bd7 Rb6 16.Bf5 Ke5 17.Bd7 Rd6 18.Bb5 Kd4 19.Kf1 Rb6 20.Bd7 Kd3 21.Bh3 Ra6 22.Kg2 Rf6 23.Kg3 Ke2 24.Bg4+ Kd2 25.Bh5 Rf5 26.Bg4 Rf8 27.Bh5 Ke1 28.f4

To explain the winning procedure in words: Black switches the attack on the Pawn by bringing the King to e1/e2 and the Rook to the f-file, a plan which White is unable to prevent. This forces f2-f4, after which the win is easy.


The second erroneous analysis is in the position -- White Kg3,Bg5,Ph4; Black Ke4,Rf8,Ph5 -- from the game Salwe - Rubinstein, Prague 1909. The Pawns are mutually blocked on the h-file and the White King is confined to a six square rectangle stretching from g3 to h1.

Averbakh no.434
[FEN "5r2/8/8/6Bp/4k2P/6K1/8/8 b - - 0 1"]

The players continued 1...Rf7 2.Bh6 Rf3+ 3.Kg2 Rd3 4.Bg5 Kf5 5.Kf2 Kg4 6.Ke2. Averbakh gave these moves without comment, then showed how White could have preserved the draw a few moves later.

What Averbakh overlooked, but the tablebase finds immediately, is that White was lost in the initial position. After 1...Rf7, Black wins in 48 moves. The move 3...Rd3 throws away the win, 4.Bg5 gives it back, and 4...Kf5 throws it away again. The explanation for this is easy, even if the execution is not.

To win, Black needs to keep White's King confined to the g3-h1 rectangle. Black's winning procedure is to bring the King to e1-e2, where it prevents the White King from escaping the rectangle. Then Black has mate threats that force the Bishop to defend its Pawn on the e1-h4 diagonal. Once this is accomplished, Black can force the Bishop away from the diagonal and win the Pawn. This reduces to an elementary endgame where, even though the Bishop is on the right color to defend against R and h-Pawn, the Pawn is far enough from the Queening square to give Black a forced win.

The underlying principle behind both of Averbakh's positions is that a Rook and King can often dominate a Bishop that is tied down to defending a point. Once the Bishop is out of the way, the entire defense collapses.


millie said...

incredible! You know, there may be something to nigel short's famous comment that computers are to chess what chainsaws are to the amazonian rainforest, that to a certain degree they threaten to destroy the wonder and mystery of chess. I am not sure how I feel either way. But this 40 move long plan that converts a win out of what appears to be a fortress is nonetheless impressive, if purely academic.

jrcharousek said...

Mark appears to be using the original Russian version of Yuri Averbakh which as he outlines gives an incorrect line that leads to a draw. However he may be interested to know that the English translation printed in 1978 (Rook v Minor Piece Endings) gives an update to winning analysis subsequently discovered. To quote from diagram 109 Salwe - Rubinstein, Prague 1909 "Black succeeded in winning this game, and on the basis of this the position was considered to be won for Black. Then in the 1953 USSR Chess Yearbook, B. Baranov showed that White had defended incorrectly at the crucial stage, allowing his king to be cut off beyond the QB-file and that by correct defence he could have avoided this and drawn. More recently I. Maizelis (Shakhmatny Bulletin 1963) has demonstrated an alternative winning precedure for Black - that of driving the white king onto the KR-file. On the basis of this analysis, position 109 must again be considered won for Black." The analysis by Mazeilis is then given with additional reflections on Baranov. Hope this is interesting.