25 January 2011

Tablebase 1 - Levenfish & Smyslov ½

After writing Levenfish's Rook Endings, I set off to investigate some of the points raised at the end of that post about Levenfish and Smyslov's classic. My first action, as with all endgame books written before the computer age, was to check the analysis on positions with six pieces or less by comparing it with a tablebase. The first three chapters of Rook Endings,

  1. Introduction
  2. Rook and Pawn vs. Rook
  3. Rook and Two vs. Rook
i.e. two Kings plus two Rooks plus max two Pawns, lend themselves to this sort of analysis. As you would expect, the analysis was impeccable, until I checked the position shown in the following diagram. The authors wrote,
The diagram is very interesting. White's King is cut off from the Pawns, and maneuvers with the King and Rook fail to improve White's position, e.g.
  • 1.Rg8 Kh5, or
  • 1.Re5 Rg1 2.Re3 Kh5 3.Ke5, or
  • 1.Kd4 Re2 2.Kd3 Re1 3.Kd2 Re8 4.Rc5 Rg8 5.Rc3 Kh5 6.Ke2 Kg4 7.Kf2 Kh3 with a draw
Therefore, there is only one other possible winning try: 1.g4 [...]

The tablebase disagrees, saying that all 14 of White's legal moves, with the exception of the four moves that hang the Rook, are winning. The fastest win, in 40 moves, is indeed 1.g4, but the three others (1.Rg8, 1.Re5, and 1.Kd4) win in 42, 42, and 41 moves respectively. Furthermore, the authors' analysis of 1.g4 is faulty.

Levenfish & Smyslov no.101
White to Move

How to explain this total breakdown in evaluation by two of the world's leading grandmasters and endgame specialists of their day? Of course, it's impossible to say for sure, but I suspect they overlooked an important mechanism available to White. Here is the tablebase analysis of the variation starting 1.Rg8.

1.Rg8 Kh5 2.Rg5+ Kh6 3.g4 Ra1 4.Re5 Rg1 5.Rh5+ Kg6 6.Rg5+ Kf6 7.Ke4 Re1+ 8.Kf3 Rf1+ 9.Kg2 Ra1 10.Rf5+ Kg6 11.h5+ Kh6 12.Rf6+ Kg7 13.Rd6 Ra3 14.h6+ Kh7 15.Kf2 Ra5 16.Kg3 Rb5 17.Kh4 Rb1 18.Kh5 Rh1+ 19.Kg5 Ra1 20.Rd7+ Kg8 21.Kh5 Ra2 22.g5 Ra5 23.Kg6 Ra6+ 24.Kf5 Ra5+ 25.Kf6 Ra6+ 26.Ke5 Ra5+ 27.Rd5 Ra6 28.Rd6 Ra1 29.g6 Re1+ 30.Kf4 Rf1+ 31.Kg3 Kf8 32.h7 Ke7 33.Kg2 Ra1 34.Rd2 Ra6 35.h8=Q

To explain the winning procedure in words, the White King first chases the Black Rook from behind the Pawns (9.Kg2). Then White simultaneously advances all four pieces to push the Black King to its first rank (20...Kg8). Finally, White uses a bridge-building mechanism similar to the one used in the Lucena position (27.Rd5) to stop the Black Rook from checking on the side.

As for the analysis after 1.g4, Levenfish & Smyslov give 1.g4 Rh1 2.Rh5+ Kg6 3.Kd6 Rh2 4.Ke7(?) Kg7(?), with the comment 'the threat was Ke7-f8-g8 followed by Rh7'. The tablebase isn't intimidated by this 'threat', giving 4...Re2+! (only move), and if 5.Kf8, then 5...Rf2+ 6.Kg8 Rf4! (only move). Instead of 4.Ke7?, White wins with 4.Ke6, among other moves.

The rest of the section on K+R+gh vs. K+R is correct. When the authors wrote of no.101, 'The diagram is very interesting', little did they suspect how interesting it really was.


Later: There's a glitch in the analysis after the diagram. I gave 1.Rg8 Kh5 2.Rg5+ Kh6, which just repeats the diagrammed position, when the move 3.g4 is identical to 1.g4. Then I looked at the two other lines, starting 1.Re5 and 1.Kd4, and discovered that White also plays g3-g4 as soon as possible. These eventually transpose into the same optimal solution given after 1.g4.

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