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| Elementary endgames (Part 8) | ||||||||||
| Rook plus a lone Pawn vs. a Rook may look simple, but appearances are deceiving. | ||||||||||
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Ask an expert which endgame is the most common and the answer is likely to be, 'Rook and Pawn endgames, of course!' Why is this? Rook endgames are more frequent than Queen endgames. There is only one Queen for each side, where the other pieces are all represented twice. But what about the minor pieces? The Rooks are often the last pieces to enter the battle. They usually enter the game via a center file, which they can do only after the minor pieces have been developed. Then, before they can advance into the enemy position, they need to wait for the file to open. While they are waiting, the minor pieces fighting on the front line are being exchanged. Ask the same expert which endgame is the most difficult and the answer will also be, 'Rook and Pawn endgames!' They are characterized by tactical complications as the Rooks, operating in four directions, simultaneously attack enemy Pawns, check the enemy King, and defend their own Pawns. Since many Rook and Pawn endgames eventually reduce to a Rook plus a lone Pawn vs. a Rook, these endgames are among the most common elementary endgames. We've already seen Rooks and Pawns in action in several other articles on elementary endgames (see the link box at the bottom of this article):
The Lucena position The Lucena position, which would better be called the Lucena maneuver, was introduced in part 4. It is so important that we present it here a second time with more details about its mechanics. In the following diagram note that the White Pawn has reached the 7th rank, where it is blocked by its own King. The King can't move to the h-file, because the Black Rook just shuttles between h2 and h3. It also can't move to the f-file, because the Black King guards f7 and f8. The only way to make progress is for the White Rook to force the Black King off the e-file.
If the White King comes out without any further preparation it gets bombarded with checks from the Black Rook. 1...Ke7 2.Re1+ Kd7 3.Kf7 Rf2+ 4.Kg6 Rg2+ 5.Kf6 Rf2+ 6.Ke5 Rg2 Since the White King can't move any farther than the 5th rank, it needs its own Rook on the 4th rank to shield it from checks. From this we understand the winning maneuver. 3.Re4 Rh1 4.Kf7 Rf1+ 5.Kg6 Rg1+ 6.Kf6 Rf1+ 7.Kg5 Rg1+ 8.Rg4 You can be sure that the Lucena position will occur from time to time in your games. The Philidor position The following diagram shows another common theme which could be called the Philidor maneuver. The White Pawn is only on the 5th rank, while the Black King sits on the promotion square. White would like to play Ke6, forcing the Black King to flee the threatened mate, but Black has the resources to prevent this.
Black to move occupies the 6th rank with the Rook, preventing the White King from advancing. 1...Ra6 2.Rb7 Rc6 3.Ra7 Rb6 At the moment White advances the Pawn, the Black Rook shifts to the back rank and continues checking the White King from the rear. 4.e6 (Black can't allow 5.Kf6 and must act immediately.) 4...Rb1 The Pawn has advanced and the White King has no protection from the Black Rook. With White to move in the diagrammed position, Black can hold the draw, but the variations are more complicated; we'll look at 1.Kf6 later (see Keres 162 below). Checking distance A common theme in Rook endgames is the notion of checking distance, the number of squares between the Rook and the King that the Rook is checking. In the following diagram White threatens to win with 1.Rf1+.
Black must react by checking the White King from the side. Even so, the King is able to defend itself from the checks by approaching the Rook. 1...Ra8+ 2.Kc7 Ra7+ 3.Kc8 Ra8+ 4.Kb7. To prevent the Pawn from promoting, the Rook must now move somewhere on the 8th rank, when 5.Kc7 forces Pawn promotion. White wins. The following diagram is similar to the previous. All pieces except the Black Rook have shifted one file to the right.
Now the White King is unable to approach its tormentor without losing the Pawn. The extra file between the King and the Rook is the difference between a win and a draw. 1...Ra8+ 2.Kd7 Ra7+ 3.Kd6 Ra6+ 4.Kd5 Ra5+ An idea related to checking distance is the notion of the long side and the short side of the Pawn. In the previous diagram [Keres 150] the Pawn on the e-file divides the board into two sides : the a-, b-, c-, and d-files are on one side of the Pawn, while the f-, g-, and h-files are on the other side. The four files to the left are on the long side, while the three files to the right are on the short side. In [Keres 149] the sides are switched. The Pawn on the d-file divides the board into a short side on the left and a long side on the right. The concept lets us formulate a nice rule of thumb. When the Black King is unable to stay in front of the Pawn, it should go to the short side of the Pawn, leaving the long side for the Rook. The Rook must take up the furthest distance from the enemy King available on the long side. In [Keres 149] the King defended itself from the Rook, which was checking on the short side. In [Keres 150] the King was unable to defend itself, because the Rook was checking from the long side. As with all rules of thumb there are exceptions, one of which is shown in the following diagram.
Note the similarity to the previous diagram, with the Black King on g8 instead of g7. Now the White King can abandon the Pawn because the White Rook will take up the defense after delivering an intermediate check. After 1...Ra8+ 2.Kd7 Ra7+ 3.Kd6 Ra6+ 4.Kc5 Ra8 5.Kc6 Ra6+ (5...Kg7 6.Ra1! Rb8 7.Kc7) 6.Kb7, Black can't play 6...Re6, because of the devastating 7.Rf8+. Pawn on the 6th rank Positions with the Pawn on the 7th rank are the most critical, and they help us to understand positions where the Pawn has not yet reached the 7th. In the following diagram, Black fights to keep the Pawn from advancing.
White on the move can make no progress. The Pawn can't reach the 7th rank without allowing the Black King to approach.
In the following diagram the White Rook prevents the Black Rook from getting maximum checking distance on the long side of the Pawn.
1...Rb8 2.Kd6+ Kf6 3.Kd7 Kg7 4.Ke7 Rb1 5.Ra8 Rb7+ 6.Kd6 Rb6+ 7.Kd7 Rb7+ 8.Kc6 Re7 9.Kd6 Rb7 10.e7 and wins
That last variation was long and complicated. A general principle is one thing, but playing specific positions is another. Fortunately, endgames of Rook and Pawn vs. Rook fall into a class of endgames that are subject to precise computer solution using a technique called retrograde analysis on a tablebase. Eugene Nalimov is one of the computer chess experts who has worked on the technique. A Nalimov tablebase server with all endgames of up to five pieces is available on the Web, courtesy of Lokasoft (see the link box again). Since the two Kings are counted in these numbers, that means that perfect solutions are known for as many as three other pieces. It is to the great credit of early endgame composers and analysts that their long and difficult solutions are confirmed by retrograde analysis. For the following positions, we give only Keres' main solution along with the maximum number of moves necessary to deliver checkmate from that position.
Pawn on lower ranks The following diagram is an example with the Pawn on the 5th rank. Compare this with the Philidor position [Keres 130] above.
Black lacks two advantages which helped to draw in the Philidor position. (1) The Black King is not in front of the Pawn. In fact, it sits in the worst place : on the long side of the Pawn. (2) The Black Rook is not able to harass the White King by checking from the side. White on the move wins. 1.Kc7. The Nalimov tablebase says 'M30' for this move, meaning that White will checkmate Black in 30 moves at most. The game might continue 1...Ra1 2.Rb8 Ra7+ 3.Rb7 Ra8 4.Kd7 Kf6 5.d6 Kf7 6.Rb1 Ra7+ 7.Kc8 Ke6 8.d7 Ra8+ 9.Kb7 Rd8 10.Kc6. Going back to the diagram, the White Rook is not well placed. The Nalimov tablebase confirms that Black to move draws. 1...Ra1 2.Rc8 Rd1 3.Rc2 Ke8 4.Ra2 Rd3 5.Ra8+ Kf7 6.Ra7+ Ke8 We saw another example of Pawn on the 5th rank in the Philidor position [Keres 130], where White to move plays 1.Kf6. Black can still draw, but the method is not simple. In his original analysis, Philidor thought that White should win. Only 1...Re1 and 1...Rf1 draw; other moves lose. Now let's look at positions where the Pawn is only on the 4th rank. The next diagram shows an example of checking distance on a file.
The White King is unable to make progress alone. 1.Kc4 Rc8+ 2.Kb5 Rd8 3.Kc5 Rc8+ 4.Kd6 Rd8+ 5.Ke5 Re8+ 6.Kf5 Rd8. This is one of the few positions where a Rook is placed better in front of a Pawn than behind it.
Nalimov says that White will mate in no more than 34 moves. Keres gives the win as 1.Kb4 Rb8+ 2.Ka5 Rc8 3.Kb5 Rb8+ 4.Ka6 Rc8 5.Rd4 Ke6 6.Kb7 Rc5 7.Kb6 Rc8 8.c5. At the crucial moment, White played Rd4, defending the Pawn from the side and freeing the King to advance. This maneuver only works when the Black King is unable to harass the White Rook. The same ideas work with the Pawn on the 3rd rank. These are equivalent to positions with a Pawn on the 2nd rank, which can advance two ranks on its first move.
White to move plays 1.Re4. Nalimov confirms that this (and 1.Re2) are the best moves, checkmating Black in at most 48 moves. Keres gives the following continuation. 1...Kf5 2.Re3 Kf6 3.Kc3 Rc8+ 4.Kd4 Rb8 5.Kc5 Rc8+ 6.Kd6 Rb8 7.Rf3+ Kg5 8.Kc5 Rc8+ 9.Kd4 Rb8 10.Kc3 Rc8+ 11.Kb2 Rb8 12.Rf1 Kg6 The players have reached the same position as in the diagram with the White Rook and Black King are both one square to the right. 13.Kc3 Rc8+ 14.Kd4 Rb8 15.Kc4 Rc8+ 16.Kd5 Rb8 17.Rb1 Kf7 18.b4 Ke7 19.Kc6 'A tremendous piece of analysis by Grigoriev, full of subtle and surprising points', says Keres.
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