[blind-chess] Chess Article #54: The Rook and Pawn Versus Rook endgame (Part One)
- From: Roderick Macdonald <rmacd@xxxxxxxx>
- To: Blind Chess Mailing List <blind-chess@xxxxxxxxxxxxx>
- Date: Wed, 16 Jun 2010 19:21:43 -1000 (HST)
Chess Article #54:
The Rook and pawn versus rook endgame
Adapted and Condensed from
Wikipedia, the Free Encyclopedia
Part One of Three Parts
The chess endgame of a rook and pawn versus rook is of fundamental
importance, and has been widely studied. Endings with rooks and
pawns are the most common type to occur in games, occurring in
about 8 to 10 percent of all games (de la Villa 2008:18), (Emms
2008:6). Rook and pawn endings with more pawns have the potential
of being reduced to this type of endgame. John Nunn wrote entire
352-page book about this ending, Secrets of Rook Endings (Nunn
2007:126). Volume 2 of the Encyclopedia of Chess Endings devotes 92
pages to the analysis of 428 positions of this type (Matanovic
1985:14-105). Precise play is usually required in these positions.
Some complicated wins require sixty moves (Speelman, Tisdall & Wade
1993:7). In some cases, thirty-five moves are required to advance
the pawn once (Thompson 1986).
Diagram #1:
White: King at d1, Rook at d6, Pawn at b2
Black: King at h6, Rook at a8
Black to move, White converts to a won position in 60 moves
The play of this type of ending revolves around whether or not the
pawn can be promoted, or if the rook has to be sacrificed to keep
it from promoting. If the pawn promotes, that side will have an
overwhelming material advantage. If the pawn is about to promote,
the defending side may give up his rook for the pawn, resulting in
an easily-won endgame for the superior side. In a few cases, the
superior side gives up his rook in order to promote the pawn,
resulting in a won queen versus rook position (see Pawnless chess
endgames#Queen versus rook).
A general rule of thumb (with exceptions) is: if the king on the
side without the pawn can reach the queening square of the pawn,
the game is a draw; otherwise it is a win for the opponent (except
with a rook pawn, i.e. a- or h- file) (Fine & Benko 2003:294ff).
The side with the pawn can cut off the opposing king or strive for
the Lucena position, which is a win. The defender can aim for the
Philidor position (which is a draw) or try to set up one of the
other defensive techniques that draw.
++1. Terminology
* In the following discussion and positions, assume that the
side with the pawn is white.
* Ranks are counted from that player's side of the board. Thus,
"the rook's third rank" would be the third rank counting from
that player's side of the board. The ranks for the white
pieces correspond to the rank in algebraic notation whereas
the ranks for the black pieces are reversed.
* In these positions with one pawn, the pawn's file divides the
board into a "short side" and a "long side", in which the long
side consists of more files than the short side.
* Pawns are referred to by the file on which they reside: a rook
pawn is on the a- or h-file, a knight pawn is on the b- or g-
file, a bishop pawn is on the c- or f-file. A central pawn is
a queen pawn or a king pawn, on the d- or e-file.
++2. Pawn on the sixth or seventh rank
In his 1958 book Chess Endgames, Nikolay Kopaev gave these general
guidelines for when the pawn is on the sixth or seventh rank:
* When the black king is cut off two or more files from the
pawn, White always wins
* If the black king is on the long side of the pawn and his rook
is on the short side, White wins with very few exceptions.
* If the pawn is on the seventh rank, the only defense involves
checks from the side. If the pawn is on the sixth rank, a
defense of checks from the rear is possible.
* The defense of checking from the side normally requires three
empty files between the pawn and the black rook. Sometimes it
is possible with only two files when the pawn is on the
seventh rank.
* In order for a defense of checking from behind to be
successful, the white king must be behind the pawn, not in
front of it.
* There are tactical possibilities: (1) deflecting the black
rook, and (2) creating a shelter for the white king (Minev
2004:72).
++3. Winning methods
In order to force a win with the extra pawn, normally the black
king must be cut off from the pawn by the white rook along a rank
or file, and that is not always sufficient.
++3.a Black king is cut off along a rank
Diagram #2:
White: King at e5, rook at h4, , Pawn at d5
Black: King at e3, Rook at e8
Cutting off the king. The black king is cut off along a rank, so
White wins easily.
If the black king is cut off from the pawn along a rank (as in
diagram #2), White wins easily if the king is behind the pawn:
1. Kd6 Rd8+
2. Ke6 Re8+
3. Kd7 Rg8
Checks from the front or side does not help Black.
4. d6 Rg7+
5. Kc8 Rg8+
6. Kc7 Rg7+
7. d7
and the pawn will soon queen (Seirawan 2003:86).
When cutting the defending king off by a rank, a Perfect Cut is
when the pawn is on the same rank as the defending king. An
Imperfect Cut is when the king is on the rank ahead of the pawn.
These general rules apply:
1. The defending king should be cut off on a rank on the long
side of the pawn. Otherwise, the position is not dangerous for
the defense if the defending rook is on the long side.
2. With a Perfect Cut, the position is always won with a bishop
pawn or knight pawn on any rank. A central pawn wins if it is
on the fourth rank or beyond.
3. With an Imperfect Cut, the position is a draw if the defending
rook is on the file adjacent to the pawn. In addition, the
defense has more possibilities against a central pawn (de la
Villa 2008:141-45).
diagram #3: de la Villa, position 10.17
white: King at b3, Rook at c5, Pawn at b4
Black: King at d4, Rook at b8
White has a perfect cut of the king along a rank
In this position, White has a pefect cut and wins:
1. ... Ra8
2. Rc6 Rb8
3. Ra6 Kd5
4. Ka4! Kc4
5. Rc6+! Kd5
6. b5 Ra8+
7. Kb4
This is the same position but advanced one rank. Now the process is
repeated:
7. ... Rb8
8. Rc7 Kd6
9. Ra7 Kd5
10. Ka5 Kc5
11. Rc7+ Kd6
12. b6 Ra8+
13. Kb5 Ra1
White threatened Rh7, Pb7, and Kb6 so Black tries checks from the
rear. However, play will soon lead to a Lucena position (see
below), which wins for White (de la Villa 2008:141-42).
++3.b Black king is cut off from the pawn's file
When the black king is cut off from the pawn's file the outcome
depends on where the black king is in relation to the pawn. Black's
king is often cut off from the pawn along a file. Some general
rules (with exceptions) are:
* If the pawn is a rook pawn, the position is usually a draw.
* If the pawn is on the fifth rank (or sixth or seventh rank)
with its king near, and the black king is cut off from the
pawn's file, White has a won position.
* If the pawn is on the third or fourth rank, (a) if it is a
bishop pawn or central pawn, White always wins if the black
king is cut off by two files for fourth rank pawn and the
black king is cut off by three files for third rank pawn (see
"The Rule Of Five" below) (i.e. White's rook is two files over
from his pawn and the black king is on the other side), and
(b) if the pawn is a knight pawn, White always wins if the
black king is cut off by three files.
* If the pawn is on the second rank and the black king is on the
fourth or fifth rank, White wins only if the opposing king is
cut off five files from the pawn.
* In some cases White wins even if the black king is closer
(Fine & Benko 2003:298-305).
++3.b1 Rule of five
Diagram #4:
White: King at d3, Rook at f1, Pawn at d4
Black: King at g5, rook at d8
The rule of five. White to move. The pawn is on the fourth rank,
the king is cut off by two files, White wins.
The rule of five is for positions in which the pawn is protected
and the opposing king is cut off by files: Add the number of rank
of the pawn to the number of files the defender's king is cut off.
If the sum is more than five, it is usually a win. Otherwise it is
normally a draw. (Soltis 2003:138), (Mednis 1998:41-42). For
example, in diagram #4, white wins by:
1. Kc4 Rc8+
2. Kb5
(the white king must have this file available)
2. ... Rd8
3. Kc5 Rc8+
4. Kb6! Rd8
5. Rd1! Kf6
6. Kc7 Ra8
7. d5
and White will win.
Diagram #5: Chiron, 1923
White: King at b3, Rood at d1, Pawn at b4
Black: King at e6, Rook at b8
The rule of five seems to apply, but Black draws because the pawn
is a knight pawn.
The position by Chiron is basically the same, except moved over two
files. Now the white king has less room to maneuver on the left of
the pawn's file, and Black can prevent the advance of the pawn and
draw. If White starts with 1. Ka4, the rook checks the king, and
the king is forced back to b3. White can try:
1. Rd4 Ke5
2. Kc3 Rc8+
3. Rc4 Rb8
4. Rc6 Kd5
5. Ra6 Rc8+
6. Kb3 Rc6!
7. Ra8 Kd6
(or 7. Ra7 Rc1)
and the black king reaches the pawn's file, for a draw. Another try
for White is:
1. Rd2 Ke5
2. Rd7 Ke6
3. Rc7 Kd6
4. Rc5 Kd7
5. Ka4 Ra8+
6. Ra5 Rb8
7. Ra7+ Kc6
8. Ka5 Rb5+
9. Ka4 Rb8
and the position is drawn. If the pieces are moved one file to the
right, White has a win (Korchnoi 2002:12-13).
diagram #6:
Capablanca
White: King at e3, Rook at d2, Pawn at f2
Black: King at c5, Rook at h2
White wins because Black's rook is not in position for frontal
checks
In the discussion above about the defending king being cut off by
files, it is assumed that the defending rook is already in position
to check the attacking king along files (usually from his first
rank). In this position by Josi Capablanca, White wins because the
white pawn can reach its fourth rank before the black rook can
check along files. If the black rook were already at h8 and it were
Black's move, Black would draw by checking the king and by playing
... Rf8 when the white king moves to f1 (Capablanca de Firmian
2006:121). With White to move in the diagramm #6 position:
1. Rd1 Rh8
2. f4 Re8+
3. Kf3 Rf8
4. Kg4 Rg8+
5. Kh5 Rh8+
6. Kg6, etc,
and White will win. With Black to move,
1. ... Kc6
2. Rd8 Rh7
3. f3 (3. f4 draws after 3. ... Rd7 or 3. ... Kc7)
3. ... Re7+
4. Kf2 Rf7
5. Kg3 etc, and White wins.
++3.b2 Lucena position
Diagram #7:
White: King at b8, Rook at c1, Pawn at b7
Black: King at d8, Rook at a2
The Lucena position, White wins.
The Lucena position is one of the most famous and important
positions in chess endgame theory. It is a win for the side with
the pawn. The essential characteristics are that White's king is on
the queening square in front of his pawn, the pawn is on the b
through g files, and the black king is cut off on a file.
White wins in the position in diagram #7 by 1. Rd1+, forcing the
black king one file farther away, then bringing rook to the fourth
rank, then bringing out the king, which will be checked by Black's
rook. White maneuvers his king to the fifth rank (without giving up
the pawn) and then when the black rook checks, White interposes his
rook and has a winning position. See Lucena position for more
details (Fine & Benko 2003:297-98).
++3.b3 Alternate method for bishop pawns and central pawns
Diagram #8:
White: King at e8, rook at d2, Pawn at e7
Black: King at c7, Rook at f1
White wins, using the alternate method for bishop pawns and central
pawns
The Lucena position is a win for White if the pawn is not a rook
pawn. There is another way of winning if the pawn is a bishop pawn
or central pawn.
In diagram #8, 1. Rc2+ would start the process of winning with the
process above. However, White also wins by
1. Rh2 Rf3
2. Rh8 Rf1
3. Rf8 Re1
4. Kf7
(Emms 2008:17-18). Now either
4. ... Kd7
5. e8=Q+
wins, or the white king can approach the black rook on the two
files next to the pawn's file until it can no longer check:
4. ... Rf1+
5. Kg6 Rg1+
6. Kf5 Rf1+
7. Kg4 Rg1+
8. Kf3 Rf1+
9. Ke2
and the black rook can no longer attack and the pawn promotes.
++3.c Other methods
Diagram #9:
White: King at e8, Rook at d2, Pawn at e7
Black: King at c7, Rook at e1
Horowitz and Kling, 1851
White to move wins
It may not be necessary to build a bridge to win, if the king is on
its pawn's promotion square. White wins in this position:
1. Rc2+ Kb8
(or 1... Kd6 2. Kd8 Rxe7 3. Rd2+ Ke6 4. Re2 wins)
2. Rf2 Rh1
3. Kf7 Rh7+
4. Ke6 Rh8
5. Kd7 Rh7
6. Kd8
wins (Horwitz & Kling 1986:143).
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