Fortress (chess)
Encyclopedia
In chess
, the fortress is an endgame drawing
technique in which the side behind in material sets up a zone of protection around their king
that cannot be penetrated by the opponent. This only works when the opponent does not have a passed pawn
or cannot create one, unless that pawn can be stopped (e.g. see the opposite-colored bishops
example). An elementary fortress is a theoretically drawn
(i.e. a book draw) position with reduced material in which a passive defense will maintain the draw .
Fortresses commonly have four characteristics:
Fortresses pose a problem for computer chess
: computers are unable to reason about fortress-type positions except to the extent that their endgame tablebase
allows.
on the board
, is where the defending king is able to take refuge in a corner of the board and cannot be chased away or checkmated by the superior side. These two diagrams furnish two classic examples. In both cases, Black simply shuffles his king between a8 and the available square adjacent to a8 (a7, b7, or b8, depending on the position of the white king and pawn). White has no way to dislodge Black's king, and can do no better than a draw by stalemate
or some other means.
Note that the bishop and wrong rook pawn
ending (i.e. where the pawn is a rook pawn whose promotion
square is the color opposite to that of the bishop) at right is a draw even if the pawn is on the seventh rank or further back on the a-file. Heading for a bishop and wrong rook pawn ending is a fairly common drawing resource available to the inferior side .
The knight
and rook pawn position at right, however, is only a draw if White's pawn is already on the seventh rank, making this drawing resource available to the defender much less frequently. White wins if the pawn is not yet on the seventh rank and is protected by the knight from behind. With the pawn on the seventh rank, Black has a stalemate defense with his king in the corner .
A fortress is often achieved by a sacrifice
, such as of a piece for a pawn. In the game between Grigory Serper and Hikaru Nakamura
, in the 2004 U.S. Chess Championship
, White would lose after 1. Nd1 Kc4 or 1. Nh1 Be5 or 1. Ng4 Bg7. Instead he played 1. Nxe4! Kxe4 2.Kf1! heading for h1. After another 10 moves the position in the second diagram was reached. Black has no way of forcing White's king away from the corner, so he played 12... Kf2 and after 13. h4 gxh4 the game was drawn by stalemate.
The back-rank defense in some rook and pawn versus rook endgames is another type of fortress in a corner (see diagram at left). The defender perches his king on the pawn's queening square, and keeps his rook
on the back rank (on the "long side" of the king, not, e.g., on h8 in the diagram position) to guard against horizontal checks. If 1.Rg7+ in the diagram position, Black heads into the corner with 1...Kh8! Note that this defense works only against rook pawns and knight pawns .
In the ending of a rook versus a bishop, the defender can form a fortress in the "safe" corner—the corner that is not of the color on which the bishop resides (see diagram). White must release the potential stalemate, but he cannot improve his position .
In this position from de la Villa, White draws if his king does not leave the corner. It is also a draw if the bishop is on the other color .
The white king is not able to cross the rank of the black rook and the white queen
is unable to do anything useful.
Positions such as these (when the defending rook and king are near the pawn and the opposing king cannot attack from behind) are drawn when: (see diagram)
Otherwise, the queen wins .
and Ferriz, White sacrificed a rook for a knight in order to exchange a pair of pawns and reach this position, and announced that it was a draw because (1) the queen cannot mate alone, and (2) the black king and pawn cannot approach to help . However, endgame tablebase
analysis shows Black to have a forced win in 19 moves starting with 50... Qc7+ (the only winning move), again illustrating how tablebases are refining traditional endgame theory.
vs. Korchnoi
, Wijk aan Zee
1997, White was able to hold a draw with a rook versus a queen, even with the sides having an equal number of pawns. He kept his rook on the fifth rank blocking in Black's king, and was careful not to lose his rook to a fork
or allow a queen sacrifice
for the rook in circumstances where that would win for Black. The players agreed to a draw
after:
48.Kg2 Kg6 49.Rh5 Qe2+ 50.Kg3 Qf1 51.Kf4 Qe1 52.Rd5 Qc1+ 53.Kg3 Qc7+ 54.Kg2 Qf4 55.Rh5 Kf6 56.Rd5 Ke6 57.Rh5 Qd2+ 58.Kg3 f6 59.Rf5 Qc1 60.Rh5 Qg1+ 61.Kf4 Qe1 62.Rb5 Qc1+ 63.Kg3 Qg1+ 64.Kf4 Qh2+ 65.Ke3 Kf7 66.Rh5 Qg1+ 67.Kf4 Kg6 68.Rd5 Qh2+ 69.Ke3 Kf7 70.Rh5 Qg1+ 71.Kf4 Ke6 72.Rb5 Qh2+ 73.Ke3 Kd6 74.Rf5 Qb2 75.Rh5 Ke6 76.Kf4 Qc3 77.Kg3 Qc7+ 78.Kg2 Qf7 79.Rb5 Qe8 80.Rf5 Qg6 81.Rb5 ½–½
a pawn (leaving him three pawns down) to reach a fortress.
After 4... Be2 5. Kh6 Bd1 6. h5 Black just waits by playing 6... Be2 .
. Usually the defending side will not be able to get to one of these positions.
. For example:
position is not reached, but some of them take up to seventy-one moves, so the fifty-move rule comes into play. From the diagram:
and White cannot prevent ... Bb6, which gets back to the Lolli position .
There are several drawing positions with two knights against a queen. The best way is to have the knights adjacent to each other on a file or rank, with their king between them and the enemy king. This is not a true fortress since it is not static. The position of the knights may have to change depending on the opponent's moves. In this position (Lolli, 1763),
and Black has an ideal defensive position.
If the knights cannot be adjacent to each other on a file or rank, the second best position is if they are next to each other diagonally (see diagram).
The third type of defensive formation is with the knights protecting each other, but this method is more risky .
Ree
-Hort
, Wijk aan Zee
1986 (diagram at left), Black had the material disadvantage of rook and bishop against a queen. Dvoretsky writes that Black would probably lose after the natural 1...Bf2+? 2.Kxf2 Rxh4 because of 3.Kg3 Rh7 4.Kf3, followed by a king march to c6, or 3.Qg7!? Rxf4+ 4.Kg3 Rg4+ 5.Kf3, threatening 6.Qf6 or 6.Qc7 . Instead, Hort forced a draw with 1...Rxh4!! 2.Kxh4 Bd4! (imprisoning White's queen) 3.Kg3 Ke7 4.Kf3 Ba1 (diagram at right), and the players agreed to a draw. White's queen has no moves, all of Black's pawns are protected, and his bishop will shuttle back and forth on the squares a1, b2, c3, and d4.
1924 tournament, former world champion
Emanuel Lasker
was in trouble against his namesake Edward Lasker
, but surprised everyone by discovering a new endgame fortress . Despite having only a knight for a rook and pawn, White draws by moving his knight back and forth between b2 and a4. Black's only real winning try is to get his king to c2. However, to do so Black has to move his king so far from the pawn that White can play Ka3-b2 and Nc5xb3, when the rook versus knight ending is an easy draw. The game concluded:
93.Nb2 Ke4 94.Na4 Kd4 95.Nb2 Rf3 96.Na4 Re3 97.Nb2 Ke4 98.Na4 Kf3 99.Ka3! Ke4 If 99...Ke2, 100.Nc5 Kd2 101.Kb2! (101.Nxb3+?? Kc2 and Black wins) and 102.Nxb3 draws. 100.Kb4 Kd4 101.Nb2 Rh3 102.Na4 Kd3 103.Kxb3 Kd4+ ½–½
if 7. f7 Bxf7!: the pawn can be safely captured when the white king is on h6
The position at left, a chess problem
by W.E. Rudolph (La Strategie 1912), illustrates the defense perimeter. White already has a huge material disadvantage, but forces a draw by giving up his remaining pieces to establish an impenetrable defense perimeter with his pawns. White draws with 1.Ba4+! Kxa4 (1...Kc4 2.Bb3+! Kb5 3.Ba4+ repeats the position) 2.b3+ Kb5 3.c4+ Kc6 4.d5+ Kd7 5.e6+! Kxd8 6.f5! (diagram at right). Now Black is up two rooks and a bishop (normally an overwhelming material advantage) but has no hope of breaking through White's defense perimeter. The only winning attempts Black can make are to place his rooks on b5, c6, etc. and hope that White captures them. White draws by ignoring all such offers and simply shuffling his king about .
The above example may seem fanciful, but Black achieved a similar defense perimeter in
Arshak Petrosian
-Hazai, Schilde
1970 (diagram at left). In the position at left, Black has a difficult endgame, since White can attack and win his a-pawn by force, and he has no counterplay. Black tried the extraordinary 45...Qb6!?, to which White replied with the obvious 46.Nxb6+? This is actually a critical mistake, enabling Black to establish an impenetrable fortress. White should have carried out his plan of winning Black's a-pawn, for example with 46.Qc1 (threatening 47.Nxb6+ cxb6 48.h4! gxh4 49.Qh1 and Qh3, winning) Qa7 47.Qd2 followed by Kb3, Nc3, Ka4, and Na2-c1-b3. 46...cxb6 Now Black threatens 47...h4, locking down the entire board with his pawns, so White tries to break the position open. 47.h4 gxh4 48.Qd2 h3! 49.gxh3 Otherwise 49...h2 draws. 49...h4! (diagram at right) Black has established his fortress, and now can draw by simply moving his king around. The only way White could attempt to breach the fortress would be a queen sacrifice at some point (for example Qxa5 or Qxe5), but none of these give White winning chances as long as Black keeps his king near the center. The players shuffled their kings, and White's queen, around for six more moves before agreeing to a draw
.
In Smirin
-HIARCS
, Smirin-Computers match 2002, the super-grandmaster looked to be in trouble against the computer, which has the bishop pair, can tie White's king down with ...g3, and threatens to invade with its king on the light squares. Smirin, however, saw that he could set up a fortress with his pawns. The game continued 46...g3 47.h3! A surprising move, giving Black a formidable protected passed pawn on the sixth rank, but it begins to build White's fortress, keeping Black's king out of g4. 47...Bc5 48.Bb4! Now Smirin gives HIARCS the choice between an opposite-colored bishops endgame (in which, moreover, White will play Be7 and win the h-pawn if Black's king comes to the center) and a bishop versus knight ending in which Smirin envisions a fortress. 48...Bxb4 49.axb4 Kf7 Black could try to prevent White's coming maneuver with 49...Bd3, but then White could play 50.Nf3 Kh5 (forced) 51.Nd4. 50.Nb5! Ke6 51.Nc3! Completing the fortress. Now Black's king has no way in, and his bishop can do nothing, since White's King can prevent ...Bf1, attacking White's only pawn on a light square. The game concluded: 51...Bc2 52.Kg2 Kd6 53.Kg1 Kc6 54.Kg2 b5 55.Kg1 Bd3 56.Kg2 Be4+ 57.Kg1 Bc2 58.Kg2 Bd3 59.Kg1 Be4 60.Kf1 ½–½
s show that the bishops generally win, but it takes up to 66 moves. It takes several moves to force Black out of the temporary fortress in the corner; then precise play with the bishops prevents Black from forming the fortress in another corner. The position in the diagram was thought to be a draw by Kling
and Horwitz
but computer analysis shows that White wins in 45 moves (either by checkmate or by winning the knight). All of the long wins in this endgame go through this type of semi-fortress position .
This game between József Pintér
and David Bronstein
demonstrates the human play of the endgame. The defender has two ideas: (1) keep the king off the edge of the board and (2) keep the knight close to the king. White reaches the semi-fortress after 71. Nb2!, which falls after 75... Kb5!. White gets to a semi-fortress again in another corner after 90. Ng2+. After 100. Ke3 White cannot hold that semi-fortress any longer, but forms one in another corner after 112. Nb7!. On move 117 White claimed a draw
by the fifty move rule
.
and describes an impasse other than stalemate
. It usually involves the repetition of moves in which neither side can make progress or safely deviate. Typically a material advantage is balanced by a positional advantage. Fortresses and perpetual check
are examples of positional draws . Sometimes they salvage a draw from a position that seems hopeless because of a material deficit . Grandmaster John Nunn
describes a positional draw as a position in which one side has enough material to normally win and he is not under direct attack, but some special feature of the position (often a blockade) prevents him from winning .
A simple example is shown in the game between Lajos Portisch
and Lubomir Kavalek. White could have won easily with 1. Be1 Kc6 2. b4. However, play continued 1. b4? Nb8 2. b5 Nc6+! The only way to avoid the threatened 3...Nxa5 is 3. bxc6 Kxc6, but the resultant position is a draw because the bishop is on the wrong color to be able to force the rook pawn's promotion
(see above, wrong bishop
, and wrong rook pawn
) .
Luděk Pachman
cites the endgame position at right as a simple example of a positional draw. White on move simply plays waiting moves with the bishop (Bb1-c2-d3). As for Black, "If he is unwilling to allow the transition to the drawn ending of Rook versus Bishop, nothing else remains for him but to move his Rook at [e5] continuously up and down the [e-file]." Pachman explains, "The indecisive result here contradicts the principles concerning the value of the pieces and is caused by the bad position of the black pieces (pinned rook at [e4])." .
This position from a game between Mikhail Botvinnik
and Paul Keres
in the 1951 USSR Championship
is drawn because the black king cannot get free and the rook must stay on the c-file. The players agreed to a draw
four moves later .
The first diagram shows a position from a game between former World Champion
Mikhail Tal
and future World Champion Bobby Fischer
from the 1962 Candidates Tournament
in Curaçao. After 41 moves Tal had the advantage but Fischer sacrificed
the exchange
(a rook for a knight). The game was drawn on the 58th move .
In this position from a game between Pal Benko
and International Master Jay Bonin, White realized that the blockade cannot be broken and the game is a draw despite the extra material .
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
, the fortress is an endgame drawing
Draw (chess)
In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...
technique in which the side behind in material sets up a zone of protection around their king
King (chess)
In chess, the king is the most important piece. The object of the game is to trap the opponent's king so that its escape is not possible . If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture on the next move. If this cannot be...
that cannot be penetrated by the opponent. This only works when the opponent does not have a passed pawn
Passed pawn
In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth rank, i.e. there are no opposing pawns in front of it on the same file nor on an adjacent file. A passed pawn is sometimes colloquially called a passer...
or cannot create one, unless that pawn can be stopped (e.g. see the opposite-colored bishops
Bishop (chess)
A bishop is a piece in the board game of chess. Each player begins the game with two bishops. One starts between the king's knight and the king, the other between the queen's knight and the queen...
example). An elementary fortress is a theoretically drawn
Draw (chess)
In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...
(i.e. a book draw) position with reduced material in which a passive defense will maintain the draw .
Fortresses commonly have four characteristics:
- Useful pawnPawn (chess)The pawn is the most numerous and weakest piece in the game of chess, historically representing infantry, or more particularly armed peasants or pikemen. Each player begins the game with eight pawns, one on each square of the rank immediately in front of the other pieces...
breakthroughs are not possible - If the stronger side has pawns, they are firmly blocked
- The stronger side's kingKing (chess)In chess, the king is the most important piece. The object of the game is to trap the opponent's king so that its escape is not possible . If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture on the next move. If this cannot be...
cannot penetrate, either because it is cut off or near the edge of the boardChessboardA chessboard is the type of checkerboard used in the board game chess, and consists of 64 squares arranged in two alternating colors... - ZugzwangZugzwangZugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...
positions cannot be forced, because the defender has waiting moves available .
Fortresses pose a problem for computer chess
Computer chess
Computer chess is computer architecture encompassing hardware and software capable of playing chess autonomously without human guidance. Computer chess acts as solo entertainment , as aids to chess analysis, for computer chess competitions, and as research to provide insights into human...
: computers are unable to reason about fortress-type positions except to the extent that their endgame tablebase
Endgame tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.The tablebase...
allows.
Fortress in a corner
Perhaps the most common type of fortress, often seen in endgames with only a few piecesChess piece
Chess pieces or chessmen are the pieces deployed on a chessboard to play the game of chess. The pieces vary in abilities, giving them different values in the game...
on the board
Chessboard
A chessboard is the type of checkerboard used in the board game chess, and consists of 64 squares arranged in two alternating colors...
, is where the defending king is able to take refuge in a corner of the board and cannot be chased away or checkmated by the superior side. These two diagrams furnish two classic examples. In both cases, Black simply shuffles his king between a8 and the available square adjacent to a8 (a7, b7, or b8, depending on the position of the white king and pawn). White has no way to dislodge Black's king, and can do no better than a draw by stalemate
Stalemate
Stalemate is a situation in chess where the player whose turn it is to move is not in check but has no legal moves. A stalemate ends the game in a draw. Stalemate is covered in the rules of chess....
or some other means.
Note that the bishop and wrong rook pawn
Wrong rook pawn
In chess endgames with a bishop, a pawn that is a rook pawn may be the wrong rook pawn. With a single bishop, the result of a position may depend on whether or not the bishop controls the square on the chessboard on which the pawn would promote. Since a side's rook pawns promote on...
ending (i.e. where the pawn is a rook pawn whose promotion
Promotion (chess)
Promotion is a chess rule describing the transformation of a pawn that reaches its eighth rank into the player's choice of a queen, knight, rook, or bishop of the same color . The new piece replaces the pawn on the same square and is part of the move. Promotion is not limited to pieces that have...
square is the color opposite to that of the bishop) at right is a draw even if the pawn is on the seventh rank or further back on the a-file. Heading for a bishop and wrong rook pawn ending is a fairly common drawing resource available to the inferior side .
The knight
Knight (chess)
The knight is a piece in the game of chess, representing a knight . It is normally represented by a horse's head and neck. Each player starts with two knights, which begin on the row closest to the player, one square from the corner...
and rook pawn position at right, however, is only a draw if White's pawn is already on the seventh rank, making this drawing resource available to the defender much less frequently. White wins if the pawn is not yet on the seventh rank and is protected by the knight from behind. With the pawn on the seventh rank, Black has a stalemate defense with his king in the corner .
A fortress is often achieved by a sacrifice
Sacrifice (chess)
In chess, a sacrifice is a move giving up a piece in the hopes of gaining tactical or positional compensation in other forms. A sacrifice could also be a deliberate exchange of a chess piece of higher value for an opponent's piece of lower value....
, such as of a piece for a pawn. In the game between Grigory Serper and Hikaru Nakamura
Hikaru Nakamura
Hikaru Nakamura is an American chess Grandmaster . He has been ranked among the top six players in the world by FIDE....
, in the 2004 U.S. Chess Championship
U.S. Chess Championship
The U.S. Chess Championship is an invitational tournament held to determine the national chess champion of the United States. Since 1936, it has been held under the auspices of the U.S. Chess Federation. Until 1999, the event consisted of a round-robin tournament of varying size...
, White would lose after 1. Nd1 Kc4 or 1. Nh1 Be5 or 1. Ng4 Bg7. Instead he played 1. Nxe4! Kxe4 2.Kf1! heading for h1. After another 10 moves the position in the second diagram was reached. Black has no way of forcing White's king away from the corner, so he played 12... Kf2 and after 13. h4 gxh4 the game was drawn by stalemate.
The back-rank defense in some rook and pawn versus rook endgames is another type of fortress in a corner (see diagram at left). The defender perches his king on the pawn's queening square, and keeps his rook
Rook (chess)
A rook is a piece in the strategy board game of chess. Formerly the piece was called the castle, tower, marquess, rector, and comes...
on the back rank (on the "long side" of the king, not, e.g., on h8 in the diagram position) to guard against horizontal checks. If 1.Rg7+ in the diagram position, Black heads into the corner with 1...Kh8! Note that this defense works only against rook pawns and knight pawns .
In the ending of a rook versus a bishop, the defender can form a fortress in the "safe" corner—the corner that is not of the color on which the bishop resides (see diagram). White must release the potential stalemate, but he cannot improve his position .
- 1. Rc3 Ba2
- 2. Rc2 Bb3
- 3. Rc7 Bg8
In this position from de la Villa, White draws if his king does not leave the corner. It is also a draw if the bishop is on the other color .
Rook and pawn versus queen
In the diagram at right, Black draws by moving his rook back and forth between the d6 and f6 squares, or moves his king when checked, staying behind the rook and next to the pawn. This fortress works when all of these conditions are met:- the pawn is still on its second rank
- the pawn is on files b through g
- the pawn is protecting its rook on the third rank
- the opposing king is beyond the defender's third rank
- the defending king protects its pawn .
The white king is not able to cross the rank of the black rook and the white queen
Queen (chess)
The queen is the most powerful piece in the game of chess, able to move any number of squares vertically, horizontally, or diagonally. Each player starts the game with one queen, placed in the middle of the first rank next to the king. With the chessboard oriented correctly, the white queen starts...
is unable to do anything useful.
- 1. Qd5+ Rd6
- 2. Qb5+ Kd8
- 3. Qb8+ Kd7
- 4. Qb5+ ½-½
Positions such as these (when the defending rook and king are near the pawn and the opposing king cannot attack from behind) are drawn when: (see diagram)
- the pawn is on the c, d, e, or f file and the second, sixth, or seventh rank
- the pawn is anywhere on the b or g file
- the pawn is on the a or h file and the third or seventh rank.
Otherwise, the queen wins .
Similar example
In this 1959 game between WhitakerNorman Tweed Whitaker
Norman Tweed Whitaker was an International Master of chess. After more than ten years of campaigning, he was awarded the title by FIDE in 1965 , based on his earlier play . He was involved in a confidence trick involving the Lindbergh kidnapping and went to prison several times...
and Ferriz, White sacrificed a rook for a knight in order to exchange a pair of pawns and reach this position, and announced that it was a draw because (1) the queen cannot mate alone, and (2) the black king and pawn cannot approach to help . However, endgame tablebase
Endgame tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.The tablebase...
analysis shows Black to have a forced win in 19 moves starting with 50... Qc7+ (the only winning move), again illustrating how tablebases are refining traditional endgame theory.
Example with more pawns
From the diagram at right, in SalovValery Salov
Valery Salov is a Russian chess grandmaster.Salov was awarded the International Master title in 1984 and the Grandmaster title in 1986. He was the World under-17 Champion in 1980 and European Junior Champion in 1983-84...
vs. Korchnoi
Viktor Korchnoi
Viktor Lvovich Korchnoi ; pronounced in the original Russian as "karch NOY"; Ви́ктор Льво́вич Корчно́й, born March 23, 1931 is a professional chess player, author and currently the oldest active grandmaster on the tournament circuit...
, Wijk aan Zee
Wijk aan Zee
Wijk aan Zee is a small town on the coast of the North Sea in the municipality of Beverwijk in the province of North Holland of the Netherlands. The prestigious Tata Steel chess tournament formerly Corus chess tournament and before that called Hoogovens tournament takes place there every year.Due...
1997, White was able to hold a draw with a rook versus a queen, even with the sides having an equal number of pawns. He kept his rook on the fifth rank blocking in Black's king, and was careful not to lose his rook to a fork
Fork (chess)
In chess, a fork is a tactic that uses a single piece to attack multiple pieces at the same time. The attacker usually hopes to gain material by capturing one of the opponent's pieces. The defender often finds himself in a difficult position in which he cannot counter all threats. The attacking...
or allow a queen sacrifice
Sacrifice (chess)
In chess, a sacrifice is a move giving up a piece in the hopes of gaining tactical or positional compensation in other forms. A sacrifice could also be a deliberate exchange of a chess piece of higher value for an opponent's piece of lower value....
for the rook in circumstances where that would win for Black. The players agreed to a draw
Draw by agreement
In chess, a draw by agreement is the outcome of a game due to the agreement of both players to a draw. A player may offer a draw to his opponent at any stage of a game; if the opponent accepts, the game is a draw. The relevant portion of the FIDE laws of chess is article 9.1...
after:
48.Kg2 Kg6 49.Rh5 Qe2+ 50.Kg3 Qf1 51.Kf4 Qe1 52.Rd5 Qc1+ 53.Kg3 Qc7+ 54.Kg2 Qf4 55.Rh5 Kf6 56.Rd5 Ke6 57.Rh5 Qd2+ 58.Kg3 f6 59.Rf5 Qc1 60.Rh5 Qg1+ 61.Kf4 Qe1 62.Rb5 Qc1+ 63.Kg3 Qg1+ 64.Kf4 Qh2+ 65.Ke3 Kf7 66.Rh5 Qg1+ 67.Kf4 Kg6 68.Rd5 Qh2+ 69.Ke3 Kf7 70.Rh5 Qg1+ 71.Kf4 Ke6 72.Rb5 Qh2+ 73.Ke3 Kd6 74.Rf5 Qb2 75.Rh5 Ke6 76.Kf4 Qc3 77.Kg3 Qc7+ 78.Kg2 Qf7 79.Rb5 Qe8 80.Rf5 Qg6 81.Rb5 ½–½
Opposite-colored bishops
In endings with bishops of opposite colors (i.e. where one player has a bishop that moves on light squares, while the other player's bishop moves on dark squares), it is often possible to establish a fortress, and thus hold a draw, when one player is one, two, or occasionally even three pawns behind. A typical example is seen in the diagram at right. White, although three pawns behind, has established a drawing fortress, since Black has no way to contest White's stranglehold over the light squares. White simply keeps his bishop on the h3 to c8 diagonal .Example from game
In an endgame with opposite-colored bishops, positional factors may be more important than material. In this position, Black sacrificesSacrifice (chess)
In chess, a sacrifice is a move giving up a piece in the hopes of gaining tactical or positional compensation in other forms. A sacrifice could also be a deliberate exchange of a chess piece of higher value for an opponent's piece of lower value....
a pawn (leaving him three pawns down) to reach a fortress.
- 1... Kf5!
- 2. Kxf7 Bh5+
- 3. Kg7 Bd1
- 4.Be7 ½-½
After 4... Be2 5. Kh6 Bd1 6. h5 Black just waits by playing 6... Be2 .
Queen versus two minor pieces
Here are drawing fortresses with two minor pieces versus a queenQueen (chess)
The queen is the most powerful piece in the game of chess, able to move any number of squares vertically, horizontally, or diagonally. Each player starts the game with one queen, placed in the middle of the first rank next to the king. With the chessboard oriented correctly, the white queen starts...
. Usually the defending side will not be able to get to one of these positions.
Bishop and knight
The bishop and knight fortress is another type of fortress in a corner. If necessary, the king can move to one of the squares adjacent to the corner, and the bishop can retreat to the corner. This gives the inferior side enough tempo moves to avoid zugzwangZugzwang
Zugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...
. For example:
- 1. Kb5 Ka7
- 2. Qd8 Ba8
- 3. Ka5 Bb7.
Two bishops
In the two bishop versus queen ending, the queen wins if the LolliGiambattista Lolli
Giambattista Lolli was an Italian chess player. Lolli was one of the most important chess theoreticians of his time. He is most famous for his book Osservazioni teorico-pratiche sopra il giuoco degli scacchi , published 1763 in Bologna...
position is not reached, but some of them take up to seventy-one moves, so the fifty-move rule comes into play. From the diagram:
- 1. Qe7+ Kc8
- 2. Qe6+ Kb7
- 3. Qd6 Ba7
- 4. Qe7+ Kb6!
- 5. Qd8+ Kb7!
- 6. Ka5 Bc5!
and White cannot prevent ... Bb6, which gets back to the Lolli position .
Two knights
In the two knights fortress, the knights are next to each other and their king should be between them and the attacking king. The defender must play accurately, though .There are several drawing positions with two knights against a queen. The best way is to have the knights adjacent to each other on a file or rank, with their king between them and the enemy king. This is not a true fortress since it is not static. The position of the knights may have to change depending on the opponent's moves. In this position (Lolli, 1763),
- 1. Qd1 Nd2+
- 2. Ke2 Nb3
and Black has an ideal defensive position.
If the knights cannot be adjacent to each other on a file or rank, the second best position is if they are next to each other diagonally (see diagram).
The third type of defensive formation is with the knights protecting each other, but this method is more risky .
With pawns
Sometimes the two minor pieces can achieve a fortress against a queen even where there are pawns on the board. InRee
Hans Ree
Hans Ree is a Dutch Grandmaster of chess and is a columnist and chess writer for the NRC Handelsblad. He contributes to the leading chess magazines New In Chess and ChessCafe.com...
-Hort
Vlastimil Hort
Vlastimil Hort is a chess Grandmaster of Czech nationality. During the 1960s and 1970s he was one of the world's strongest players and reached the Candidates stage of competition for the world chess championship, but was never able to compete for the actual title.Hort was born in Kladno,...
, Wijk aan Zee
Wijk aan Zee
Wijk aan Zee is a small town on the coast of the North Sea in the municipality of Beverwijk in the province of North Holland of the Netherlands. The prestigious Tata Steel chess tournament formerly Corus chess tournament and before that called Hoogovens tournament takes place there every year.Due...
1986 (diagram at left), Black had the material disadvantage of rook and bishop against a queen. Dvoretsky writes that Black would probably lose after the natural 1...Bf2+? 2.Kxf2 Rxh4 because of 3.Kg3 Rh7 4.Kf3, followed by a king march to c6, or 3.Qg7!? Rxf4+ 4.Kg3 Rg4+ 5.Kf3, threatening 6.Qf6 or 6.Qc7 . Instead, Hort forced a draw with 1...Rxh4!! 2.Kxh4 Bd4! (imprisoning White's queen) 3.Kg3 Ke7 4.Kf3 Ba1 (diagram at right), and the players agreed to a draw. White's queen has no moves, all of Black's pawns are protected, and his bishop will shuttle back and forth on the squares a1, b2, c3, and d4.
Knight versus a rook and pawn
At the great New YorkNew York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
1924 tournament, former world champion
World Chess Championship
The World Chess Championship is played to determine the World Champion in the board game chess. Men and women of any age are eligible to contest this title....
Emanuel Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...
was in trouble against his namesake Edward Lasker
Edward Lasker
Edward Lasker was a leading German-American chess and Go player. He was awarded the title of International Master of chess by FIDE. Lasker was an engineer by profession, and an author.-Background:...
, but surprised everyone by discovering a new endgame fortress . Despite having only a knight for a rook and pawn, White draws by moving his knight back and forth between b2 and a4. Black's only real winning try is to get his king to c2. However, to do so Black has to move his king so far from the pawn that White can play Ka3-b2 and Nc5xb3, when the rook versus knight ending is an easy draw. The game concluded:
93.Nb2 Ke4 94.Na4 Kd4 95.Nb2 Rf3 96.Na4 Re3 97.Nb2 Ke4 98.Na4 Kf3 99.Ka3! Ke4 If 99...Ke2, 100.Nc5 Kd2 101.Kb2! (101.Nxb3+?? Kc2 and Black wins) and 102.Nxb3 draws. 100.Kb4 Kd4 101.Nb2 Rh3 102.Na4 Kd3 103.Kxb3 Kd4+ ½–½
Bishop versus rook and bishop pawn on the sixth rank
A bishop can make a fortress versus a rook and a bishop pawn on the sixth rank, if the bishop is on the color of the pawn's seventh rank square and the defending king is in front of the pawn. In this position, White would win if he gotten the king to the sixth rank ahead of the pawn. Black draws by keeping the bishop on the diagonal from a2 to e6, except when giving check. The bishop keeps the white king off e6 and checks him if he goes to g6, to drive him away. A possible continuation:- 1... Ba2
- 2. Kf4 (2. f7 is an interesting attempt, but then Black moves 2... Kg7! and then 3... Bxf7, with a draw. 2... Kg7 prevents 3. Kf6, which would win.)
- 2... Bc4
- 3. Kg5 Bd5! (the only move to draw, since the bishop must be able to check the king if it goes to g6)
- 4. Rc7 Ba2!
- 5. Kg6 Bb1+!
- 6. Kh6 Ba2!
- 7. Ra7
if 7. f7 Bxf7!: the pawn can be safely captured when the white king is on h6
- 7... Bc4, draw because White cannot make progress .
Defense perimeter (pawn fortress)
A defense perimeter is a drawing technique in which the side behind in material or otherwise at a disadvantage sets up a perimeter, largely or wholly composed of a pawn chain, that the opponent cannot penetrate. Unlike other forms of fortress, a defense perimeter can often be set up in the middlegame with several pieces remaining on the board.The position at left, a chess problem
Chess problem
A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved. For instance, a position might be given with the instruction that White is to move first, and checkmate Black in two...
by W.E. Rudolph (La Strategie 1912), illustrates the defense perimeter. White already has a huge material disadvantage, but forces a draw by giving up his remaining pieces to establish an impenetrable defense perimeter with his pawns. White draws with 1.Ba4+! Kxa4 (1...Kc4 2.Bb3+! Kb5 3.Ba4+ repeats the position) 2.b3+ Kb5 3.c4+ Kc6 4.d5+ Kd7 5.e6+! Kxd8 6.f5! (diagram at right). Now Black is up two rooks and a bishop (normally an overwhelming material advantage) but has no hope of breaking through White's defense perimeter. The only winning attempts Black can make are to place his rooks on b5, c6, etc. and hope that White captures them. White draws by ignoring all such offers and simply shuffling his king about .
The above example may seem fanciful, but Black achieved a similar defense perimeter in
Arshak Petrosian
Arshak Petrosian
Arshak B. Petrosian is an Armenian chess player and National Coach. FIDE awarded him the International Grandmaster title in 1984. He became a prominent Soviet tournament player during the 1980s, winning games against such noted grandmasters as Alexey Shirov, Rafael Vaganian, and Alexander...
-Hazai, Schilde
Schilde
Schilde is a municipality located in the Belgian province of Antwerp. The municipality comprises the towns of Schilde proper and 's Gravenwezel. On January 1, 2006 Schilde had a total population of 19,575. The total area is 35.99 km² which gives a population density of 544 inhabitants per km². It...
1970 (diagram at left). In the position at left, Black has a difficult endgame, since White can attack and win his a-pawn by force, and he has no counterplay. Black tried the extraordinary 45...Qb6!?, to which White replied with the obvious 46.Nxb6+? This is actually a critical mistake, enabling Black to establish an impenetrable fortress. White should have carried out his plan of winning Black's a-pawn, for example with 46.Qc1 (threatening 47.Nxb6+ cxb6 48.h4! gxh4 49.Qh1 and Qh3, winning) Qa7 47.Qd2 followed by Kb3, Nc3, Ka4, and Na2-c1-b3. 46...cxb6 Now Black threatens 47...h4, locking down the entire board with his pawns, so White tries to break the position open. 47.h4 gxh4 48.Qd2 h3! 49.gxh3 Otherwise 49...h2 draws. 49...h4! (diagram at right) Black has established his fortress, and now can draw by simply moving his king around. The only way White could attempt to breach the fortress would be a queen sacrifice at some point (for example Qxa5 or Qxe5), but none of these give White winning chances as long as Black keeps his king near the center. The players shuffled their kings, and White's queen, around for six more moves before agreeing to a draw
Draw by agreement
In chess, a draw by agreement is the outcome of a game due to the agreement of both players to a draw. A player may offer a draw to his opponent at any stage of a game; if the opponent accepts, the game is a draw. The relevant portion of the FIDE laws of chess is article 9.1...
.
In Smirin
Ilya Smirin
Ilya Yulievich Smirin is a Soviet-Israeli chess Grandmaster., his Elo rating was 2650, making him the 59th-highest rated player in the world...
-HIARCS
HIARCS
HIARCS is a commercial computer chess program developed by Mark Uniacke. Its name is an acronym stands for higher intelligence auto response chess system.-Overview:...
, Smirin-Computers match 2002, the super-grandmaster looked to be in trouble against the computer, which has the bishop pair, can tie White's king down with ...g3, and threatens to invade with its king on the light squares. Smirin, however, saw that he could set up a fortress with his pawns. The game continued 46...g3 47.h3! A surprising move, giving Black a formidable protected passed pawn on the sixth rank, but it begins to build White's fortress, keeping Black's king out of g4. 47...Bc5 48.Bb4! Now Smirin gives HIARCS the choice between an opposite-colored bishops endgame (in which, moreover, White will play Be7 and win the h-pawn if Black's king comes to the center) and a bishop versus knight ending in which Smirin envisions a fortress. 48...Bxb4 49.axb4 Kf7 Black could try to prevent White's coming maneuver with 49...Bd3, but then White could play 50.Nf3 Kh5 (forced) 51.Nd4. 50.Nb5! Ke6 51.Nc3! Completing the fortress. Now Black's king has no way in, and his bishop can do nothing, since White's King can prevent ...Bf1, attacking White's only pawn on a light square. The game concluded: 51...Bc2 52.Kg2 Kd6 53.Kg1 Kc6 54.Kg2 b5 55.Kg1 Bd3 56.Kg2 Be4+ 57.Kg1 Bc2 58.Kg2 Bd3 59.Kg1 Be4 60.Kf1 ½–½
Other examples
Here are some other drawing fortresses .Fortresses against a bishop
Fortresses against a knight
Fortresses against a rook
A semi-fortress
The endgame of two bishops versus a knight was thought to be a draw for more than one hundred years. It was known that the temporary defensive fortress in this position could be broken down after a number of moves, but it was assumed that the fortress could be reformed in another corner. Computer endgame tablebaseEndgame tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.The tablebase...
s show that the bishops generally win, but it takes up to 66 moves. It takes several moves to force Black out of the temporary fortress in the corner; then precise play with the bishops prevents Black from forming the fortress in another corner. The position in the diagram was thought to be a draw by Kling
Josef Kling
Josef Kling was a German chess master and chess composer. In 1851 he wrote Chess Studies with Bernhard Horwitz.-External links:* at Chessgames.com...
and Horwitz
Bernhard Horwitz
Bernhard Horwitz was a German English chess master and chess writer.Horwitz was born in Neustrelitz, and went to school in Berlin, where he studied art. From 1837 to 1843, he was part of a group of German chess players known as "The Pleiades".He moved to London in 1845...
but computer analysis shows that White wins in 45 moves (either by checkmate or by winning the knight). All of the long wins in this endgame go through this type of semi-fortress position .
This game between József Pintér
József Pintér
József Pintér is a Hungarian chess Grandmaster and chess writer. He won the Hungarian Chess Championship in 1978 and 1979. Pinter gained his grandmaster title in 1982...
and David Bronstein
David Bronstein
David Ionovich Bronstein was a Soviet chess grandmaster, who narrowly missed becoming World Chess Champion in 1951. Bronstein was described by his peers as a creative genius and master of tactics...
demonstrates the human play of the endgame. The defender has two ideas: (1) keep the king off the edge of the board and (2) keep the knight close to the king. White reaches the semi-fortress after 71. Nb2!, which falls after 75... Kb5!. White gets to a semi-fortress again in another corner after 90. Ng2+. After 100. Ke3 White cannot hold that semi-fortress any longer, but forms one in another corner after 112. Nb7!. On move 117 White claimed a draw
Draw (chess)
In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...
by the fifty move rule
Fifty move rule
The fifty-move rule in chess states that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves . The intended reason for the rule is so that a player with no chance to win cannot be obstinate and play on indefinitely , or seek a win...
.
Positional draw
A "positional draw" is a concept most commonly used in endgame studiesEndgame study
An endgame study, or just study, is a composed chess position—that is, one that has been made up rather than one from an actual game—presented as a sort of puzzle, in which the aim of the solver is to find a way for one side to win or draw, as stipulated, against any moves the other side...
and describes an impasse other than stalemate
Stalemate
Stalemate is a situation in chess where the player whose turn it is to move is not in check but has no legal moves. A stalemate ends the game in a draw. Stalemate is covered in the rules of chess....
. It usually involves the repetition of moves in which neither side can make progress or safely deviate. Typically a material advantage is balanced by a positional advantage. Fortresses and perpetual check
Perpetual check
In the game of chess, perpetual check is a situation in which one player can force a draw by an unending series of checks. Such a situation typically arises when the player who is checking cannot deliver checkmate; while failing to continue the series of checks gives the opponent at least a chance...
are examples of positional draws . Sometimes they salvage a draw from a position that seems hopeless because of a material deficit . Grandmaster John Nunn
John Nunn
John Denis Martin Nunn is one of England's strongest chess players and once belonged to the world's top ten. He is also a three times world champion in chess problem solving, a chess writer and publisher, and a mathematician....
describes a positional draw as a position in which one side has enough material to normally win and he is not under direct attack, but some special feature of the position (often a blockade) prevents him from winning .
A simple example is shown in the game between Lajos Portisch
Lajos Portisch
Lajos Portisch is a Hungarian chess Grandmaster, whose positional style earned him the nickname, the "Hungarian Botvinnik"...
and Lubomir Kavalek. White could have won easily with 1. Be1 Kc6 2. b4. However, play continued 1. b4? Nb8 2. b5 Nc6+! The only way to avoid the threatened 3...Nxa5 is 3. bxc6 Kxc6, but the resultant position is a draw because the bishop is on the wrong color to be able to force the rook pawn's promotion
Promotion (chess)
Promotion is a chess rule describing the transformation of a pawn that reaches its eighth rank into the player's choice of a queen, knight, rook, or bishop of the same color . The new piece replaces the pawn on the same square and is part of the move. Promotion is not limited to pieces that have...
(see above, wrong bishop
Wrong bishop
The wrong bishop is a situation in chess endgame when a bishop on the other color of square of the chessboard would either win a game instead of draw or salvage a draw from an inferior position...
, and wrong rook pawn
Wrong rook pawn
In chess endgames with a bishop, a pawn that is a rook pawn may be the wrong rook pawn. With a single bishop, the result of a position may depend on whether or not the bishop controls the square on the chessboard on which the pawn would promote. Since a side's rook pawns promote on...
) .
Luděk Pachman
Ludek Pachman
Luděk Pachman was a Czechoslovak-German chess grandmaster, chess writer, and political activist. In 1972, after being imprisoned and tortured almost to death by the Communist regime in Czechoslovakia, he was allowed to emigrate to West Germany...
cites the endgame position at right as a simple example of a positional draw. White on move simply plays waiting moves with the bishop (Bb1-c2-d3). As for Black, "If he is unwilling to allow the transition to the drawn ending of Rook versus Bishop, nothing else remains for him but to move his Rook at [e5] continuously up and down the [e-file]." Pachman explains, "The indecisive result here contradicts the principles concerning the value of the pieces and is caused by the bad position of the black pieces (pinned rook at [e4])." .
This position from a game between Mikhail Botvinnik
Mikhail Botvinnik
Mikhail Moiseyevich Botvinnik, Ph.D. was a Soviet and Russian International Grandmaster and three-time World Chess Champion. Working as an electrical engineer and computer scientist at the same time, he was one of the very few famous chess players who achieved distinction in another career while...
and Paul Keres
Paul Keres
Paul Keres , was an Estonian chess grandmaster, and a renowned chess writer. He was among the world's top players from the mid-1930s to the mid-1960s....
in the 1951 USSR Championship
USSR Chess Championship
This is a list of all the winners of the USSR Chess Championship. It was the strongest national chess championship ever held, with eight world chess champions and four world championship finalists among its winners...
is drawn because the black king cannot get free and the rook must stay on the c-file. The players agreed to a draw
Draw by agreement
In chess, a draw by agreement is the outcome of a game due to the agreement of both players to a draw. A player may offer a draw to his opponent at any stage of a game; if the opponent accepts, the game is a draw. The relevant portion of the FIDE laws of chess is article 9.1...
four moves later .
The first diagram shows a position from a game between former World Champion
World Chess Championship
The World Chess Championship is played to determine the World Champion in the board game chess. Men and women of any age are eligible to contest this title....
Mikhail Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....
and future World Champion Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...
from the 1962 Candidates Tournament
Candidates Tournament
The Candidates Tournament is a chess tournament organized by the world chess federation FIDE since 1950, as the final contest to determine the challenger for the World Chess Championship...
in Curaçao. After 41 moves Tal had the advantage but Fischer sacrificed
Sacrifice (chess)
In chess, a sacrifice is a move giving up a piece in the hopes of gaining tactical or positional compensation in other forms. A sacrifice could also be a deliberate exchange of a chess piece of higher value for an opponent's piece of lower value....
the exchange
The exchange (chess)
The exchange in chess refers to a situation in which one player loses a minor piece but captures the opponent's rook. The side which wins the rook is said to have won the exchange, while the other player has lost the exchange, since the rook is usually more valuable...
(a rook for a knight). The game was drawn on the 58th move .
In this position from a game between Pal Benko
Pál Benko
Pal Benko is a chess grandmaster, author, and composer of endgame studies and chess problems.- Early life :Benko was born in France but was raised in Hungary. He was Hungarian champion by age 20. He emigrated to the United States in 1958, after defecting following the World Student Team...
and International Master Jay Bonin, White realized that the blockade cannot be broken and the game is a draw despite the extra material .
See also
- Chess endgame
- Glossary of chess
- Opposite-colored bishops endgame
- Swindle (chess)Swindle (chess)In chess, a swindle is a ruse by which a player in a losing position tricks his opponent, and thereby achieves a win or draw instead of the expected loss. It may also refer more generally to obtaining a win or draw from a clearly losing position. I. A. Horowitz and Fred Reinfeld distinguish among...
- Wrong rook pawnWrong rook pawnIn chess endgames with a bishop, a pawn that is a rook pawn may be the wrong rook pawn. With a single bishop, the result of a position may depend on whether or not the bishop controls the square on the chessboard on which the pawn would promote. Since a side's rook pawns promote on...