Fortress (chess)

In chess, the fortress is an endgame drawing technique in which the side behind in sets up a zone of protection that the opponent cannot penetrate. This might involve keeping the enemy king out of one's position, or a zone the enemy cannot force one out of (e.g. see the opposite-colored bishops example). An elementary fortress is a theoretically drawn (i.e. a ) 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 fail to recognize fortress-type positions and are unable to achieve the win against them despite claiming a winning advantage .
Fortress in a corner.
Perhaps the most common type of fortress, often seen in endgames with only a few pieces 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) in the diagram is a draw even if the pawn is on the seventh rank or further back on the a-. 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 in the diagram, however, is a draw only 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 .
Example game: Serper vs. Nakamura, 2004.
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
Heading for h1. After another 10 moves the position in the following diagram was reached: 
Black has no way of forcing White's king away from the corner, so he played
and after 13.h4 gxh4 the game was drawn by stalemate.
Back-rank defense.
The back-rank defense in some rook and pawn versus rook endgames is another type of fortress in a corner (see diagram). 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 .
Rook vs. bishop.
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 .
Pawn and bishop.
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, so it is not a case of the wrong bishop .
Rook and pawn versus queen.
In the diagram, 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 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 .
Example from game.
In this position, with Black to move, Black can reach a drawing fortress. 
and now 3...Ka3 and several other moves reach the fortress. In the actual game, Black made the weak move 3...Rd3? and lost .
Similar example.
In this 1959 game between Whitaker 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), taking advantage of the fact that the rook is currently unprotected – again illustrating how tablebases are refining traditional endgame theory.
Example with more pawns.
From the diagram, in Salov 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:
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. 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–c8 diagonal .
Example from game.
In an endgame with opposite-colored bishops, positional factors may be more important than material. In this position, Black sacrifices 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 .
Queen versus two minor pieces.
Here are drawing fortresses with two versus a queen . 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 zugzwang. For example: 
Two bishops.
In the two bishop versus queen ending, the queen wins if the Lolli position is not reached, but some of them take up to seventy-one moves to either checkmate or win a bishop, so the fifty-move rule comes into play. From the diagram:
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),
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. In
Ree-Hort, Wijk aan Zee 1986 (first diagram), 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 (second diagram), 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 York City 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:
If 99...Ke2, 100.Nc5 Kd2 101.Kb2! (101.Nxb3+?? Kc2 and Black wins) and 102.Nxb3 draws. 
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 had 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:
2.f7 is an interesting attempt, but then Black plays 2...Kg7! and then 3...Bxf7, with a draw. 2...Kg7 prevents 3.Kf6, which would win.
The only move to draw, since the bishop must be able to check the king if it goes to g6.
If 7.f7 Bxf7!: the pawn can be safely when the white king is on h6.
Draw, because White cannot make progress .
Defense perimeter (pawn fortress).
A "defense perimeter" is a drawing technique in which the side behind in 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 in the first diagram, 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. c4+ Kc6 4. Ba4+!, forcing Rb5, wins for White) 2. b3+ Kb5 3. c4+ Kc6 4. d5+ Kd7 5. e6+! Kxd8 6. f5! (second diagram). 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 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 (first diagram). 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! (second diagram) 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 , 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 .
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 tablebases 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 .
Positional draw.
A "positional draw" is a concept most commonly used in endgame studies 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 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 promotion (see above, wrong bishop, and wrong rook pawn) .
Luděk Pachman cites the endgame position in the diagram 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-. 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 .
Can White stop the h-pawn from queening? The position looks lost for White but he does have a defence which seems to defy the rules of logic. White will calmly construct a "fortress" which will hide his pieces from attack. The only weakness in White's "fortress" is the g-pawn. This pawn has to be defended by the bishop and the only square where this can be done safely is from h6.
1. Bf6!
White threatens to stop the advance of the h-pawn with ...Be5+;
building the fortress immediately does not work: 1.f6? h2 2.Kf8 h1=Q 3.Kg7 (3.Kg8 Qg2 4.Bf8 Qa8 5.Kg7 Kd7 6.Kg8 Ke6 7.Kg7 Kf5 8.Kg8 Bb3 9.Kg7 Qh1−+) 3...Kd7 4.Bb4 Ke6 5.Bd2 Kf5 6.Be3 Qf3 7.Bd2 Qe2 8.Bc1 Qd1 9.Be3 Qd3 10.Bc1 Qc3−+;
1... Kd6 2. Be7+ 
2.fxg6? This move destroys the fortress 2...fxg6 3.Be7+ Kc6−+. Chess computer programs have difficulty assessing "fortress" positions because the normal values for the pieces do not apply.
2... Ke5 3. Bd8!
White can draw in another way without the need of a "fortress": 3.fxg6 fxg6 4.Bd8 Kd6 5.Nf6! h2 6.Ne4+ Ke6 7.Nf2 Bd5 8.Bf6 h1=Q 9.Nxh1 Bxh1=;
3... Kd6
The threat was ...Bc7+
4. Be7+ Kc6
White has achieved the closing of the long diagonal a8–h1. The only way to avoid this would be for Black to repeat moves. Now White can build his "fortress" without the worry of the queen getting to the back rank via the long diagonal.
5. f6! h2 6. Bf8! h1=Q 7. Bh6!
with the idea of 8.Kf8 and 9.Kg7. White will be safe behind the barrier of pawns. It is a positional draw.