Zugzwang
Encyclopedia
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. The fact that the player must make a move means that his position will be significantly weaker than the hypothetical one in which it was his opponent's turn to move.
In game theory, it specifically means that it directly changes the outcome of the game from a win to a loss. The term is used less precisely in games such as chess; i.e., the game theory definition is not necessarily used in chess , . For instance, it may be defined loosely as "a player to move cannot do anything without making an important concession" . Putting the opponent in zugzwang is a common way to help the superior side win a game. In some cases it is necessary to make the win possible .
The term zugzwang is frequently used in chess. A player whose turn it is to move who has no move that does not worsen his position is said to be in zugzwang . Thus every move would make his position worse, and he would be better off if he could pass and not move. Sometimes different chess authors use the term zugzwang in different ways .In some writings it is used very loosely. For example, in Understanding Chess Endgames, on page 200 John Nunn
is discussing the "second-rank defense" in the rook and bishop versus rook endgame. White wants to maintain the king and rook on the second rank. At one point Nunn says that zugzwang temporarily forces the king off the first rank. But it is only temporary and does not break White's defense. In some literature a reciprocal zugzwang (see below) is called zugzwang and a one-sided zugzwang is called a squeeze .
The term zugzwang was used in German-language
chess literature in 1858 (or earlier) . The first known use of the term in English
was by World Champion
Emanuel Lasker
in 1905 . The concept of zugzwang (as distinguished from the word) must have been known to players many centuries earlier, since it is necessary to win the elementary king and rook versus king endgame, among others. The concept is also seen in an endgame study
published in 1604 by Alessandro Salvio
, one of the first writers on the game. It also appeared in Shatranj
studies dating back to the early 9th century, over 1000 years before the first known use of the term zugzwang.
In a chess endgame, being in zugzwang usually means going from a drawn
position to a loss or a won position to a draw, but it can be from a win to a loss, or a substantial loss of material which probably affects the outcome of the game. A chess position of reciprocal zugzwang or mutual zugzwang is equivalent to the more precise definition of zugzwang in game theory. Opposition
is a special kind of zugzwang . Trébuchet is a special type of zugzwang that is discussed below.
Positions with zugzwang occur fairly often in chess endgames. For instance, twelve of the 105 endgames in the book Endgame Virtuoso Anatoly Karpov involve zugzwang . National Master Alex Angos wrote an entire book about zugzwang, You Move ... I Win! . According to John Nunn
, positions of reciprocal zugzwang (see below) are surprisingly important in the analysis of endgames , .
The remainder of this article is about zugzwang in chess.
The great majority of positions are of the first type. In chess literature, most writers call positions of the second type zugzwang, and the third type reciprocal zugzwang or mutual zugzwang. Some writers call the second type a squeeze and the third type zugzwang .
Normally in chess, having tempo
is desirable because the player who is to move has the advantage of being able to choose a move that improves his situation. Zugzwang typically occurs when all the moves available are "bad" moves, tangibly weakening the moving player's position (usually from a draw to a loss or from a win to a draw) .
Zugzwang most often occurs in the endgame when the number of pieces, and so the number of possible moves, is reduced, and the exact move chosen is often critical. The diagram at top right shows the simplest possible example of zugzwang. If it is White's move, he must either stalemate
Black with 1.Kc6 or abandon the pawn
, allowing 1...Kxc7 with a draw. If it is Black's move, the only legal move is 1...Kb7, which allows White to win with 2.Kd7 followed by queening
the pawn on the next move.
The diagram at below right is another simple example. Black, on move, must allow White to play Kc5 or Ke5, when White wins one or more pawns
and can advance his own pawn toward promotion
). White, on move, must retreat his king
, when Black is out of danger . The squares d4 and d6 are corresponding squares
. Whenever the white king is on d4 with White to move, the black king must be on d6 to prevent the advance of the white king.
In many cases, the player having the move can put the other player in zugzwang by using triangulation
; that article has an illustrative example. Zugzwang is very common in king and pawn endgames, where it is frequently achieved through triangulation. Pieces other than the king can also triangulate to achieve zugzwang – e.g., see the queen
versus rook
position at Philidor position
. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies
.
Andy Soltis notes that many players do not appreciate zugzwang, thinking that it is an obscure concept that never occurs in their games. Without zugzwang, it would be very hard to win a chess game, even with an extra piece .
Edward Winter
, in German
, the term "zugzwang":
The earliest known use of the term "zugzwang" in English
was on page 166 of the February 1905 issue of Lasker's
Chess Magazine . The term did not become common in English-language chess sources until the 1930s, after the publication of the English translation of Nimzowitsch's My System
in 1929 .
The concept of zugzwang, if not the term, must have been known to players for many centuries. Zugzwang is required to win the elementary (and common) king and rook versus king endgame , and the king and rook (or differently-named pieces with the same powers) have been chess pieces since the earliest versions of the game .
The earliest use of zugzwang (other than in basic checkmate
s) may be in this study by Zairab Katai, which was published sometime between 813 and 833. (This study was actually from the predecessor of chess Shatranj
but the moves of the king, rook, and knight
are the same. Masters of this era composed many studies in which Black was in zugzwang so that any move fatally weakened his position.) After
puts Black in zugzwang, since 3... Kc4 4. Kg3! Kd4 5. Re1 and White wins .
The concept of zugzwang is also seen in the 1585 endgame study
by Giulio Cesare Polerio at right, published in 1604 by Alessandro Salvio
, one of the earliest writers on the game. gives the position as by Polerio in 1585. The only way for White to win is 1.Ra1!! Kxa1 2.Kc2!, placing Black in zugzwang. His only legal move is 2...g5, whereupon White promotes
a pawn first and then checkmate
s with 3.hxg5 h4 4.g6 h3 5.g7 h2 6.g8(Q) h1(Q) 7.Qg7# .
Joseph Bertin
in The Noble Game of Chess (1735), which Hooper and Whyld consider "the first worthwhile chess textbook in the English language", referred to the concept of zugzwang, albeit without using that word, when he set forth as the 18th of his 19 rules about chess play, "To play well the latter end of a game, you must calculate who has the move, on which the game always depends." .
François-André Danican Philidor
wrote in 1777 of the position at below right that after White plays 36.Kc3, Black "is obliged to move his rook from his king, which gives you an opportunity of taking his rook by a double check, or making him mate
" .Philidor analyzed 36.Kc3 Rh2 37.Qb5+ Ka1 38.Qa6+ Kb1 39.Qb6+ Ka2 40.Qa7+ Kb1 41.Qg1+, winning Black's rook by a fork
(or "double check" in Philidor's now-obsolete terminology). Lasker explicitly cited a mirror image of this position (White: king on f3, queen on h4; Black: king on g1, rook on g2) as an example of zugzwang in Lasker's Manual of Chess . The British master George Walker
analyzed a similar position in the same endgame, giving a maneuver that resulted in the superior side reaching the initial position, but now with the inferior side on move and in zugzwang. Walker wrote of the superior side's decisive move: "throwing the move upon Black, in the initial position, and thereby winning" .
The great American
player Paul Morphy
(1837–1884), like Salvio and Philidor an unofficial World Champion
, is credited with composing the position at right "while still a young boy". After 1.Ra6!, Black is in zugzwang and must allow mate on the next move with 1...bxa6 2.b7# or 1...B (moves) 2.Rxa7# .
between Bobby Fischer
and Mark Taimanov
. In the position in the diagram, Black is in zugzwang because he would rather not move, but he must: a king move would lose the knight, while a knight move would allow the passed pawn
to advance . The game continued:
and Black is again in zugzwang. The game ended shortly (because the pawn will slip through and promote
) :
to f7 or e8 to attack the pawn on g6. Play continued:
Now the bishop is able to make a tempo
move. It is able to move while still attacking the pawn on g6, and preventing the black king from moving to c6.
and Black is in zugzwang. Knights are unable to make a tempo move , so moving the knight would allow the bishop to capture the kingside pawns. The black king must give way.
and White has a won position. Either one of White's queenside pawns will promote or the white king will attack and win the black kingside pawns and a kingside pawn will promote. Black resigned seven moves later , , . Andy Soltis says that this is "perhaps Fischer's most famous endgame" .
and Glenn Flear
at Wijk aan Zee shows an instance of "zugzwang" where the obligation to move makes the defense more difficult but it does not mean the loss of the game. A draw by agreement
was reached eleven moves later .
value of zero in game theory
.
The diagram on the right shows a position of reciprocal zugzwang. If Black is to move, he must move 1... Kd7 and lose because White will move 2. Kb7, promote the pawn, and win. If White is to move, he must either move 1. Kc6 which is a draw because it stalemate
s Black or he must abandon the pawn, which is also a draw after Black captures the pawn. Both sides would be in zugzwang if it were their move, so it is a reciprocal zugzwang , .
In a position with reciprocal zugzwang, only the player to move is actually in zugzwang. However, the player who is not in zugzwang must play carefully because one inaccurate move can cause him to be put in zugzwang . That is in contrast to regular zugzwang, because the superior side usually has a waiting move to put the opponent in zugzwang .
Black has the opposition
and draws because 5. c7+ Kc8 6. Kc6 is stalemate.
If Black is to move, White wins
and White wins with
or
. White to move in this position draws, but Black to move loses. Karpov's 49th move in the actual game avoided the zugzwang and the game was drawn . This is one of 209 mutual zugzwang positions in the rook and pawn versus rook endgame .
The second position is an analysis position from the ninth game of the 1984 World Chess Championship
between Anatoly Karpov and Garry Kasparov
. The alternate move 45... Ke6 is considered and this position could result after move 57. White to move draws; Black to move loses. It would have been White's move in this analysis position. Kasparov played a different 45th move and Karpov won after seventy moves , .
, thus allowing their opponent to capture it and proceed to promote
the remaining pawn .
2... Kd4?? loses because after 3. Kf5 Black is on the wrong side of the trébuchet.
and Black wins the pawn and the game (see King and pawn versus king endgame) .
Another simple example is seen in the diagram at right. Black, on move, must play 1...b3, allowing 2.axb3#. White, on move, must move his king away, allowing 1...b3, with an easy win for Black.
and Henrique Mecking
, whoever is to move loses. (It would have been White's move had the analysis position occurred in the game.)
, whoever moves loses. In the game it was Black's move, who resigned .
are squares of mutual zugzwang. When there is only one pair of corresponding squares they are called mined squares . A player will fall into zugzwang if he moves his king onto the square and his opponent is able to move onto the corresponding square. In the diagram on the right, if either king moves onto the square marked with the dot of the same color, he falls into zugzwang if the other king moves into the mined square near him .
In addition, zugzwang is required in many king and pawn versus king endgames in order to force promotion
of the pawn and in other king and pawn endgames with more pawns . (See pawnless chess endgame and fortress (chess)
for some discussion of some of these endings.)
and Peter Acs
, it saves the game for the defense:
This position is a draw and the players agreed to a draw
a few moves later .
In this position from Benko, White should win but he makes an error and gets into zugzwang which enables Black to draw.
and Black draws because White is in Zugzwang .
by Amelung. White to move wins by taking the opposition after 1. Kb7! and putting Black in zugzwang, e.g. 1... Kc4 2. Kb6 b3 3. Ka5 Kc3 4. Ka4 b2 5. Ka3 and White wins the pawn. In 1956 Ilyia Maizelis pointed out that Black to move can take the opposition and put White in zugzwang:
and White cannot make progress .
versus Aron Nimzowitsch
, Copenhagen
1923, is often called the "Immortal Zugzwang Game".According to Nimzowitsch, writing in the Wiener Schachzeitung in 1925, this term originated in "Danish chess circles" . Some consider the final position to be an extremely rare instance of zugzwang occurring in the middlegame . It ended with White resigning in the position in the diagram.
White has a few pawn moves which do not lose material, but eventually he will have to move one of his pieces. If he plays 1.Rc1 or Rd1, then 1...Re2 traps White's queen; 1.Kh2 fails to 1...R5f3, also trapping the queen, since White cannot play 2.Bxf3 because the bishop is pinned
to the king; 1.g4 runs into 1...R5f3 2.Bxf3? Rh2 mate. Angos analyzes 1.a3 a5 2.axb4 axb4 3.h4 Kh8 (waiting) 4.b3 Kg8 and White has run out of waiting moves and must lose material. Best in this line is 5.Nc3!? bxc3 6.bxc3, which just leaves Black with a serious positional advantage and an extra pawn . Other moves lose material in more obvious ways.
However, since Black would win even without the zugzwang , it is debatable whether the position is true zugzwang. Even if White could pass his move he would still lose, albeit more slowly, after 1...R5f3 2.Bxf3 Rxf3, trapping the queen and thus winning queen and bishop for two rooks . Wolfgang Heidenfeld
thus considers it a misnomer to call this a true zugzwang position . See also Immortal Zugzwang Game: Objections to the sobriquet.
versus Emanuel Lasker
in the 1896-97 World Chess Championship
, is an early example of zugzwang in the middlegame. After Lasker's 34...Re8-g8!, Steinitz resigned because he has no playable moves. . However, according to ChessGames.com
and some print sources, Steinitz played on another five moves before resigning: 35.Re1 Qxf5 36.Re5 Qf3 37.d5 Qg3+ 38.Kh1 Qxe5 39.dxc6+ Kxc6 0-1 . White's bishop cannot move because that would allow the crushing ...Rg2+. The queen cannot move without abandoning either its defense of the bishop on g5 or of the g2 square, where it is preventing ...Qg2#. White's move 35.f6 loses the bishop: 35...Rxg5 36. f7 Rg2+, forcing mate
. The move 35.Kg1 allows 35...Qh1+ 36.Kf2 Qg2+ followed by capturing the bishop. The rook cannot leave the first rank, as that would allow 35...Qh1#. Rook moves along the first rank other than 35.Rg1 allow 35...Qxf5, when 36.Bxh4 is impossible because of 36...Rg2+; for example, 35.Rd1 Qxf5 36.d5 Bd7, winning. That leaves only 35.Rg1, when Black wins with 35...Rxg5! 36.Qxg5 (36.Rxg5? Qh1#) Qd6+ 37.Rg3 hxg3+ 38.Qxg3 Be8 39.h4 Qxg3+ 40.Kxg3 b5! 41.axb5 a4! and Black queens
first . Colin Crouch calls the final position, "An even more perfect middlegame zugzwang than ... Sämisch-Nimzowitsch ... in the final position Black has no direct threats, and no clear plan to improve the already excellent positioning of his pieces, and yet any move by White loses instantly" .
, USSR 1974 1.d4 c5 2.d5 e5 3.e4 d6 4.Nc3 Be7 5.Nf3 Bg4 6.h3 Bxf3 7.Qxf3 Bg5! 8.Bb5+ Kf8! Black exchanges off his bad bishop, but does not allow White to do the same. 9.Bxg5 Qxg5 10.h4 Qe7 11.Be2 h5 12.a4 g6 13.g3 Kg7 14.0-0 Nh6 15.Nd1 Nd7 16.Ne3 Rhf8 17.a5 f5 18.exf5 e4! 19.Qg2 Nxf5 20.Nxf5+ Rxf5 21.a6 b6 22.g4? hxg4 23.Bxg4 Rf4 24.Rae1 Ne5! 25.Rxe4 Rxe4 26.Qxe4 Qxh4 27.Bf3 Rf8!! 28. Bh1 28.Qxh4? Nxf3+ and 29...Nxh4 leaves Black a piece ahead. Ng4 29.Qg2 (see diagram at left) Rf3!! 30.c4 Kh6!! (diagram at right) Now all of White's piece moves allow checkmate or ...Rxf2 with a crushing attack (e.g. 31.Qxf3 Qh2#; 31.Rb1 Rxf2 32.Qxg4 Qh2#). That leaves only moves of White's b-pawn, which Black can ignore, e.g. 31.b3 Kg7 32.b4 Kh6 33.bxc5 bxc5 and White has run out of moves.Notes based on those in Soltis 1978, pp. 55-56. 0-1
1971 is a grisly example of zugzwang in the middlegame. White's queen, rook, knight, and king have a total of one legal move (Qh3), which loses the queen, rook and king on successive moves (... gxh3 followed by ... Qxg2#). The game concluded: 37.b5 Kh8 37...Nf5 and Nd4-e2 was crushing, but letting White self-destruct is even quicker. 38.a4 Kh7 39.a5 Kg8 0-1 After 40.axb6 axb6, white is forced to play 41.Qh3, and then it is mate in two: gxh3 42.Kh2 Qxg2#.
explains that the pawns on d4 and e4 are blocked and pinned, the knight is bound to the defense of e4, the rook is bound to the defense of d4, and the pawn on b4 is bound to the defense of the knight. Krabbé analyzes as best for Black 74...b3! 75.Rxd4 Rxd4 76.Rxc3 Rd8 77.Rxb3 Re8 78.Re3 Re5 79.Rc3 (79.Kxf6? Rxa5 82.Kg6 Ra1 83.f6 Rg1+ wins) Re8 80.Re3 Re5 81.Rc3 and the game will end in a draw by repetition of moves. Instead, Black played 74...Nb5? 75.Rxe4 Nd6 76.Re6 Rc6 77.Rxd4 Rxh6+ 78.Kxh6 Nxf5+ 79.Kg6 1-0.
a bishop on h3. After 1. Kh4! Black is placed in zugzwang after moving his b- and h-pawns. The game continued:
Now Black is in zugzwang and resigned , .
Bobby Fischer
and Héctor Rossetto
, 33. Bb3! puts Black in zugzwang . If Black moves the king, White plays Rb8, winning a piece (...Rxc7 Rxf8); if Black moves the rook, 33...Ra8 or R...e8, then 34.c8=Q+ and the black rook will be lost after 35.Qxa8, 35.Qxe8 or 35.Rxe7+ (depending on Black's move); if Black moves the knight, Be6 will win Black's rook. That leaves only pawn moves, and they quickly run out . The game concluded:
and Meiden, Black is in a full board zugzwang. Any move by a black piece loses at least a pawn .
coined the term Zugzwang Lite
to describe a situation, sometimes arising in symmetrical opening
variations, where White's "extra move" is a burden . He cites as an example of this phenomenon Hodgson
versus Arkell
, Newcastle
2001. The position at left arose after 1.c4 c5 2.g3 g6 3.Bg2 Bg7 4.Nc3 Nc6 5.a3 a6 6.Rb1 Rb8 7.b4 cxb4 8.axb4 b5 9.cxb5 axb5 Here Rowson remarks, "Both sides want to push their d-pawn and play Bf4/...Bf5, but White has to go first so Black gets to play ...d5 before White can play d4. This doesn't matter much, but it already points to the challenge that White faces here; his most natural continuations allow Black to play the moves he wants to. I would therefore say that White is in 'Zugzwang Lite' and that he remains in this state for several moves." The game continued 10.Nf3 d5 11.d4 Nf6 12.Bf4 Rb6 13.0-0 Bf5 14.Rb3 O-O 15.Ne5 Ne4 16.h3 h5!? 17.Kh2 The position is still almost symmetrical, and White can find nothing useful to do with his extra move. Rowson whimsically suggests 17.h4!?, forcing Black to be the one to break the symmetry. 17...Re8! Rowson notes that this is a useful waiting move, covering e7, which needs protection in some lines, and possibly supporting an eventual ...e5 (as Black in fact played on his 22nd move). White cannot copy it, since after 18.Re1? Nxf2 Black would win a pawn
. After 18.Be3?! Nxe5! 19.dxe5 Rc6! Black seized the initiative and went on to win in 14 more moves.
Another instance of Zugzwang Lite occurred in Lajos Portisch
versus Mikhail Tal
, Candidates Match 1965, again from the Symmetrical Variation of the English Opening
, after 1.Nf3 c5 2.c4 Nc6 3.Nc3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.d3 a6 8.a3 Rb8 9.Rb1 b5 10.cxb5 axb5 11.b4 cxb4 12.axb4 d6 13.Bd2 Bd7. Soltis wrote, "It's ridiculous to think Black's position is better. But Mikhail Tal said it is easier to play. By moving second he gets to see White's move and then decide whether to match it." 14.Qc1 Here, Soltis wrote that Black could maintain equality by keeping the symmetry: 14...Qc8 15.Bh6 Bh3. Instead, he plays to prove that White's queen is misplaced. 14...Rc8! 15.Bh6 Nd4! Threatening 15...Nxe2+. 16.Nxd4 Bxh6 17.Qxh6 Rxc3 18.Qd2 Qc7 19.Rfc1 Rc8 Although the pawn structure is still symmetrical, Black's control of the c-file gives him the advantage. Black ultimately reached an endgame two pawns up, but White managed to hold a draw in 83 moves. See First-move advantage in chess#Symmetrical openings for more details.
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...
which also applies to various other games. The term finds its formal definition in combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
, 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. The fact that the player must make a move means that his position will be significantly weaker than the hypothetical one in which it was his opponent's turn to move.
In game theory, it specifically means that it directly changes the outcome of the game from a win to a loss. The term is used less precisely in games such as chess; i.e., the game theory definition is not necessarily used in chess , . For instance, it may be defined loosely as "a player to move cannot do anything without making an important concession" . Putting the opponent in zugzwang is a common way to help the superior side win a game. In some cases it is necessary to make the win possible .
The term zugzwang is frequently used in chess. A player whose turn it is to move who has no move that does not worsen his position is said to be in zugzwang . Thus every move would make his position worse, and he would be better off if he could pass and not move. Sometimes different chess authors use the term zugzwang in different ways .In some writings it is used very loosely. For example, in Understanding Chess Endgames, on page 200 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....
is discussing the "second-rank defense" in the rook and bishop versus rook endgame. White wants to maintain the king and rook on the second rank. At one point Nunn says that zugzwang temporarily forces the king off the first rank. But it is only temporary and does not break White's defense. In some literature a reciprocal zugzwang (see below) is called zugzwang and a one-sided zugzwang is called a squeeze .
The term zugzwang was used in German-language
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
chess literature in 1858 (or earlier) . The first known use of the term in English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
was by 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...
in 1905 . The concept of zugzwang (as distinguished from the word) must have been known to players many centuries earlier, since it is necessary to win the elementary king and rook versus king endgame, among others. The concept is also seen in an endgame study
Endgame 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...
published in 1604 by Alessandro Salvio
Alessandro Salvio
Alessandro Salvio was an Italian chess player who is considered to be the unofficial world champion around the year 1600. He started an Italian chess academy in Naples, Italy, and wrote a book called Trattato dell'Inventione et Arte Liberale del Gioco Degli Scacchi, which was published in Naples...
, one of the first writers on the game. It also appeared in Shatranj
Shatranj
Shatranj is an old form of chess, which came to the Western world from India. Modern chess has gradually developed from this game.-Etymology and origins:...
studies dating back to the early 9th century, over 1000 years before the first known use of the term zugzwang.
In a chess endgame, being in zugzwang usually means going from a 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,...
position to a loss or a won position to a draw, but it can be from a win to a loss, or a substantial loss of material which probably affects the outcome of the game. A chess position of reciprocal zugzwang or mutual zugzwang is equivalent to the more precise definition of zugzwang in game theory. Opposition
Opposition (chess)
In chess, opposition is the situation occurring when two kings face each other on a rank or file, with only one square in between them. In such a situation, the player not having to move is said to "have the opposition" . It is a special type of zugzwang and most often occurs in endgames with...
is a special kind of zugzwang . Trébuchet is a special type of zugzwang that is discussed below.
Positions with zugzwang occur fairly often in chess endgames. For instance, twelve of the 105 endgames in the book Endgame Virtuoso Anatoly Karpov involve zugzwang . National Master Alex Angos wrote an entire book about zugzwang, You Move ... I Win! . According to 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....
, positions of reciprocal zugzwang (see below) are surprisingly important in the analysis of endgames , .
The remainder of this article is about zugzwang in chess.
Introduction
There are three types of chess positions:- both sides would benefit if it were their turn to move
- only one player would be at a disadvantage if it were his turn to move
- both players would be at a disadvantage if it were their turn to move.
The great majority of positions are of the first type. In chess literature, most writers call positions of the second type zugzwang, and the third type reciprocal zugzwang or mutual zugzwang. Some writers call the second type a squeeze and the third type zugzwang .
Normally in chess, having tempo
Tempo (chess)
In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer move, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo"...
is desirable because the player who is to move has the advantage of being able to choose a move that improves his situation. Zugzwang typically occurs when all the moves available are "bad" moves, tangibly weakening the moving player's position (usually from a draw to a loss or from a win to a draw) .
Zugzwang most often occurs in the endgame when the number of pieces, and so the number of possible moves, is reduced, and the exact move chosen is often critical. The diagram at top right shows the simplest possible example of zugzwang. If it is White's move, he must either 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....
Black with 1.Kc6 or abandon the pawn
Pawn (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...
, allowing 1...Kxc7 with a draw. If it is Black's move, the only legal move is 1...Kb7, which allows White to win with 2.Kd7 followed by queening
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...
the pawn on the next move.
The diagram at below right is another simple example. Black, on move, must allow White to play Kc5 or Ke5, when White wins one or more pawns
Pawn (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...
and can advance his own pawn toward 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...
). White, on move, must retreat his 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...
, when Black is out of danger . The squares d4 and d6 are corresponding squares
Corresponding squares
Corresponding squares in chess occur in some chess endgames, usually ones that are mostly blocked. If squares x and y are corresponding squares, it means that if one player moves to x then the other player must move to y in order to hold his position...
. Whenever the white king is on d4 with White to move, the black king must be on d6 to prevent the advance of the white king.
In many cases, the player having the move can put the other player in zugzwang by using triangulation
Triangulation (chess)
Triangulation is a tactic used in chess to put one's opponent in zugzwang. That is, it gets to the same position with the other player to move, when it is a disadvantage for that player to move, e.g. he has to give up a blockade and let the other player penetrate his position...
; that article has an illustrative example. Zugzwang is very common in king and pawn endgames, where it is frequently achieved through triangulation. Pieces other than the king can also triangulate to achieve zugzwang – e.g., see the 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...
versus 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...
position at Philidor position
Philidor position
The Philidor position usually refers to an important chess endgame which illustrates a drawing technique when the defender has a king and rook versus a king, rook, and a pawn. It is also known as the third rank defense, because of the importance of the rook on the third rank cutting off the...
. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies
Endgame 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...
.
Andy Soltis notes that many players do not appreciate zugzwang, thinking that it is an obscure concept that never occurs in their games. Without zugzwang, it would be very hard to win a chess game, even with an extra piece .
History
According to chess historianHistorian
A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. If the individual is...
Edward Winter
Edward Winter (chess historian)
Edward Winter is an English journalist, archivist, historian, collector and author about the game of chess. He writes a regular column on that subject, Chess Notes, and is also a regular columnist for ChessBase.-Chess Notes:...
, in German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, the term "zugzwang":
had been in regular use in the nineteenth century. Pages 353-358 of the September 1858 Deutsche Schachzeitung had an unsigned article 'Zugzwang, Zugwahl und Privilegien'. F. Amelung employed the terms Zugzwang, Tempozwang and Tempozugzwang on pages 257-259 of the September 1896 issue of the same magazine. When a perceived example of Zugzwang occurred in the third game of the 1896-97 world championship match between Steinitz and Lasker, after 34...Rg8, the Deutsche Schachzeitung (December 1896, page 368) reported that 'White has died of Zugzwang'.
The earliest known use of the term "zugzwang" in English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
was on page 166 of the February 1905 issue of Lasker's
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...
Chess Magazine . The term did not become common in English-language chess sources until the 1930s, after the publication of the English translation of Nimzowitsch's My System
My System
My System is a book on chess theory written by Aron Nimzowitsch. Originally over a series of five brochures from 1925 to 1927, the book — one of the early works on hypermodernism — introduced many new concepts to followers of the modern school of thought...
in 1929 .
The concept of zugzwang, if not the term, must have been known to players for many centuries. Zugzwang is required to win the elementary (and common) king and rook versus king endgame , and the king and rook (or differently-named pieces with the same powers) have been chess pieces since the earliest versions of the game .
The earliest use of zugzwang (other than in basic checkmate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
s) may be in this study by Zairab Katai, which was published sometime between 813 and 833. (This study was actually from the predecessor of chess Shatranj
Shatranj
Shatranj is an old form of chess, which came to the Western world from India. Modern chess has gradually developed from this game.-Etymology and origins:...
but the moves of the king, rook, and 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...
are the same. Masters of this era composed many studies in which Black was in zugzwang so that any move fatally weakened his position.) After
- 1. Re3! Ng1
- 2. Kf5! Kd4
- 3. Kf4
puts Black in zugzwang, since 3... Kc4 4. Kg3! Kd4 5. Re1 and White wins .
The concept of zugzwang is also seen in the 1585 endgame study
Endgame 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...
by Giulio Cesare Polerio at right, published in 1604 by Alessandro Salvio
Alessandro Salvio
Alessandro Salvio was an Italian chess player who is considered to be the unofficial world champion around the year 1600. He started an Italian chess academy in Naples, Italy, and wrote a book called Trattato dell'Inventione et Arte Liberale del Gioco Degli Scacchi, which was published in Naples...
, one of the earliest writers on the game. gives the position as by Polerio in 1585. The only way for White to win is 1.Ra1!! Kxa1 2.Kc2!, placing Black in zugzwang. His only legal move is 2...g5, whereupon White promotes
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...
a pawn first and then checkmate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
s with 3.hxg5 h4 4.g6 h3 5.g7 h2 6.g8(Q) h1(Q) 7.Qg7# .
Joseph Bertin
Joseph Bertin
Captain Joseph Bertin was one of the first authors to write about the game of chess. David Hooper and Kenneth Whyld in The Oxford Companion to Chess call his book The Noble Game of Chess "the first worthwhile chess book in the English language". B...
in The Noble Game of Chess (1735), which Hooper and Whyld consider "the first worthwhile chess textbook in the English language", referred to the concept of zugzwang, albeit without using that word, when he set forth as the 18th of his 19 rules about chess play, "To play well the latter end of a game, you must calculate who has the move, on which the game always depends." .
François-André Danican Philidor
François-André Danican Philidor
François-André Danican Philidor , often referred to as André Danican Philidor during his lifetime, was a French composer and chess player. He contributed to the early development of the opéra comique...
wrote in 1777 of the position at below right that after White plays 36.Kc3, Black "is obliged to move his rook from his king, which gives you an opportunity of taking his rook by a double check, or making him mate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
" .Philidor analyzed 36.Kc3 Rh2 37.Qb5+ Ka1 38.Qa6+ Kb1 39.Qb6+ Ka2 40.Qa7+ Kb1 41.Qg1+, winning Black's rook by 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 "double check" in Philidor's now-obsolete terminology). Lasker explicitly cited a mirror image of this position (White: king on f3, queen on h4; Black: king on g1, rook on g2) as an example of zugzwang in Lasker's Manual of Chess . The British master George Walker
George Walker (chess player)
George Walker was an English chess player and author of The Celebrated Analysis of A D Philidor , The Art of Chess-Play: A New Treatise on the Game of Chess , A Selection of Games at Chess played by Philidor , Chess Made Easy , and Chess Studies .In 1839 visited...
analyzed a similar position in the same endgame, giving a maneuver that resulted in the superior side reaching the initial position, but now with the inferior side on move and in zugzwang. Walker wrote of the superior side's decisive move: "throwing the move upon Black, in the initial position, and thereby winning" .
The great American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
player Paul Morphy
Paul Morphy
Paul Charles Morphy was an American chess player. He is considered to have been the greatest chess master of his era and an unofficial World Chess Champion. He was a chess prodigy...
(1837–1884), like Salvio and Philidor an unofficial 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....
, is credited with composing the position at right "while still a young boy". After 1.Ra6!, Black is in zugzwang and must allow mate on the next move with 1...bxa6 2.b7# or 1...B (moves) 2.Rxa7# .
Fischer versus Taimanov, second match game
Some zugzwang positions occurred in the second game of the 1971 candidates matchCandidates 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...
between 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...
and Mark Taimanov
Mark Taimanov
Mark Evgenievich Taimanov is a leading Soviet and Russian chess player and concert pianist.-Chess:He was awarded the International Grandmaster title in 1952 and played in the Candidates Tournament in Zurich in 1953, where he tied for eighth place. From 1946 to 1956, he was among the world's top...
. In the position in the diagram, Black is in zugzwang because he would rather not move, but he must: a king move would lose the knight, while a knight move would allow the 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...
to advance . The game continued:
- 85... Nf3
- 86. h6 Ng5
- 87. Kg6
and Black is again in zugzwang. The game ended shortly (because the pawn will slip through and promote
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...
) :
- 87... Nf3
- 88. h7 Ne5+
- 89. Kf6 1-0.
Fischer versus Taimanov, fourth match game
In the position on the right, White has just gotten his king to a6, where it attacks the black pawn on b6, tying down the black king to defending it. White now needs to get his bishopBishop (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...
to f7 or e8 to attack the pawn on g6. Play continued:
- 57... Nc8
- 58. Bd5 Ne7
- 59. Bc4! Nc6
- 60. Bf7 Ne7
Now the bishop is able to make a tempo
Tempo (chess)
In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer move, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo"...
move. It is able to move while still attacking the pawn on g6, and preventing the black king from moving to c6.
- 61. Be8
and Black is in zugzwang. Knights are unable to make a tempo move , so moving the knight would allow the bishop to capture the kingside pawns. The black king must give way.
- 61... Kd8
- 62. Bxg6! Nxg6
- 63. Kxb6 Kd7
- 64. Kxc5
and White has a won position. Either one of White's queenside pawns will promote or the white king will attack and win the black kingside pawns and a kingside pawn will promote. Black resigned seven moves later , , . Andy Soltis says that this is "perhaps Fischer's most famous endgame" .
Tseshkovsky versus Flear, 1988
This position from a 1988 game between Vitaly TseshkovskyVitaly Tseshkovsky
Vitaly Valerianovich Tseshkovsky is a Russian chess Grandmaster and a former champion of the USSR.Tseshkovsky was born in Siberia into a Polish family ....
and Glenn Flear
Glenn Flear
Glenn Curtis Flear is a British chess grandmaster now living in Montpellier, France. He is the author of several books, some on chess openings and some on the endgame....
at Wijk aan Zee shows an instance of "zugzwang" where the obligation to move makes the defense more difficult but it does not mean the loss of the game. A draw by agreement
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...
was reached eleven moves later .
Reciprocal zugzwang
A special case of zugzwang is reciprocal zugzwang or mutual zugzwang, which is a position such that who ever is to move is in zugzwang. Positions of reciprocal zugzwang are surprisingly important in the analysis of endgames , . A position of mutual zugzwang is closely related to a game with a ConwayJohn Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
value of zero in game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
.
The diagram on the right shows a position of reciprocal zugzwang. If Black is to move, he must move 1... Kd7 and lose because White will move 2. Kb7, promote the pawn, and win. If White is to move, he must either move 1. Kc6 which is a draw because it 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....
s Black or he must abandon the pawn, which is also a draw after Black captures the pawn. Both sides would be in zugzwang if it were their move, so it is a reciprocal zugzwang , .
In a position with reciprocal zugzwang, only the player to move is actually in zugzwang. However, the player who is not in zugzwang must play carefully because one inaccurate move can cause him to be put in zugzwang . That is in contrast to regular zugzwang, because the superior side usually has a waiting move to put the opponent in zugzwang .
Second example
Another example is shown in the diagram on the right – if White is to move the game is drawn; if Black is to move he loses. With White to move:- 1. Kd5 Kd7
- 2. c5 Kc7
- 3. c6 Kc8!
- 4. Kd6 Kd8!
Black has the opposition
Opposition (chess)
In chess, opposition is the situation occurring when two kings face each other on a rank or file, with only one square in between them. In such a situation, the player not having to move is said to "have the opposition" . It is a special type of zugzwang and most often occurs in endgames with...
and draws because 5. c7+ Kc8 6. Kc6 is stalemate.
If Black is to move, White wins
- 1. ... Kd7
- 2. Kb6 Kc8
- 3. Kc6 Kd8
and White wins with
- 4. Kb7
or
- 4. c5 , (see king and pawn versus king endgame).
Examples from play
The position at right is a position that could have occurred in the 1961 game between Viacheslav Kalashnikov and the young Anatoly KarpovAnatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...
. White to move in this position draws, but Black to move loses. Karpov's 49th move in the actual game avoided the zugzwang and the game was drawn . This is one of 209 mutual zugzwang positions in the rook and pawn versus rook endgame .
The second position is an analysis position from the ninth game of the 1984 World Chess Championship
World Chess Championship 1984
The World Chess Championship 1984 was a match between challenger Garry Kasparov and defending champion Anatoly Karpov for the World Chess Championship title...
between Anatoly Karpov and Garry Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....
. The alternate move 45... Ke6 is considered and this position could result after move 57. White to move draws; Black to move loses. It would have been White's move in this analysis position. Kasparov played a different 45th move and Karpov won after seventy moves , .
Trébuchet
An extreme type of reciprocal zugzwang, called trébuchet is shown in the third diagram. It is also called a full-point mutual zugzwang because a full point (win versus loss) is at stake . Whoever is to move in this position loses the game—they must abandon their own 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...
, thus allowing their opponent to capture it and proceed to promote
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...
the remaining pawn .
Examples
This diagram shows a position in which a trébuchet can be reached to win the game. The first king to reach the blocked pawns will win. Play continues:- 1. Kxh6 Kxc3
- 2. Kg5 Kd3!
2... Kd4?? loses because after 3. Kf5 Black is on the wrong side of the trébuchet.
- 3. Kf5 Kd4!
and Black wins the pawn and the game (see King and pawn versus king endgame) .
Another simple example is seen in the diagram at right. Black, on move, must play 1...b3, allowing 2.axb3#. White, on move, must move his king away, allowing 1...b3, with an easy win for Black.
Example in study
This position is a mutual zugzwang from a 1792 study. The first player to move runs out of moves and loses .Analysis from game
In this analysis from a 1978 game between Miguel NajdorfMiguel Najdorf
Miguel Najdorf was a Polish-born Argentine chess grandmaster of Jewish origin, famous for his Najdorf Variation....
and Henrique Mecking
Henrique Mecking
Henrique Mecking was a leading Brazilian chess Grandmaster in the 1970s. He was a very strong player at an early age , drawing comparisons to Bobby Fischer, although he did not achieve the International Grandmaster title until 1971...
, whoever is to move loses. (It would have been White's move had the analysis position occurred in the game.)
Example in game
In this position from a game at the 1967 Chess OlympiadChess Olympiad
The Chess Olympiad is a biennial chess tournament in which teams from all over the world compete against each other. The event is organised by FIDE, which selects the host nation.-Birth of the Olympiad:The first Olympiad was unofficial...
, whoever moves loses. In the game it was Black's move, who resigned .
In endgame study
Marc Bourzutschky has used computer analysis to find some complicated trébuchet positions. If White is to move in this position, Black quickly drives White's king toward the corner and mates no later than move 8, e.g. 1.Kb2 (1.Nhg7 Qf4+ or 1.Nh4 Qe3+ also leaves White's king in trouble) Qg2+ 2.Kb3 Qb7+! 3.Ka3 Qb6 4.Nf4+ Kc4! 5.Ka2 Qb3+! 6.Ka1 Kb4 7.Ng7 Ka3 8.Nge6 Qb2#. Black on move must give ground, enabling White to gradually improve the positions of his pieces, e.g. 1...Kc4 (1...Kc3 allows 2.Nf2! Qxf2?? 3.Ne4+) 2.Kd2! Kd5 3.Ne3+ Ke5 4.Ng7 and White mates by move 42 according to Bourzutschky.– scroll down to No. 282Mined squares
Corresponding squaresCorresponding squares
Corresponding squares in chess occur in some chess endgames, usually ones that are mostly blocked. If squares x and y are corresponding squares, it means that if one player moves to x then the other player must move to y in order to hold his position...
are squares of mutual zugzwang. When there is only one pair of corresponding squares they are called mined squares . A player will fall into zugzwang if he moves his king onto the square and his opponent is able to move onto the corresponding square. In the diagram on the right, if either king moves onto the square marked with the dot of the same color, he falls into zugzwang if the other king moves into the mined square near him .
Zugzwang required to win
In some endgames it is necessary to place the opponent in zugzwang in order to force a win. These include:- rook (and king) versus king checkmateCheckmateCheckmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
- two bishops versus king checkmate
- two knights versus pawn checkmate
- Bishop and knight checkmateBishop and knight checkmateThe bishop and knight checkmate in chess is the checkmate of a lone king which can be forced by a bishop, knight, and king. With the stronger side to move and with perfect play, checkmate can be forced in at most thirty-three moves from any starting position where the defender cannot quickly win...
- queen versus rook
- queen versus knight
- queen versus two knights, and
- queen versus two bishops .
In addition, zugzwang is required in many king and pawn versus king endgames in order to force 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...
of the pawn and in other king and pawn endgames with more pawns . (See pawnless chess endgame and fortress (chess)
Fortress (chess)
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...
for some discussion of some of these endings.)
Zugzwang helps the defense
Zugzwang usually works in favor of the stronger side, but sometimes it aids the defense. In this position based on a game between Zoltán VargaZoltán Varga (chess player)
Zoltán Varga is a Hungarian chess grandmaster. On the July 2009 FIDE list his Elo rating is 2473.-External links:*...
and Peter Acs
Peter Acs
Péter Ács is a Hungarian chess grandmaster . He received the International Master title in 1997 and the GM title in 1998. In 2001 he won the World Junior Chess Championship. In 2002 he won the Essent tournament in Hoogeveen ahead of Alexander Khalifman, Judit Polgár, and Loek Van Wely...
, it saves the game for the defense:
- 1... Kc4!! Reciprocal zugzwang
- 2. Nc3 Kb4 Reciprocal zugzwang again
- 3. Kd3 Bg7 Reciprocal zugzwang again
- 4. Kc2 Bh6
- 5. Kd3 Bg7
- 6. Nd5+ Kxa4
- 7. Ke4 Kb5
- 8. Kf5 Kc5
- 9. Kg6 Bd4
- 10. Nf4 Kd6
- 11. h6 Ke7
- 12. h7 Bb2
This position is a draw and 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...
a few moves later .
In this position from Benko, White should win but he makes an error and gets into zugzwang which enables Black to draw.
- 1. Kd6? Bb7
- 2. Bd7 Bf3
- 3. Be6 Bb7!
and Black draws because White is in Zugzwang .
In a study
This position is a 1901 endgame studyEndgame 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...
by Amelung. White to move wins by taking the opposition after 1. Kb7! and putting Black in zugzwang, e.g. 1... Kc4 2. Kb6 b3 3. Ka5 Kc3 4. Ka4 b2 5. Ka3 and White wins the pawn. In 1956 Ilyia Maizelis pointed out that Black to move can take the opposition and put White in zugzwang:
- 1... Kc5!
- 2. Kb7 Kb5!
- 3. Ka7 Ka5!
and White cannot make progress .
Zugzwang in the middlegame and complex endgames
Alex Angos notes that, "As the number of pieces on the board increases, the probability for zugzwang to occur decreases." As such, zugzwang is very rarely seen in the middlegame .Sämisch versus Nimzowitsch
The game Fritz SämischFriedrich Sämisch
Friedrich Sämisch was a German chess grandmaster .-Main results:* 2nd at Berlin 1920...
versus Aron Nimzowitsch
Aron Nimzowitsch
Aron Nimzowitsch was a Russian-born Danish unofficial chess grandmaster and a very influential chess writer...
, Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
1923, is often called the "Immortal Zugzwang Game".According to Nimzowitsch, writing in the Wiener Schachzeitung in 1925, this term originated in "Danish chess circles" . Some consider the final position to be an extremely rare instance of zugzwang occurring in the middlegame . It ended with White resigning in the position in the diagram.
White has a few pawn moves which do not lose material, but eventually he will have to move one of his pieces. If he plays 1.Rc1 or Rd1, then 1...Re2 traps White's queen; 1.Kh2 fails to 1...R5f3, also trapping the queen, since White cannot play 2.Bxf3 because the bishop is pinned
Pin (chess)
In chess, a pin is a situation brought on by an attacking piece in which a defending piece cannot move without exposing a more valuable defending piece on its other side to capture by the attacking piece...
to the king; 1.g4 runs into 1...R5f3 2.Bxf3? Rh2 mate. Angos analyzes 1.a3 a5 2.axb4 axb4 3.h4 Kh8 (waiting) 4.b3 Kg8 and White has run out of waiting moves and must lose material. Best in this line is 5.Nc3!? bxc3 6.bxc3, which just leaves Black with a serious positional advantage and an extra pawn . Other moves lose material in more obvious ways.
However, since Black would win even without the zugzwang , it is debatable whether the position is true zugzwang. Even if White could pass his move he would still lose, albeit more slowly, after 1...R5f3 2.Bxf3 Rxf3, trapping the queen and thus winning queen and bishop for two rooks . Wolfgang Heidenfeld
Wolfgang Heidenfeld
Wolfgang Heidenfeld was a chess player.Heidenfeld was born in Berlin. He was forced to move from Germany to South Africa because he was a Jew. There, he won the South African Chess Championship eight times, and he represented South Africa in the Chess Olympiad in 1958...
thus considers it a misnomer to call this a true zugzwang position . See also Immortal Zugzwang Game: Objections to the sobriquet.
Steinitz versus Lasker
This game between Wilhelm SteinitzWilhelm Steinitz
Wilhelm Steinitz was an Austrian and then American chess player and the first undisputed world chess champion from 1886 to 1894. From the 1870s onwards, commentators have debated whether Steinitz was effectively the champion earlier...
versus Emanuel Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...
in the 1896-97 World Chess Championship
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....
, is an early example of zugzwang in the middlegame. After Lasker's 34...Re8-g8!, Steinitz resigned because he has no playable moves. . However, according to ChessGames.com
Chessgames.com
ChessGames.com is a large chess community on the Internet, with over 156,000 members. The site maintains a large database of historical chess games where every game has a distinct message board for comments and analysis. Basic membership is free and the site is open to players at all levels of...
and some print sources, Steinitz played on another five moves before resigning: 35.Re1 Qxf5 36.Re5 Qf3 37.d5 Qg3+ 38.Kh1 Qxe5 39.dxc6+ Kxc6 0-1 . White's bishop cannot move because that would allow the crushing ...Rg2+. The queen cannot move without abandoning either its defense of the bishop on g5 or of the g2 square, where it is preventing ...Qg2#. White's move 35.f6 loses the bishop: 35...Rxg5 36. f7 Rg2+, forcing mate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
. The move 35.Kg1 allows 35...Qh1+ 36.Kf2 Qg2+ followed by capturing the bishop. The rook cannot leave the first rank, as that would allow 35...Qh1#. Rook moves along the first rank other than 35.Rg1 allow 35...Qxf5, when 36.Bxh4 is impossible because of 36...Rg2+; for example, 35.Rd1 Qxf5 36.d5 Bd7, winning. That leaves only 35.Rg1, when Black wins with 35...Rxg5! 36.Qxg5 (36.Rxg5? Qh1#) Qd6+ 37.Rg3 hxg3+ 38.Qxg3 Be8 39.h4 Qxg3+ 40.Kxg3 b5! 41.axb5 a4! and Black queens
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...
first . Colin Crouch calls the final position, "An even more perfect middlegame zugzwang than ... Sämisch-Nimzowitsch ... in the final position Black has no direct threats, and no clear plan to improve the already excellent positioning of his pieces, and yet any move by White loses instantly" .
Podgaets versus Dvoretsky
Soltis writes that his "candidate for the ideal zugzwang game" is the following game : Podgaets-DvoretskyMark Dvoretsky
Mark Izrailovich Dvoretsky is a world-renowned Russian chess trainer, writer and International Master.He was awarded the International Master title in 1975 and for a while, was widely regarded as the strongest IM in the world...
, USSR 1974 1.d4 c5 2.d5 e5 3.e4 d6 4.Nc3 Be7 5.Nf3 Bg4 6.h3 Bxf3 7.Qxf3 Bg5! 8.Bb5+ Kf8! Black exchanges off his bad bishop, but does not allow White to do the same. 9.Bxg5 Qxg5 10.h4 Qe7 11.Be2 h5 12.a4 g6 13.g3 Kg7 14.0-0 Nh6 15.Nd1 Nd7 16.Ne3 Rhf8 17.a5 f5 18.exf5 e4! 19.Qg2 Nxf5 20.Nxf5+ Rxf5 21.a6 b6 22.g4? hxg4 23.Bxg4 Rf4 24.Rae1 Ne5! 25.Rxe4 Rxe4 26.Qxe4 Qxh4 27.Bf3 Rf8!! 28. Bh1 28.Qxh4? Nxf3+ and 29...Nxh4 leaves Black a piece ahead. Ng4 29.Qg2 (see diagram at left) Rf3!! 30.c4 Kh6!! (diagram at right) Now all of White's piece moves allow checkmate or ...Rxf2 with a crushing attack (e.g. 31.Qxf3 Qh2#; 31.Rb1 Rxf2 32.Qxg4 Qh2#). That leaves only moves of White's b-pawn, which Black can ignore, e.g. 31.b3 Kg7 32.b4 Kh6 33.bxc5 bxc5 and White has run out of moves.Notes based on those in Soltis 1978, pp. 55-56. 0-1
Harper versus Zuk
Harper-Zuk, Halloween Open, Burnaby, British ColumbiaBritish Columbia
British Columbia is the westernmost of Canada's provinces and is known for its natural beauty, as reflected in its Latin motto, Splendor sine occasu . Its name was chosen by Queen Victoria in 1858...
1971 is a grisly example of zugzwang in the middlegame. White's queen, rook, knight, and king have a total of one legal move (Qh3), which loses the queen, rook and king on successive moves (... gxh3 followed by ... Qxg2#). The game concluded: 37.b5 Kh8 37...Nf5 and Nd4-e2 was crushing, but letting White self-destruct is even quicker. 38.a4 Kh7 39.a5 Kg8 0-1 After 40.axb6 axb6, white is forced to play 41.Qh3, and then it is mate in two: gxh3 42.Kh2 Qxg2#.
Van Dongen versus Wijsman
An unusual example of zugzwang in a complicated endgame occurred in the position at right. On the previous move Black, with a winning position, had played 73...d4? and White responded 74.Rd2-d3!!, when Black, a knight up with three dangerous passed pawns, suddenly must fight for a draw. Tim KrabbéTim Krabbé
Tim Krabbé is a Dutch journalist and novelist.Krabbé was born in Amsterdam. His writing has appeared in most major periodicals in the Netherlands. He is known to Dutch readers for his novel De Renner , first published in 1978...
explains that the pawns on d4 and e4 are blocked and pinned, the knight is bound to the defense of e4, the rook is bound to the defense of d4, and the pawn on b4 is bound to the defense of the knight. Krabbé analyzes as best for Black 74...b3! 75.Rxd4 Rxd4 76.Rxc3 Rd8 77.Rxb3 Re8 78.Re3 Re5 79.Rc3 (79.Kxf6? Rxa5 82.Kg6 Ra1 83.f6 Rg1+ wins) Re8 80.Re3 Re5 81.Rc3 and the game will end in a draw by repetition of moves. Instead, Black played 74...Nb5? 75.Rxe4 Nd6 76.Re6 Rc6 77.Rxd4 Rxh6+ 78.Kxh6 Nxf5+ 79.Kg6 1-0.
Zhilin versus Chernov
In the game between Vitaly Valentinovich Zhilin and Chernov (or Tchernov) in the 1960 USSR championship, White was a pawn down and just sacrificedSacrifice (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 bishop on h3. After 1. Kh4! Black is placed in zugzwang after moving his b- and h-pawns. The game continued:
- 1. Kh4! b6
- 2. Kh5 b5
- 3. Kh4 h5
- 4. Kxh5
Now Black is in zugzwang and resigned , .
Fischer versus Rossetto
In this 1959 game between future World ChampionWorld 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....
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...
and Héctor Rossetto
Héctor Rossetto
Héctor Decio Rossetto was one of the best chess players in Argentine history.He earned the title of International Master in 1950 and the Grandmaster title in 1960....
, 33. Bb3! puts Black in zugzwang . If Black moves the king, White plays Rb8, winning a piece (...Rxc7 Rxf8); if Black moves the rook, 33...Ra8 or R...e8, then 34.c8=Q+ and the black rook will be lost after 35.Qxa8, 35.Qxe8 or 35.Rxe7+ (depending on Black's move); if Black moves the knight, Be6 will win Black's rook. That leaves only pawn moves, and they quickly run out . The game concluded:
- 33...a5
- 34.a4 h6
- 35.h3 g5
- 36.g4 fxg4
- 37.hxg4 1-0 .
Example from Euwe and Meiden
In this example from a master versus amateur game in the book by EuweMax Euwe
Machgielis Euwe was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion . Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978.- Early years :Euwe was born in Watergraafsmeer, near Amsterdam...
and Meiden, Black is in a full board zugzwang. Any move by a black piece loses at least a pawn .
Zugzwang Lite
Jonathan RowsonJonathan Rowson
Jonathan Rowson is Scotland's third chess Grandmaster, after Paul Motwani and Colin McNab, and has played first board at recent Chess Olympiads. He is also a chess author.-Career:...
coined the term Zugzwang Lite
Lite
Lite is a variant spelling of "light", a concept of weight, and may refer to:*Diet food or diet beverages:**Diet soda, a diet version of soda pop**Low-alcohol beer or low-calorie beer ***Miller Lite, a brand of light beer...
to describe a situation, sometimes arising in symmetrical opening
Chess opening
A chess opening is the group of initial moves of a chess game. Recognized sequences of opening moves are referred to as openings as initiated by White or defenses, as created in reply by Black. There are many dozens of different openings, and hundreds of named variants. The Oxford Companion to...
variations, where White's "extra move" is a burden . He cites as an example of this phenomenon Hodgson
Julian Hodgson
Julian Michael Hodgson is an English International Grandmaster and former British Champion of chess.He first came to the notice of the chess world for his phenomenal prowess as a junior; he was London under-18 champion at 12 years of age and won the British Boys under-21 title aged just...
versus Arkell
Keith Arkell
Keith Charles Arkell is an English Grandmaster of chess.As a long-time resident of the West Midlands, he has lived in Rednal, Droitwich and Worcester. His brother Nicholas was also a strong player....
, Newcastle
Newcastle upon Tyne
Newcastle upon Tyne is a city and metropolitan borough of Tyne and Wear, in North East England. Historically a part of Northumberland, it is situated on the north bank of the River Tyne...
2001. The position at left arose after 1.c4 c5 2.g3 g6 3.Bg2 Bg7 4.Nc3 Nc6 5.a3 a6 6.Rb1 Rb8 7.b4 cxb4 8.axb4 b5 9.cxb5 axb5 Here Rowson remarks, "Both sides want to push their d-pawn and play Bf4/...Bf5, but White has to go first so Black gets to play ...d5 before White can play d4. This doesn't matter much, but it already points to the challenge that White faces here; his most natural continuations allow Black to play the moves he wants to. I would therefore say that White is in 'Zugzwang Lite' and that he remains in this state for several moves." The game continued 10.Nf3 d5 11.d4 Nf6 12.Bf4 Rb6 13.0-0 Bf5 14.Rb3 O-O 15.Ne5 Ne4 16.h3 h5!? 17.Kh2 The position is still almost symmetrical, and White can find nothing useful to do with his extra move. Rowson whimsically suggests 17.h4!?, forcing Black to be the one to break the symmetry. 17...Re8! Rowson notes that this is a useful waiting move, covering e7, which needs protection in some lines, and possibly supporting an eventual ...e5 (as Black in fact played on his 22nd move). White cannot copy it, since after 18.Re1? Nxf2 Black would win a pawn
Pawn (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...
. After 18.Be3?! Nxe5! 19.dxe5 Rc6! Black seized the initiative and went on to win in 14 more moves.
Another instance of Zugzwang Lite occurred in Lajos Portisch
Lajos Portisch
Lajos Portisch is a Hungarian chess Grandmaster, whose positional style earned him the nickname, the "Hungarian Botvinnik"...
versus 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....
, Candidates Match 1965, again from the Symmetrical Variation of the English Opening
English Opening
In chess, the English Opening is the opening where White begins:A flank opening, it is the fourth most popular and, according to various databases, anywhere from one of the two most successful to the fourth most successful of White's twenty possible first moves. White begins the fight for the...
, after 1.Nf3 c5 2.c4 Nc6 3.Nc3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.d3 a6 8.a3 Rb8 9.Rb1 b5 10.cxb5 axb5 11.b4 cxb4 12.axb4 d6 13.Bd2 Bd7. Soltis wrote, "It's ridiculous to think Black's position is better. But Mikhail Tal said it is easier to play. By moving second he gets to see White's move and then decide whether to match it." 14.Qc1 Here, Soltis wrote that Black could maintain equality by keeping the symmetry: 14...Qc8 15.Bh6 Bh3. Instead, he plays to prove that White's queen is misplaced. 14...Rc8! 15.Bh6 Nd4! Threatening 15...Nxe2+. 16.Nxd4 Bxh6 17.Qxh6 Rxc3 18.Qd2 Qc7 19.Rfc1 Rc8 Although the pawn structure is still symmetrical, Black's control of the c-file gives him the advantage. Black ultimately reached an endgame two pawns up, but White managed to hold a draw in 83 moves. See First-move advantage in chess#Symmetrical openings for more details.
Quotation
- "Zugzwang is like getting trapped on a safety island in the middle of a highway when a thunderstorm starts. You don't want to move but you have to." - Arthur BisguierArthur BisguierArthur Bernard Bisguier is an American chess Grandmaster, chess promoter, and writer. Bisguier won two U.S. Junior Championships , three U.S. Open Chess Championship titles , and the 1954 United States Chess Championship title. He played for the United States in five chess Olympiads...
See also
- Combinatorial game theoryCombinatorial game theoryCombinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
, in which all mutual zugzwangs are equivalent to 0. - Corresponding squaresCorresponding squaresCorresponding squares in chess occur in some chess endgames, usually ones that are mostly blocked. If squares x and y are corresponding squares, it means that if one player moves to x then the other player must move to y in order to hold his position...
- Seki
- Key squareKey squareIn chess, particularly in endgames, a key square is a square such that if a player's king can occupy it, he can force some gain such as the promotion of a pawn or the capture of an opponent's pawn. Key squares are useful mostly in endgames involving only kings and pawns...
- King and pawn versus king endgame
- Null-move heuristicNull-move heuristicIn computer chess programs, the null-move heuristic is a heuristic technique used to enhance the speed of the alpha-beta pruning algorithm.- Rationale :...
- Opposition (chess)Opposition (chess)In chess, opposition is the situation occurring when two kings face each other on a rank or file, with only one square in between them. In such a situation, the player not having to move is said to "have the opposition" . It is a special type of zugzwang and most often occurs in endgames with...
- Triangulation (chess)Triangulation (chess)Triangulation is a tactic used in chess to put one's opponent in zugzwang. That is, it gets to the same position with the other player to move, when it is a disadvantage for that player to move, e.g. he has to give up a blockade and let the other player penetrate his position...