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Zugzwang (; ) is a situation found in chess and other wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal move will worsen their position.
Although the term is used less precisely in games such as chess, it is used specifically in combinatorial game theory to denote a move that directly changes the outcome of the game from a win to a loss. Putting the opponent in zugzwang is a common way to help the superior side win a game, and in some cases it is necessary in order to make the win possible. More generally, the term can also be used to describe a situation where passing the turn, if this were allowed, would be the best move.
The term zugzwang was used in German chess literature in 1858 or earlier, and the first known use of the term in English was by World Champion Emanuel Lasker in 1905. The concept of zugzwang was known to chess players many centuries before the term was coined, appearing in an endgame study published in 1604 by Alessandro Salvio, one of the first writers on the game, and in shatranj studies dating back to the early 9th century, over 1000 years before the first known use of the term. International chess notation uses the symbol "⊙" to indicate a zugzwang position.
Positions with zugzwang occur fairly often in chess Chess endgame, especially in king and pawn endgames and elementary checkmates (such as a rook and king against a lone king). According to John Nunn, positions of reciprocal zugzwang are surprisingly important in the analysis of endgames.
According to chess historian Edward Winter, the term had been in use in German chess circles in the 19th century.
The earliest known use of the term zugzwang in English was on page 166 of the February 1905 issue of Emanuel Lasker 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.
Other than basic , the earliest published use of zugzwang may be in this study by Zairab Katai, which was published sometime between 813 and 833, discussing shatranj. After
The concept of zugzwang is also seen in the 1585 endgame study by Giulio Cesare Polerio, published in 1604 by Alessandro Salvio, one of the earliest writers on the game. The only way for White to win is 1.Ra1 Kxa1 2.Kc2, placing Black in zugzwang. The only legal move is 2...g5, whereupon White promotes a pawn first and then with 3.hxg5 h4 4.g6 h3 5.g7 h2 6.g8=Q h1=Q 7.Qg7.
Joseph Bertin refers to zugzwang in The Noble Game of Chess (1735), wherein he documents 19 rules about chess play. His 18th rule is: "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 illustrated 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 checkmate". 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 (triangulation) 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".
Paul Morphy is credited with composing the position illustrated "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#.
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 their situation. Zugzwang typically occurs when "the player to move cannot do anything without making an important concession".
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 first diagram shows the simplest possible example of zugzwang. If it is White's move, they 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 second diagram 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 their own pawn toward promotion. White, on move, must retreat their 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. This often occurs in king and pawn endgames. Pieces other than the king can also triangulate to achieve zugzwang, such as in the KQ v KR Philidor position. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame study.
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 them to be put in zugzwang. That is in contrast to regular zugzwang, because the superior side usually has a or can triangulate to put the opponent in zugzwang.
The diagram shows a position of reciprocal zugzwang. If Black is to move, 1... Kd7 is forced, which loses because White will move 2. Kb7, promote the pawn, and win. If White is to move the result is a draw as White must either stalemate Black with 1. Kc6 or allow Black to the pawn. Since each side would be in zugzwang if it were their move, it is a reciprocal zugzwang.
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 .
| + Podgaets vs. Dvoretsky, USSR 1974 |
Soltis writes that his "candidate for the ideal zugzwang game" is the following game , Podgaets–Mark Dvoretsky, 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 , 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 If instead 28.Qxh4 then 28...Nxf3+ followed by 29...Nxh4 leaves Black a piece ahead. 28... Ng4 29. Qg2 (first diagram) Rf3!! 30. c4 Kh6!! (second diagram) 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.
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 0-0 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–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. 0-0 0-0 7. d3 a6 8. a3 Rb8 9. Rb1 b5 10. cxb5 axb5 11. b4 cxb4 12. axb4 d6 13. Bd2 Bd7 (see diagram). 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."Andrew Soltis, "Going Ape", Chess Life, February 2008, pp. 10–11. 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 by breaking the symmetry. 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- gives him the advantage. Black ultimately reached an endgame two pawns up, but White managed to hold a draw in 83 moves.
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