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Triangulation is a tactic used in chess
Chess

Chess is a recreational and competitive game played between two Player . Sometimes called Western chess or international chess to distinguish it from History of chess and other chess variants, the current form of the game emerged in Southern Europe during the second half of the 15th century after evolving from similar, much older...
 to put one's opponent in zugzwang
Zugzwang

Zugzwang is a term originally used in chess which also applies to various other games. The concept finds its formal definition in combinatorial game theory....
. 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. Triangulation is also called losing a tempo
Tempo (chess)

In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer moves, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo." Similarly, when one forces his opponent to expend moves that he would not otherwise have expended, one "gains tempo" because the oppone...
 or losing a move.

Triangulation occurs most commonly in endgames with only kings
King (chess)

In chess, the King is the most important chess piece. The object of the game is to trap the opponent's king so that he would not be able to avoid capture ....
 and pawns
Pawn (chess)

The pawn is the weakest and most numerous chess piece in the game of chess, representing infantry, or more particularly armed peasants or pikemen....
 when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares.






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Triangulation is a tactic used in chess
Chess

Chess is a recreational and competitive game played between two Player . Sometimes called Western chess or international chess to distinguish it from History of chess and other chess variants, the current form of the game emerged in Southern Europe during the second half of the 15th century after evolving from similar, much older...
 to put one's opponent in zugzwang
Zugzwang

Zugzwang is a term originally used in chess which also applies to various other games. The concept finds its formal definition in combinatorial game theory....
. 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. Triangulation is also called losing a tempo
Tempo (chess)

In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer moves, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo." Similarly, when one forces his opponent to expend moves that he would not otherwise have expended, one "gains tempo" because the oppone...
 or losing a move.

Triangulation occurs most commonly in endgames with only kings
King (chess)

In chess, the King is the most important chess piece. The object of the game is to trap the opponent's king so that he would not be able to avoid capture ....
 and pawns
Pawn (chess)

The pawn is the weakest and most numerous chess piece in the game of chess, representing infantry, or more particularly armed peasants or pikemen....
 when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares. Thus, if one king triangulates by using three moves to return to the original square and the opposing king cannot do the same, he has lost a crucial tempo
Tempo (chess)

In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer moves, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo." Similarly, when one forces his opponent to expend moves that he would not otherwise have expended, one "gains tempo" because the oppone...
 and gotten to the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames .

Examples


Consider this position, with White to move. Here, Black has the opposition
Opposition (chess)

In chess, opposition is the situation occurring when two king 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" ....
, and is keeping the white king out. However, if White had the opposition (i.e. it were Black's move in this position), the black king would have to move away from d7 and allow the white king to advance. Black's king must stay close to where it is – he must prevent the c-pawn from advancing and he must not let himself be driven to the edge of the board. The squares d5 and d7 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....
. When White's king is on d5, Black's king must be on d7, with White to move in order for Black to prevent the advance of the White king. White has a triangle of squares available: d5, e5, and d4. White can win by the following maneuver:
1. Ke5! (if 1. c6 then 1... Kc8 draws. If 1... bxc6 then 2. Kc5 wins, see king and pawn versus king endgame.)
...Kc6 (if 1... Ke7 then 2. c6 and white wins by promoting
Promotion (chess)

Promotion is a chess term 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 List of chess terms#Color ....
 the b pawn)
2. Kd4 Kd7
3. Kd5
and now the triangulation is complete and we have the same position but with Black to move. White has gained the opposition and Black is now in zugzwang. There may follow:
3. ... Kc8
4. Ke6! (diagonal opposition) Kd8
5. Kd6 (vertical opposition) Kc8
6. Ke7 Kb8
7. Kd7 Ka8
8. c6
and White will win . (There are other ways for White to win after his third move.)

Other pieces

For an example of triangulation with a queen
Queen (chess)

The queen is the most powerful chess piece in the game of chess. Each player starts the game with one queen, placed in the middle of their first rank next to their King ....
, see the queen versus rook
Rook (chess)

A rook is a chess piece in the strategy board game of chess. In the past the piece was called the castle, tower, marquess, rector, and comes , and non-players still often call it a "castle"....
 position at Philidor position
Philidor position

The Philidor position usually refers to an important chess Chess endgame which illustrates a Draw technique when the defender has a king and rook versus a king, rook, and pawn ....
. The game Zugzwang#Fischer versus Taimanov, 1971, fourth match game
Zugzwang

Zugzwang is a term originally used in chess which also applies to various other games. The concept finds its formal definition in combinatorial game theory....
 shows a similar tactic with a bishop
Bishop (chess)

A bishop is a Chess 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 ....
. A rook can also perform the maneuver, but a knight
Knight (chess)

The knight is a chess piece in the game of chess, representing a knight . It is normally represented by a horse's head, leading some to refer to it informally as a "horse"....
 can not .

Triangulation with the king


Triangulation can occur in endgames other than king and pawn endgames, such as this game in the 1965 Candidates Tournament
Candidates Tournament

The Candidates Tournament was a triennial chess tournament organized by the world chess federation FIDE as the final contest to determine the challenger for the World Chess Championship....
, in which future World chess champion Boris Spassky
Boris Spassky

Boris Vasilievich Spassky is a Russian-France chess Grandmaster . He was the tenth World Chess Champion, holding the title from 1969 to 1972....
 defeated former world champion Mikhail Tal
Mikhail Tal

Mikhail Tal was a Soviet Union-Latvian chess player, a Grandmaster , and the eighth World Chess Champion.He was often called "Misha" and also "The magician from Riga" for his daring combinational style....
 and won the right to challenge the current champion Tigran Petrosian
Tigran Petrosian

Tigran Petrosian was World Chess Champion from 1963 to 1969.He is often known by the Russian version of his name, Tigran Vartanovich Petrosian ....
. White would be in zugzwang if it were his move. Black achieves this through triangulation:
64... Kd2
65. Re4 Kc3!
66. Rh4 Kd3
67. 0-1
Now it is back to the same position, but with White to move, and now White is in zugzwang. White must lose the rook or allow the f-pawn to advance towards promotion .


Triangulation with a rook


In this game between future world champion Veselin Topalov
Veselin Topalov

Veselin Topalov is a Bulgarian chess International Grandmaster and former FIDE world chess champion.Topalov became the FIDE World Chess Champion by winning the FIDE World Chess Championship 2005....
 and former world champion Anatoly Karpov
Anatoly Karpov

Anatoly Yevgenyevich Karpov is a Russian chess International Grandmaster and former World Chess Championship. He was undisputed World Champion from 1975 to 1985, repeatedly challenged to regain the title from 1986 to 1990, then was FIDE World Champion from 1993 to 1999....
, White triangulates to put Black in zugzwang:
1. Rh7+!? Kd8
2. Rh8+ Kd7
3. Rh6
back to the same position and Black is in zugzwang. The game continued:

3... Kd8
4. Rh7 zugzwang again
4... Rb4
5. Ka7 Ra4+
6. Kb6 1-0 .


Example in king and pawn endgame


Usually when a king triangulates in a king and pawn endgame, it is close to the other king and triangulation gains the opposition
Opposition (chess)

In chess, opposition is the situation occurring when two king 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" ....
, putting the opponent in zugzwang. This position (from analysis of a game between Alexey Shirov and Alexander Grischuk
Alexander Grischuk

Alexander Grischuk is a chess International Grandmaster from Russia.In the FIDE World Chess Championships 1998-2004 he made it to the semi finals....
 in New Delhi in 2000) shows an example when the kings are far apart. White triangulates to put Black in zugzwang:
1. Kh2! Kf7
2. Kg3 Ke8
3. Kg2!
and amazingly Black is in zugzwang. The game could continue:
3... g4
4. Kg3 Kf7
5. Kf4 Ke8
6. Ke5 Kf7 (Black cannot allow White to move Ke6)
7. Kd5 g3
8. Kc6 g2 (If 8... Ke8 9. d7+ Kxe7 10. Kc7 and White wins easily)
9. Kd7 g1=Q
10. e8=Q+
and White wins .

See also

  • Zugzwang
    Zugzwang

    Zugzwang is a term originally used in chess which also applies to various other games. The concept finds its formal definition in combinatorial game theory....
  • 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....
  • Opposition
    Opposition (chess)

    In chess, opposition is the situation occurring when two king 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" ....
  • Tempo (chess)
    Tempo (chess)

    In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer moves, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo." Similarly, when one forces his opponent to expend moves that he would not otherwise have expended, one "gains tempo" because the oppone...


Further reading

pages 119-21