# Triangulation (chess)

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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. Triangulation is also called "losing a tempo" or "losing a move".

Triangulation occurs most commonly in endgames with only kings and pawns 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 can't do the same, he has lost a crucial tempo and gotten to the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames harvcol|Flear|2004|p=15.

Examples

Chess diagram|=
tright
Triangulation
=
| | | | | | | |=
|pd| |kd| | | | |=
|pl| | | | | | |=
| |pl|kl|xw| | | |=
| | |xw| | | | |=
| | | | | | | |=
| | | | | | | |=
| | | | | | | |=
White to move. White needs it to be Black's move in this position, so he triangulates. The dots indicate triangulation squares for the white king.
Consider this position, with White to move. Here, Black has 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. 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! Kc6 (if 1... Ke7 then 2. c6 and white wins by promoting 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. c6and White will win harvcol|Dvoretsky|2006|p=21. (There are other ways for White to win after his third move.)

Note: 1.c6 will not win due to 1.. Kc8!

For an example of triangulation with a queen, see the queen versus rook position at Philidor position. The game Zugzwang#Fischer versus Taimanov, 1971, fourth match game shows a similar tactic with a bishop. A rook can also perform the maneuver, but a knight can not Harvcol|Müller|Pajeken|2008|pp=40, 175, 189.

Triangulation with the king

Chess diagram|=
tright
Tal-Spassky, 1965
=
| | | | | | | |=
| | | | | | | |=
| | | | | | | |=
| |pd| | |rd| |pd|=
| |pl| | | | |rl|=
| |xo|kd| |pd| |pl|=
| | |xo| |kl| | |=
| | | | | | | |=
Position before Black's 64th move.
Triangulation can occur in other endgames, such as this game in the 1965 Candidates Tournament, in which future World chess champion Boris Spassky defeated former world champion Mikhail Tal and won the right to challenge the current champion Tigran 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. 0-1Now it is back to the same position, but with White to move, and White is in zugzwang. White must lose the rook or allow the f-pawn to advance towards promotion Harvcol|Giddins|2007|p=62.

Example in king and pawn endgame

Chess diagram|=
tright
Shirov-Grischuk, 2000
=
| | | |kd| | | |=
| | | |pl|xo| | |=
| | |pl| | | | |=
| |pd| | | |pd|pd|=
| |pl| | | | | |=
| | | | | |xw| |=
| | | | | |kl|xw|=
| | | | | | | |=
White to move triangulates to put Black in zugzwang.
Usually when a king triangulates in a king and pawn endgame, it is close to the other king. This game shows an example when the kings are far apart. White triangulates to put Black in zugzwang:: 1. Kh2! Kf7: 2. Kg3 Ke8: 1. Kg2! and Black is in zugzwang harvcol|Silman|2007|pp=374-77.

Triangulation with a rook

Chess diagram|=
tright
Topalov-Karpov, 2002
=
|kl| | | | | |xw|=
|pl| |kd| | | |xw|=
| | | | | | |rl|=
| | | | | | | |=
rd| | | | | | |pd|=
| | | | | | | |=
| | | | | | | |=
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White triangulates to put Black in zugzwang.
In this game between future world champion Veselin Topalov and former world champion Anatoly Karpov, White triangulates to put Black in zugzwang:: 1. Rh7+!? Kd8: 2. Rh8+ Kd7: 3. Rh6back 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 Harvcol|Müller|Pajeken|2008|pp=173-74.

ee also

* Zugzwang
* Corresponding squares
* Opposition
* Chess endgame literature

References

* Citation
surname1 = Dvoretsky | given1 = Mark | authorlink1 = Mark Dvoretsky
year = 2006
title = Dvoretsky's Endgame Manual
edition = second
publisher = Russell Enterprises
ID=ISBN 1-888690-28-3

* Citation
title=Starting Out: Pawn Endings
year=2004
publisher=Everyman Chess
ID=ISBN 1-85744-362-4

*Citation
year=2007
title=101 Chess Endgame Tips: Golden nuggets of endgame wisdom
publisher=Gambit Publications
ID=ISBN 978-1-904600-66-4

*Citation
surname2=Pajeken|given2=Wolfgang
year=2008
title=How to Play Chess Endings
publisher=Gambit Publications
ID=ISBN 978-1-904600-86-2

*Citation
year=2007
title=Silman's Complete Endgame Course: From Beginner to Master
publisher=Siles Press
ID=ISBN 1-890085-10-3

* Citation
title=Secrets of Practical Chess
year=2007
edition = second
publisher=Gambit Publications
ID=ISBN 978-1-904600-70-1
pages 119-21

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