Triangulation (chess)

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This article uses algebraic notation to describe chess moves.

Triangulation is a tactic used in chess endgames to put one's opponent in zugzwang. It is normally used in king and pawn endgames 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 is also called losing a tempo or losing a move (Flear 2004:15).

[edit] Examples

Triangulation

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 was 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. c6

and White will win (Dvoretsky 2006:21). (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 (Müller & Pajeken 2008:40, 175, 189).

[edit] Triangulation with the king

Tal-Spassky, 1965

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 was 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 White is in zugzwang. White must lose the rook or allow the f-pawn to advance towards promotion (Giddins 2007:62).

[edit] Example in king and pawn endgame

Shirov-Grischuk, 2000

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 (Silman 2007:374-77).

[edit] Triangulation with a rook

Topalov-Karpov, 2002

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. 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 (Müller & Pajeken 2008:173-74).

[edit] See also

• Zugzwang
• Corresponding squares
• Opposition

[edit] References

• Dvoretsky, Mark (2006), Dvoretsky's Endgame Manual (second ed.), Russell Enterprises, ISBN 1-888690-28-3 
• Flear, Glenn (2004), Starting Out: Pawn Endings, Everyman Chess, ISBN 1-85744-362-4 
• Giddins, Steve (2007), 101 Chess Endgame Tips: Golden nuggets of endgame wisdom, Gambit Publications, ISBN 978-1-904600-66-4 
• Müller, Karsten & Pajeken, Wolfgang (2008), How to Play Chess Endings, Gambit Publications, ISBN 978-1-904600-86-2 
• Silman, Jeremy (2007), Silman's Complete Endgame Course: From Beginner to Master, Siles Press, ISBN 1-890085-10-3 

[edit] Further reading

• Nunn, John (2007), Secrets of Practical Chess (second ed.), Gambit Publications, ISBN 978-1-904600-70-1  pages 119-21