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 cannot do the same, he has lost a crucial tempo and reached the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames (Flear 2004:15).
|This article uses algebraic notation to describe chess moves.|
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! (if 1. c6+ then 1... Kc8 draws. If 1... bxc6+ then 2. Kc5 wins, see king and pawn versus king endgame.)
- 1...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.)
Triangulation with the king
- 56. Kg1 Ke5
Triangulation can occur in endgames other than king and pawn 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 then-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. 0-1
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 (Giddins 2007:62).
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, putting the opponent in zugzwang. This position (from analysis of a game between Alexey Shirov and Alexander Grischuk 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 (Silman 2007:374–77).
Triangulation with other pieces
For an example of triangulation with a queen, see the queen versus rook position at Philidor position. The game Fischer versus Taimanov, fourth match game shows a similar tactic with a bishop. A rook can also perform the maneuver, but a knight cannot (Müller & Pajeken 2008:40, 175, 189).
Example with a rook
- 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).
- Dvoretsky, Mark (2006), Dvoretsky's Endgame Manual (2nd 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
- Kasparov, Garry (2011), Garry Kasparov on Garry Kasparov, Part 1: 1973-1985, Everyman Chess, p. 520, ISBN 978-1-85744-672-2
- 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
- Nunn, John (2007), Secrets of Practical Chess (2nd ed.), Gambit Publications, ISBN 978-1-904600-70-1 pages 119-21
- Benko, Pal (November 2010), "Endgame Lab: Triangulation", Chess Life: 48–49