Triangulation is a

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used in

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to put one's opponent in

zugzwang Zugzwang (German for "compulsion to move", ) is a situation found in chess and other turn-based games 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 ...

(a position when it is a disadvantage to move). Triangulation is also called ''losing a

tempo In musical terminology, tempo (Italian, 'time'; plural ''tempos'', or ''tempi'' from the Italian plural) is the speed or pace of a given piece. In classical music, tempo is typically indicated with an instruction at the start of a piece (often ...

'' 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 cannot do the same, he has lost a crucial

and reached the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames.

Example

Consider this position, with White to move. Here, Black has the

opposition Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * ''The Opposition with Jordan Klepper'', a late-night television series on Comed ...

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 In chess, two squares are corresponding squares (also known as relative squares, sister squares, or coordinate squares) if the occupation of one of these squares by a king requires the enemy king to move to the other square in order to hold the pos ...

; 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 The chess endgame with a king and a pawn versus a king is one of the most important and fundamental endgames, other than the basic checkmates. It is an important endgame for chess players to master, since most other endgames have the potential of ...

.) : 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

. 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 her third move.)

Triangulation with the king

In this 1978 game between

Lev Alburt Lev Osipovich Alburt (born August 21, 1945) is a chess Grandmaster, writer and coach. He was born in Orenburg, Russia, and became three-time Ukrainian Champion. After defecting to the United States in 1979, he became three-time U.S. Champion ...

and future World Champion

Garry Kasparov Garry Kimovich Kasparov (born 13 April 1963) is a Russian chess grandmaster, former World Chess Champion, writer, political activist and commentator. His peak rating of 2851, achieved in 1999, was the highest recorded until being surpassed by ...

, Black wins by triangulating: :55... Kf5! :56. Kg1 Ke5 and White

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. After 57. Kf1 Ke4! 58. Kf2 Kf4 59. Kf1 Kg3, Black wins the white pawn.

Second example

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

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, in which future

World chess champion The World Chess Championship is played to determine the world champion in chess. The current world champion is Magnus Carlsen of Norway, who has held the title since 2013. The first event recognized as a world championship was the 1886 match ...

Boris Spassky Boris Vasilievich Spassky ( rus, Бори́с Васи́льевич Спа́сский, Borís Vasíl'yevich Spásskiy; born January 30, 1937) is a Russian chess grandmaster who was the tenth World Chess Champion, holding the title from 1969 ...

defeated former world champion

Mikhail Tal Mikhail Nekhemyevich Tal; rus, Михаил Нехемьевич Таль, ''Mikhail Nekhem'yevich Tal' '', ; sometimes transliterated ''Mihails Tals'' or ''Mihail Tal'' (9 November 1936 – 28 June 1992) was a Soviet-Latvian chess player ...

and won the right to challenge the then-current champion

Tigran Petrosian Tigran Vartanovich Petrosian (, ; 17 June 1929 – 13 August 1984) was a Soviet-Armenian chess grandmaster, and World Chess Champion from 1963 to 1969. He was nicknamed "Iron Tigran" due to his almost-impenetrable defensive playing style, ...

. 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 .

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

, putting the opponent in zugzwang. This position (from analysis of a game between

Alexey Shirov Alexei Shirov (, lv, Aleksejs Širovs; born 4 July 1972) is a Latvian and Spanish chess player. Shirov was ranked number two in the world in 1994. He won a match against Vladimir Kramnik in 1998 to qualify to play as challenger for the classi ...

and

Alexander Grischuk Alexander Igorevich Grischuk (born October 31, 1983) is a Russian chess grandmaster. Grischuk was the Russian champion in 2009. He is also a three-time world blitz chess champion (in 2006, 2012 and 2015). He has competed in five Candidates T ...

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.

Triangulation with other pieces

For an example of triangulation with a

queen Queen or QUEEN may refer to: Monarchy * Queen regnant, a female monarch of a Kingdom ** List of queens regnant * Queen consort, the wife of a reigning king * Queen dowager, the widow of a king * Queen mother, a queen dowager who is the mother ...

, see the queen versus

rook Rook (''Corvus frugilegus'') is a bird of the corvid family. Rook or rooks may also refer to: Games *Rook (chess), a piece in chess *Rook (card game), a trick-taking card game Military * Sukhoi Su-25 or Rook, a close air support aircraft * USS ...

position at

Philidor position The Philidor position (or Philidor's position) is a chess endgame involving a drawing technique for the defending side in the rook and pawn versus rook endgame. This technique is known as the ''third defense'' due to the positioning of the d ...

. The game Fischer versus Taimanov, fourth match game shows a similar tactic with a

bishop A bishop is an ordained clergy member who is entrusted with a position of authority and oversight in a religious institution. In Christianity, bishops are normally responsible for the governance of dioceses. The role or office of bishop is ca ...

. A rook can also perform the maneuver, but a

knight A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the Gr ...

cannot.

Example with a rook

In this game between future

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and former world champion

Anatoly Karpov Anatoly Yevgenyevich Karpov ( rus, links=no, Анато́лий Евге́ньевич Ка́рпов, p=ɐnɐˈtolʲɪj jɪvˈɡʲenʲjɪvʲɪtɕ ˈkarpəf; born May 23, 1951) is a Russian and former Soviet chess grandmaster, former World Ches ...

, White triangulates with his rook 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

References

Bibliography * * * * * *

External links

Interactive King Triangulation Endgame vs Chess Computer
{{chess Chess terminology Chess tactics Chess theory Chess endgames