Triangulation (chess)
Encyclopedia
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 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 .
, 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:
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:
and White will win . (There are other ways for White to win after his third move.)
and future World Champion Garry Kasparov
, Black wins by triangulating:
and White resigned. After 57. Kf1 Ke4! 58. Kf2 Kf4 59. Kf1 Kg3, Black wins the white pawn .
, 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:
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 .
, 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:
and amazingly Black is in zugzwang. The game could continue:
and White wins .
, 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 .
Veselin Topalov
and former world champion Anatoly Karpov
, White triangulates with his rook to put Black in zugzwang:
back to the same position and Black is in zugzwang. The game continued:
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
to put one's opponent in zugzwang
Zugzwang
Zugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...
. 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 move, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo"...
or losing a move.
Triangulation occurs most commonly in endgames with only kings
King (chess)
In chess, the king is the most important piece. The object of the game is to trap the opponent's king so that its escape is not possible . If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture on the next move. If this cannot be...
and pawns
Pawn (chess)
The pawn is the most numerous and weakest piece in the game of chess, historically representing infantry, or more particularly armed peasants or pikemen. Each player begins the game with eight pawns, one on each square of the rank immediately in front of the other pieces...
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 move, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo"...
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 oppositionOpposition (chess)
In chess, opposition is the situation occurring when two kings 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" . It is a special type of zugzwang and most often occurs in endgames with...
, 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.)
- 1...Kc6 (if 1... Ke7 then 2. c6 and white wins by promotingPromotion (chess)Promotion is a chess rule 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 color . The new piece replaces the pawn on the same square and is part of the move. Promotion is not limited to pieces that have...
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
Zugzwang
Zugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...
. 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.)
Triangulation with the king
In this 1978 game between Lev AlburtLev Alburt
Lev Osipovich Alburt is a chess Grandmaster and a well-respected chess writer. He was three-time Ukrainian Champion, and after defecting to the United States in 1979, became three-time U.S. Champion.-Career:...
and future World Champion Garry Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....
, Black wins by triangulating:
- 55...Kf5!
- 56. Kg1 Ke5
and White resigned. 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 Candidates TournamentCandidates Tournament
The Candidates Tournament is a chess tournament organized by the world chess federation FIDE since 1950, 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 Soviet-French chess grandmaster. He was the tenth World Chess Champion, holding the title from late 1969 to 1972...
defeated former world champion Mikhail Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....
and won the right to challenge the current champion Tigran Petrosian
Tigran Petrosian
Tigran Vartanovich Petrosian was a Soviet-Armenian grandmaster, and World Chess Champion from 1963 to 1969. He was nicknamed "Iron Tigran" due to his playing style because of his almost impenetrable defence, which emphasised safety above all else...
. 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 oppositionOpposition (chess)
In chess, opposition is the situation occurring when two kings 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" . It is a special type of zugzwang and most often occurs in endgames with...
, putting the opponent in zugzwang. This position (from analysis of a game between Alexey Shirov and Alexander Grischuk
Alexander Grischuk
Alexander Igorevich Grischuk is a Russian chess grandmaster and Russian Champion in 2009.-Chess career:In the FIDE World Chess Championship 2000, Grischuk he made it to the semifinals, losing to Alexei Shirov....
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 queenQueen (chess)
The queen is the most powerful piece in the game of chess, able to move any number of squares vertically, horizontally, or diagonally. Each player starts the game with one queen, placed in the middle of the first rank next to the king. With the chessboard oriented correctly, the white queen starts...
, see the queen versus rook
Rook (chess)
A rook is a piece in the strategy board game of chess. Formerly the piece was called the castle, tower, marquess, rector, and comes...
position at Philidor position. The game Fischer versus Taimanov, fourth match game shows a similar tactic with a bishop
Bishop (chess)
A bishop is a 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 piece in the game of chess, representing a knight . It is normally represented by a horse's head and neck. Each player starts with two knights, which begin on the row closest to the player, one square from the corner...
cannot .
Example with a rook
In this game between future FIDE World ChampionWorld Chess Championship
The World Chess Championship is played to determine the World Champion in the board game chess. Men and women of any age are eligible to contest this title....
Veselin Topalov
Veselin Topalov
Veselin Aleksandrov Topalov is a Bulgarian chess grandmaster. He currently has the sixth highest rating in the world, and was the challenger facing world champion Viswanathan Anand in the World Chess Championship 2010, losing the match 6½–5½....
and former world champion Anatoly Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...
, 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 .
See also
- Corresponding squaresCorresponding squaresCorresponding 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...
- Key squareKey squareIn chess, particularly in endgames, a key square is a square such that if a player's king can occupy it, he can force some gain such as the promotion of a pawn or the capture of an opponent's pawn. Key squares are useful mostly in endgames involving only kings and pawns...
- OppositionOpposition (chess)In chess, opposition is the situation occurring when two kings 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" . It is a special type of zugzwang and most often occurs in endgames with...
- Tempo (chess)Tempo (chess)In chess, tempo refers to a "turn" or single move. When a player achieves a desired result in one fewer move, he "gains a tempo" and conversely when he takes one more move than necessary he "loses a tempo"...
- ZugzwangZugzwangZugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...