Triangulation is atactic used inchess to put one's opponent inzugzwang (a position in which it is a disadvantage to move). Triangulation is also calledlosing atempo orlosing a move.
Triangulation occurs most commonly inendgames with onlykings andpawns 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 crucialtempo and reached the same position with the other player to move. Triangulation can occur in other endgames and even in somemiddlegames.[1]
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Consider this position, with White to move. Here, Black has theopposition 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 arecorresponding 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 inzugzwang. There may follow:
and White will win.[2] (There are other ways for White to win after her third move.)
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In this 1978 game betweenLev Alburt and future World ChampionGarry Kasparov,[3] Black wins by triangulating:
and Whiteresigned. After 57. Kf1 Ke4! 58. Kf2 Kf4 59. Kf1 Kg3, Black wins the white pawn.[4]
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Triangulation can occur in endgames other than king and pawn endgames, such as this game in the 1965Candidates Tournament, in which futureWorld chess championBoris Spassky defeated former world championMikhail Tal and won the right to challenge the then-current championTigran Petrosian.[5] 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 .[6]
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Usually when a king triangulates in a king and pawn endgame, it is close to the other king and triangulation gains theopposition, putting the opponent in zugzwang. This position (from analysis of a game betweenAlexey Shirov andAlexander Grischuk in New Delhi in 2000) shows an example when the kings are far apart.[7] White triangulates to put Black in zugzwang:
and amazingly Black is in zugzwang. The game could continue:
and White wins.[8]
For an example of triangulation with aqueen, see the queen versusrook position atPhilidor position. The gameFischer versus Taimanov, fourth match game shows a similar tactic with abishop. A rook can also perform the maneuver, but aknight cannot.[9]
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In this game between futureFIDEWorld ChampionVeselin Topalov and former world championAnatoly Karpov,[10] White triangulates with his rook to put Black in zugzwang:
back to the same position and Black is in zugzwang. The game continued:
Bibliography
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