Triangulation is an endgame tactic in chess performed with the intent of the player wasting a move and forcing the opponent into a zugzwang (a position where all possible moves lose the game). This is done by intentionally losing tempo (or a move) with the king.
It is implemented with the idea of forcing an opponent into a zugzwang (a position where every move is a bad one) which gets the player to gain some initiative, usually done but not limited to the King.
Being able to move in chess is both a blessing and a curse depending if there is actually something to be accomplished. A zugzwang for example is being forced to move even when no good moves are possible.
This is why it is sometimes better to waste a move with the goal of passing your own turn to the opponent, such is the nature of Triangulation. It is a famous endgame that I will discuss in this article.
I think this is an important discussion if we ever want to master endgames, there are positions where triangulation is necessary. To be honest this is something that I don’t apply much to my own games, not because it not a good concept.
It’s just not as popular as the other endgame principles out there. Creating this article is a win-win. I get to have a new article plus I also learned a new concept. I also want you to learn about this, let’s talk about it in detail.
Tempo refers to the amount of time or moves a player can apply to complete its goals, where a position that has utilized tempo usually has a more active game.
A knight attacking the queen for example will make that particular side gain tempo, since the queen will have to move another tile costing it time.
This is why it’s not recommended to move the same piece in the opening since you would lose “time/tempo” that could have been spent on other pieces.
However, there are situations where it’s actually better to waste a move, especially when putting an enemy into a zugzwang.
Triangulation and Zugzwang
Zugzwang is a position where a player is forced to move into a losing game since every move is will lead to a losing position.
The idea behind triangulation is to basically circle around to venture into the exact same position where it’s the opponent’s turn to move instead of yours.
Now you might think it’s stupid but it’s really not, especially if the opponent has no good moves that it requires them to make concessions.
To better illustrate this, here’s a perfect example of triangulation.
Let’s say you have this position as White:
Black has the “opposition” in this case, which if you don’t know is really important to understand this idea.
It’s actually one of the most important concept in endgames, which I highly recommend you should at least consider to learn.
I’ll leave a link here (will open in a new tab) that is very succinct, but also a very complete guide of a chess opposition.
Getting back to the topic, black having the opposition basically means that it is capable of keeping the white king away just by staying in its front.
When two kings are in front of each other, the one not having to move is said to have the “opposition” means it can keep the other away from going in.
This is actually a draw if the white king has no means of taking back the “opposition”(White is to move), since the pawns will just fall if pushed.
But there is a way! If white follow this route:
Just like a triangle? Let’s play it shall we?
Black would have to keep an eye to the pawns since white just wins if those can advance.
The game would look something like this:
Which ends up in this position:
It’s exactly the same situation from earlier! except this time black is to move where white has the “opposition”.
White can now easily end this:
If the original position is played where white is to move and black has the “opposition”, the game would instead look like this:
The White King cannot make progress since the end result will just be a draw if one of the white pawn is pushed.
Now let’s take a look on over the board samples that would further demonstrate this:
First we’ve got a match between Lev Alburt (strong player) and Garry Kasparov (future world champion) in 1978.
Albury vs. Kasparov (1978)
Albury is white while Kasparov is black in this position which seems easily winning for black, but it’s really not.
Let’s play one of the most straightforward approach:
A stalemate! a lot of variation also ends up into white drawing this, black would actually need to triangulate to return in this position with white moving first instead of black.
This is what Kasparov did:
And black has won! It’s only a matter of time like presented below:
Believe me or not, this is actually the only way to win this position for black, anything except triangulation is a draw.
Let’s head into another in-game example between Tal (former world champ) and Spassky (future world champ) in 1965.
Tal vs. Spassky (1965)
Tal is White while Spassky is black in the position below:
If you noticed this is actually a zugzwang for White, there are no rook nor pawn moves, and if the king moves then black pawn just gets advanced.
The problem is black actually gets the move here, therefore white is not in zugzwang.
But we can triangulate! to return in this exact same position with white instead having to move.
The game actually continued that way:
Which ends in this position:
And voila (same position)! white is to move and is therefore forced to allow the pawn to advance, Spassky eventually won this.
Here’s one of the ways the game could’ve ended (as a sample not from the match):
Now, you might believe that the Triangulation tactic can only apply to the king, but that’s not actually true.
There are cases where other pieces have performed such spectrums! Like the sample below that involves a rook triangulating.
Triangulation using a Rook
It was 2002 during a match between Vaselin Topalov (Fide World Champion) and Anatoly Karpov (Former World Champion) where Topalov has White and Karpov is Black.
The following position is realized over the board:
This actually has some potential for a zugzwang, since black king cannot afford to move away from the white pawn (it’ll promote) nor push the black pawn since the rook just captures.
Doing a triangulation in this kind of positions is usually a good idea just to see what concessions the opponent will produce, however we can’t triangulate with the king here (it’s trapped).
But we can with the rook! we can make it so the position will circle back to this one with black having to move instead.
Topalov performed a triangulation using the rook:
And we’re back to the same position, but black has to choose a move now.
Karpov opt to stuck the King on the last rank:
Topalov’s Rook cut the king again! another zugzwang, white has to make some kind of a compromise that gives black chances.
Karpov decides to make a rook move which finally allows the trapped white king to break free from the last rank:
Believe it or not this is winning for white; its king after all can pursue the rook while defending the white pawn at the same time, giving room for promotion.
The game was actually over at this point, black resigned and white won.
I used an engine provided by Lichess (Stockfish) to see its strongest recommendation for black and how it falls still.
This is how white would have eventually won if the match have continued:
So it’s a king/queen against king/rook ending which is winning for black (although difficult to accomplish), and Karpov believed that Topalov can win this.
This opportunity wouldn’t have occurred if the rook hadn’t triangulated.
Speed is a component to properly accomplish goals in chess which is important, but not always!
Sometimes it really is beneficial to waste moves for forcing an opponent into making a difficult choice, in other words to provoke weaknesses.
The triangulation technique does exactly that! and is something you should implement in your own games if there’s an opportunity.
Sleep well and play chess.