Triangulation - A Key Endgame Concept

Intro to Triangulation

In king and pawn endgames, the main things to remember are opposition and tempi/time. Who has the upper hand is always based on whose move it is, and oftentimes who has to yield their defense to the opponent.

In some cases, there is a dream position that you may achieve, but because it is your turn you cannot keep it. However, if it was the opponent to move, it would be an easy win.

So, how do we accomplish this? How can we manipulate our position such that we achieve the same position, but with black to move (assuming we are playing with white)? In other words, how do we lose a tempo?

The name for this is 'triangulation.' It gets its name as the king does a three move manouevre which resembles a triangle shape.

Usually this concept is taught to beginner and intermediate players as it is at the basic endgame level, but recently it was observed at the highest level possible. We will be analysing this game in this blog post.

Norway Chess

The 2024 Norway Chess is a competitive chess tournament featuring some of the best grandmasters in the world. Among the 6 players are WC Ding Liren and the top 3 players in the World (namely Carlsen, Nakamura, Caruana). Round 7 concluded today, and you can see more in the lichess coverage or on the official website. However, our interest lies in a particular game between Carlsen and Alireza Firouzja in Round 5 of the event.

Carlsen-Firouzja, Round 5

At the end I will attach a link with the full game played, but we will fast foward the game all the way to move #77.

Carlsen just played 77. Rd6 with 90 seconds on his clock. Firouzja has 23 seconds. At this point there is 10 sec increment for both players. Here is the situation: does black play Rxd6 and try and hold the resulting endgame?

Of course, with 23 seconds and a lot on the line this is hard for anyone to play with Black. Black has to maintain the rooks and play something like Rb2 and Rb1. White will take on h6, but the split f and g pawns ensure that with precise play Alireza can hold.

However, in 14 seconds Alireza plays the fatal 77...Rxd6?? losing the game on the spot. After Kxd6 Kf7 Ke5 Ke7 f6+ Kf8 we have the following critical position for our analysis:

If this position was black to play, it would be an easy win for white. If Ke8 or Kg8 then Ke6 and white will queen the pawn. Please note, if Ke8 Ke6 Kf8 f7 Kg7 Ke7 Kh7 it is important note to play f8Q?? as that would be stalemate. Instead the game is won easily by Kf6, see the second attachment. If Kf7 then Kf5 gains opposition and gets entry into g6.

So, given that it is Carlsen's turn, how does he get the same position but with Alireza to move?

https://lichess.org/broadcast/norway-chess-2024--open/round-5/VFMWFVLX/OYEUDx9y
https://lichess.org/study/Phi57x1f/OSkk5XCa (with post game analysis)