End Game Study : Triangulation with your king

In order to learn triangulation you must be aware of the concept of Key Square and Opposition if you are not aware please click on below relevant links.
Key Square
Opposition 

What is triangulation?

It is maneuver with your pieces or majesty to pass move or say it is maneuver by which you lose a tempo. In simple terminology by triangulation you get the same position with your opponent to move when it is disadvantage for your opponent to move.

Why to lose a tempo or move?

In chess it is better to gain a tempo; you might have heard those words from your coach or senior players. Yes that is true but some time you need to put your opponent in zugzwang in order to penetrate into opponent’s position. In zugzwang your opponent has to move but if he moves, he lose.

Now I would like to explain it with help of below example.

In the given position if it black to move then white can win easily as he has opposition but what if white has to move in the same position. Direct progress is not possible for example f6 then…Kf8! Draws.

How to triangulate to win the position?

You can win the position by triangulation that is move your king into triangulation shape. Kd5->Ke4->Kd4 and you can gain the same position with black to move. See the below diagram.

More specifically
Kd5 - Kf6
Ke4 – Ke7
Kd4
Now wherever black move you can get the opposition so can win the game.

….Kf8
Kd6 (Diagonal Opposition) – Ke8 
Ke6 (Direct Opposition) – Kf8 
Kd7 – Kg8
Ke7 – Kh8
f6 – gf6
Kf7 (Reaching to the Key Square of g6 pawn) and winning the position.

Practical Implication of theory

Game : Max Euwe - Hartingsvelt HV in 1922

Test Positions :

Position 1 : White to Move

Position 2 : White to Move

Position 3 : White to Move

Solution will be published in next endgame study section.

Solution for the test positions of rule of square (4th March 2013)

If you would like to retrieve last endgame study puzzles Click here.

Position 1

1. Kg6 Kb6 (1... h5 2. Kxg7 h4 3. Kxf6) (1... f5 2. Kxg7 f4 3. Kf6 f3 4. Ke7)

2. Kxg7 h5 (2... f5 3. Kf6 f4 4. Ke5 f3 5. Kd6) 3. Kxf6 h4 4. Ke5 Kxc6 5. Kf4 draw 

Position 2

1. Kb7 a5 2. Kc7 Kc5 (2... a4 3. f5) 3. Kd7 Kd5 4. Ke7 Ke4 5. Ke6 Kxf4 (5... a4

6. f5) 6. Kd5 draw

Position 3

1... h5 2. Kb4 Kb6 (2... h4 3. Kc5 h3 4. Kd6) 3. Kc4 h4 (3... Kxc6 4. Kd4) 4.

Kd5 Kc7 (4... h3 5. Kd6) 5. Ke4 draw