According to SOPE of Müller and Lamprecht this is the definition of a key square:
A square is described as a key square when its occupation by the king secures the win, no matter who is to move.
Since the Nalimov database reports a mate in 28 when white to move and a mate in 22 when it is black to move, the king on d2 is already on a keysquare according to this definition. Which proves that this definition is useless for practical situations. Besides that, it makes the choice of the keysquares (d4, e3, e2) by the authors of SOPE when they treat this position rather arbitrary. I already suspected so.
I have not thought about a better definition of a key square yet. In this position I would like to call d4 and e3 the key squares where white wants to invade.
In stead of working with numbers I found it much more clear when I work with colors.
In order to decide which color a square must have, I used the following steps:
- Determination of the invasion squares d4 and e3
- 0-move. Decision that you want to be in this position again, but with black to move in stead of white.
- 1st move. Determination that white can't move the pawn. Determination that white can play one of the following moves: c3, c2, c1, d1, e1. Determination that black has only 3 squares available: e3, f3, f4. The g- file is tabu since it is too far from the invasion squares. The 2nd rank is tabu because black must stay in the square of d3 to prevent promotion. Moving to a green square by white allows black to attack the pawn on d3, which limits the possibilities of whites next move, so 1.Kc2 is the move to play. Black can only answer with 1. ... Kf4, since he must be able to parry Kc3 with Ke3.
- 2nd move. White can do the triangulation by stepping twice on a blue square 2. Kb2 and 3.Kb3. Since black has only one blue square he can't keep up and white "loses a move".
- If black answers something different after 2.Kb2, for instance 2. ... Kf5, then white has to move to a green square. Not 3. Kc3 since that is parried by 3. ... Ke5, but to 3.Kc1. Black cannot keep up since f5 is not adjacent to a green square. Black can try 3. ... Kf4. White answers with 4.Kc2, which is a yellow square. Since black is already on a yellow square, he can't follow. If black moves to 4. ... Kf3, then white plays 5. Kd2 and he has reached the same position as the start position, but now with black to move. When black moves away from f3 then white can penetrate into the black position.