Elementary pawn endings II
The main points of the part I of this article can be summarised with the following two diagrams representing the key squares of a pawn on the 5th and one on the 4th rank.
With correct play white is quaranteed a win if his king reaches one of these key squares whereas black generally gets a draw if he manages to prevent this.
Corresponding squares
Often pawn endings boil down to a battle of the kings about posession of certain key squares. A very general method of analysing this battle is the theory of corresponding squares. This often allows finding clearcut solutions to very complicated endings although the associated system of corresponding squares can become very extensive. In our situation things luckily aren't too complicated.
Let's assume white is trying to break into one of the three key squares (e6-g6) in the next diagram with his king and black tries to prevent this.
When white's king is in f5 he threatens to enter in each of the key squares. Only way for black to secure all of the key squares is with the king in f7. Since black must immediately reply with Kf7 whenever white plays Kf5 we say that f5 and f7 correspond to each other which has been denoted with the number 1. Another way to think this is that due to the symmetry of the situation these are squares of mutual zugzwang: when the kings are in these squares the player with the move looses the battle about the key squares.
When white's king is in g5 black must, in addition of securing the two key squares (f6,g6), be ready to meet Kf5 with Kf7. Thus the only possible place for the black king is g7 and g5,g7 correspond to each other. Similarily e5 and e7 correspond to each other. Working backwards, when white's king is in f4 he threatens to enter into any of the squares marked with 1-3 so black's king should be in f8 (or f6). Thus f4 and f8 correspond each other (we prefer to leave the key square f6 without a number). Continuing this way we also find the rest of the corresponding squares in the diagram.
We have only marked the most important squares. If one desires, it's possible to continue this analysis further. For example we find out that when white plays Kd5 black can reply either Kd7 or Kf7.
Of course, we are more interested about the position with a white pawn in f4. This increases black's defensive potential: because white can't use f4 for his king, f8 now corresponds to both e4 and g4.
Let's see a short example how this works in practice. In the next position black can achieve the draw with the best play but this requires finding several only moves. The first move, in particular, may appear unintuitive for the untrained eye.
The pawn on the third or second rank
The pawn on 5th rank had three key squares right in front of it on the 6th rank but when the pawn was on the 4th rank it was necessary to ensure the access to the key squares of a pawn on the 5th rank and consequently the key squares were two rows ahead of the pawn on the 6th rank.
With the pawn on the 3rd rank the attacking side should also make sure he has the acces on the key squares of the pawn on the 4th rank before advancing. This may lead one to suspect that the key squares of a pawn on the 3rd rank might be whole three rows ahead of the pawn on the 6th rank. However, two rows is quite sufficient. To understand why this is, consider the following position.
With black to move, he must give way and white can conquer the key squares of the pawn in f4: say, 1... Ke7 2. Kg6 Ke6 3. f4 +-. But even with white to move, he can force the black monarch to give way: 1. f4! Ke7 2. Kg6! +-. White succeeds because he has a waiting move with the pawn. This is called a reserve tempo. If the pawn were on f4 to begin with, there's no such reserve tempo and, with white to move, the position would be drawn. This is the reason why the squares right in front of the pawn are not key squares for a pawn on 2nd-4th rank whereas the squares two rows ahead of it are.
Summary
We have studied the ending of king and pawn vs. king with a non-wing pawn and the defending king in front of the pawn. It's probably usefull to memorize the key squares of pawns on different ranks (3 squares right in front of the pawn and further 3 two rows ahead of the pawn for a pawn on 5th rank and 3 squares two rows ahead of the pawn for a pawn further back). In my opinion there's nothing else that really deserves memorization but one should of course study the examples for typical techniques. It's also usefull to be aware of the concept of Zugzwang and reserve tempo and have some idea what the theory of corresponding squares is all about. Finally and most importantly, one should do plenty of exercises. I'll intend to provide some in a later post but next there's a part III.
