What follows is a rough english translation of something I posted in finnish a while back.
Our topic is the elementary ending of a single pawn and king vs. a lone king. Every serious chess player should have a solid understanding of this endgame. For one thing, it's one of the simplest endings and many of the more complicated endings can, after trades, simplify into it. You need to be able to recognize well ahead in time whether or not such transformation is good for you. The relatively simple nature ot this ending also means that if you make a mistake the chances are you'll get punished. Finally, studying them also teaches some usefull techniques and concepts for the more complicated endings.
The basic idea for the defending side should obviously be to bring his king in front of the pawn when the attacker should in turn bring his king to support the pawn's advance. We'll be mainly dealing with positions containing such kings placement.
We shall use the following common notation:
- +- white is winning
- = equal
- -+ black is winning
Pawn on the 6th rank
White wins if he manges to gain control of the promotion square f8 with his king. However, with white to move this is impossible. For example 1. f7+ (with a check) Kf8 2. Kf6 ends in a stalemate! With black to move things are different: 1... Kf8 2. f7 (without a check) Kg7 3. Ke7 +- and promoting next turn. We can formulate the following rule about the pawn on the 6th rank: When the attacking side moves his king next to the pawn on his 6th rank, the defender must immediately place his own king on the 8th rank opposite to the attackers king. If this is possible, the defending side can draw, otherwise the attacker wins.
Zugzwang
If black were allowed to keep his king in f8, white could never win. Black looses because in chess, unlike in some other board games, a player must move every turn. In such a situation, where a player would rather pass this oblication because every move weakens his position, we say that he is in zugzwang. Zugzwang is rare with many pieces on the board but in the endgame it's quite common. In fact, many common endings cannot be won without the use of the zugzwang (just think rook and king vs. king!).
Wing pawn
Consider the following position:
According to the rule given above black should loose because he can't reply 1. Kg6 with Kg8. However, the lack of an i-file allows the defence 1. Kg6 Kh8 2. h7 stalemate! Thus winning with a wing pawn is considerably harder. We'll return to the case of a wing pawn in the part III of this series but for now what we shall say is only assumed to be true for a pawn on the b-g files. Between these pawns there are no major differences.
Pawn on the 5th rank
The attacking player should not advance the pawn too eagerly because then the defending side can usually reach the draw as in the first position above. Instead one should first try to improve the king so that when the pawn finally advances to the 6th rank that draw is unavailable. This may not always be possible but here's an example. The reader should make sure he/she understand (no need to memorize) all variations.
Carefull analysis shows that white wins with a pawn on the 5th rank if his king reaches one the 6 key squares depicted in the next diagram.
If white's king reaches one of these key squares he wins regardless of where the black king is (well almost, obviously black should not be able to capture the pawn!). Conversely black can usually draw if he manages to forestall white from entering one of the key squares.
Pawn on the 4th rank
When the pawn is on his 4th rank, the basic idea for the attacking side is to get his king into one of the key squares for the pawn on the 5th rank before advancing the pawn. Using this principle we find the next three key squares for the pawn on the 4th rank.
