Monday, January 01, 2007

Pawn Endgame Basics

One of the fascinating things in pawn endgames is that they are very similar to mathematics. It works with a set of rules, many of them based upon more basic rules. What I try to do these days is to deduce the well-known rules of pawn endgames from the very basic rules.

1. Square of the Pawn
The most important question for the defending King: Is he inside or outside the square of the pawn running to queen? If inside, the attacking King must help his pawn to queen. The square of the pawn is a direct function of the ability of the King to move diagonally with the same vertical speed as the pawn.

2. The Back Rank Stalemate
The position with the defending King on 8th rank, the attacking pawn on 7th rank and the attacking King on 6th rank, all on the same file, is drawn by stalemate. From this position can derived the important rule that the attacking pawn must not give check on the 7th rank. And from this Silent Seventh Rank Rule can derived the rule that the King reaching the 6th rank in front of his pawn wins the game in any case.

3. The Key Squares
A key square for the attacker is a square that wins the game for the attacking King if he manages to reach it. A key square for the defender is a square that draws the game for the defending King if he manages to reach it. In both cases the win or draw is not influenced by the position of the other King or by the fact who is to move. The ultimate key squares for the attacker are those adjacent to the promotion square while the attacking king is able to defend his pawn. All other key squares are sufficient to bring the attacker to this ultimate situation by means of zugzwang. For instance if the attacker has the opposition in front of his pawn, he will reach the ultimate key square by force.

4. Corresponding Squares
For every square in relation to a key square there is one or more corresponding squares for the opponent King. Moving to one square while the opponent King is on the corresponding square is an advantage, leading to win for the attacker or draw for the defender. Being forced to leave a square while the opponent is on the corresponding square is a disadvantage, leading to draw for the attacker and to loss for the defender. The opposition, direct or distant, is just a special case of corresponding squares when there are no other pawns around.

5. Spare Tempi
Spare tempi are a very important means to set the opponent into zugzwang. It is very important to be aware of them and take them into account. If the opponent has a spare tempo, the rule of corresponding squares is just contrary: It is an advantage then to move away from a square while the opponent is on the corresponding square. The spare tempo also explains why the key squares of a single pawn on 2nd to 4th rank are not one, but two ranks before the pawn. If the defender gives opposition, the attacker parries it with a pawn move.

6. Counter Attack
Sometimes the defender, unable to stop the attacker to queen, can get his queen in turn, securing a draw or even a win.

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