The Rule of the square

The most important rule for pawn promotion

In pawn endings, the most common goal is to promote a pawn to a queen. The reason is obvious: bringing a queen into the game would significantly alter the material balance and almost always ensure a win.

The rule of the square is a simple calculation technique that allows you to answer the question:

Can a pawn promote on its own or does it need support from its king?

Let’s start with an example position (white to move):

The only winning move is a4. You can break down the calculation needed for this position this way:

  • I play a4
  • They go Kf8
  • I play a5
  • They go Ke8
  • I play a6
  • They go Kd8
  • I play a7
  • They goKc8
  • I play a8Q+ and win :)

This is certainly doable but it’s a little error prone compared to using the rule of the square:

A pawn can promote without king assistance if the opponent’s king is outside the square of the pawn.

In the example presented, the pawn is on a2 but, since it’s white to move, a4 creates a square that ends on e8. Because the king is on the g8 square, it cannot reach the square with one move.

Here’s one way to picture the square:

And here’s another way to picture it:

The diagrams also illustrate another important point: the opponent king will not catch the pawn if it cannot enter the square in the very next move. In fact, if we go back to our first diagram (black to move):

Kf8 or Kf7 draw the game as the black king would be in time to enter the square of the pawn on e2. As often happens in endgames, the result of a position depends solely on who’s turn is. It’s a pretty amusing aspect of Chess.