The Rule of the Square

When does this apply?

The Rule of the Square is very helpful especially in pawn endgames, when the attacking king is out of reach of supporting the pawn. Using this technique a player can determine whether he/she can successfully promote the pawn, or if the enemy king will be in time to stop the pawn.

Using the Technique

Let's take this sample position:
White is trying to queen the pawn, and black is trying to stop the promotion. Clearly the white king is far away from the action and cannot support the pawn.

Case 1: White to move. Is white winning or can black draw?

Well it turns out that white is winning due to an extra tempo. The natural move here is a5, which white will go ahead and play. Pay attention to the diagram below.
The white pawn is on a5, and the promotion square is a8. This length is 4 units (an arbitrary measurement) (though the promotion square is 3 squares away).
What you can do is draw a 4x4 square, with the corners a5, a8, d8, and d5. Note that it is black to move here.
Now, even with black to move, black is not able to enter the square of the pawn. Ke5 is 1 square away, but the King is not in the square. And so it can be safely determined that white will successfully queen the pawn.

Case 2: Black to Move

Now let's go back to the original position, but this time it is black to move. And so the pawn will be on a4 and the square will be drawn as such:

Because it is black to move, you can clearly see that both Ke4 and Ke5 will allow the King to enter the square of the pawn. And so black is able to draw. A sample line is
1...Ke4 2. a5 Kd5 3. a6 Kc6 4. a7 Kb7 5. a8=Q+ Kxa8 and the game ends in a draw.

Case 3 - The black king's path is obstructed

Consider the position below. Note: the white king has been moved to f1 but this makes absolutely no difference.

This is black to move, and the square of the a4 pawn has been drawn. Considering what we have discussed, you may be inclined to say that Ke4 is a draw, as the King is in the square of the pawn.
However, this is a special case where despite Ke4 being in the square black is still losing. This is because the king will need to go diagonally left to a8 in order to stop the pawn (see below):

Unfortunately for black, his own pawn on c6 obstructs the path for the black King, and so this is the one time where Black wishes he didn't have a pawn like this. White is clearly winning because after a5 black will have to go around the pawn with Ke5 and after a6 Kd6 a7 black is not in the square.

Now of course this rule is applicable only if the white king is too far. If the white king is close enough it can of course support the pawn's promotion and lay the red carpet.

Conclusion

That brings this to a close. I hope this has been helpful. Please like and follow for more blog posts in the future. Until then, cheers!