If you are trying promote a pawn, you need to know if the king can stop you. This can be time consuming. However, by knowing the “rule of the square ” you can instantly know if the King can catch your pawn.
With White to move, once you push the pawn and it enters the 3 by 3 square, if the Black king can enter the square on his next move, it will catch you.
For example: 1)b6 Kd7 2)b7 Kc7 3)b8=Q KxQ This works for all squares, not just 3-by-3s. Try it yourself on any size square. If the king cannot enter the square after your pawn did, then he cannot catch you.
In this next example, can you quickly tell if the white pawn can queen? Could you do it with just seconds on your clock? Let’s look again at it, but this time, with the “rule of the square” in mind.
If White to move first:- 1) a4 (entering the square) Kf5 (still outside the square) 2) a5 Ke6 3) a6 Kd7 4) a7 Kc7 5) a8 = Q and the Black king doesn’t make it, a win for white.
Now if it’s black to move first:- 1) …..Kf5 he steps up to the edge of the square. 2) a4 Ke6 both pawn and King are now in the same square 3) a5 Kd7 4) a6 Kc7 5) a7 Kb7 6) a8 = Q KxQ. This position is a draw.