Discover the critical squares and use them!
The concept of critical squares looks a lot like the concept of key squares.
Where the key square is used to calculate whether or not you'll be able to promote a pawn, the critical square is used to calculate if you can win a pawn.
In this position, with blocked pawns, you see the critical squares of the d5-pawn.
This pattern of critical squares is always the same for blocked pawns. It's three squares on either side of the pawn.
Why is it useful to know about critical squares?
The importance will be clear to you if you know the following rule.
If White is able to occupy one of the critical squares with his king, he'll be able to win the d5-pawn.
Let's look at an example.
In this position White will be able to occupy one of the critical squares. If White is to play, then 1.Kg5 will do the job.
All Black can do now is try to protect his pawn.
3.... Kc6; 4.Ke6,
And now Black can no longer defend the d5-pawn.
White has won the pawn, as predicted. Does this guarantee the win as well?
Unfortunately, in this position it doesn't.
Black is able to reach a draw by playing 5....Kd7;
If you've studied the page about key squares, you'll know this is drawn position.
White will not be able to occupy any of the key squares.
Could you have foreseen this in the starting position?
I give you the starting position again, now with the key squares made visible with dots.
As you can see, the black pawn is not on a key square. This means that, once you capture the pawn, you're not automatically winning.
If we move the pawns one row up, things change dramatically (because the key squares are different there).
The critical squares (left image) and the key squares (right image).
You can see that with capturing the black pawn, the king will be on a key square.
This helps you to see very quickly if a position is winning.
You know that if you're able to occupy a critical square with your king, you'll win the Black pawn. And as soon as you capture the pawn, you'll be on a key square, so you'll promote your own pawn and win the game.
Blocked pawns have a lot of critical squares.
White wants to occupy the squares marked with a pink X.
Black has to reach a square marked with a black X.
What happens if both sides are able to occupy one of their critical squares?
Both sides are only two moves away from reaching their critical squares.
In these type of positions, the one who first makes contact with the winning square wins. Where is the winning square located?
In this position, for White the winning square is e7. For Black it's c4.
If one of the kings arrives at his winning square first, it attacks the enemy pawn.
The other king must then defend the pawn, but will only have one move to do so.
The defending king will then be brought in Zugzwang and has to let go of its pawn.
Let's play this position.
1.Kf5, Kb6; (We already know that defending the pawn doesn't help).
2.Kf6! (not 2.Ke6, Kc5; Now White can't defend its pawn and loses), Kb5;
Both sides have arrived at their critical squares.
3.Ke7!, occupying the winning square.
White threatens to win the d6-pawn.
3....Kc5 (the pawn has to be protected);
The d6-pawn is protected for now. But the winning square isn't called winning square for no reason.
Black has no legal move left to protect his pawn. White will capture the pawn next move and will be free to promote his own pawn.
You now know what critical squares are and how to use them.
From now on, if you see blocked pawns, I hope you'll remember two things.
1: the critical squares you have to conquer (or defend).
2: the winning square you have to occupy if your opponent reaches his critical square as well.