You want to know if your king and pawn endgame will win? Use the rule of the square to calculate quickly.
Instead of the tedious process of counting all the moves, the rule of the square will provide a fast answer to the question.
Look at the following position.
You've probably noticed that the white king can't help its pawn?
The challenge now is to calculate if the white pawn can promote.
Can you do this?
If you didn't know the rule of the square, how did you do it?
Did you do it the hard way, by counting moves?
Let's do this together. White needs two moves to reach the seventh rank. If white is to move first, the black king will then stand on e6. (1. g5, Kd5; 2. g6, Ke6;) The white pawn will promote next move and there's nothing black can do to prevent this.
If you're like me, you'll find this process of counting the moves not very easy. Maybe it works well in a simple position like the above. But how about a more complicated position?
Ok, let's make this task very simple now.
If you're not yet familiar with the rule of the square, this may simplify your chess life.
Draw a diagonal from the pawn to the eighth rank. Now imagine a square that encloses the pawn, the queening square and the diagonal like below.
And here comes the Rule of the square : if the king can enter this square of the passed pawn, then it can capture the pawn before (or as soon as) it promotes.
Now, let's repeat our task. Find out if the pawn can promote safely.
If it's white's turn, the king will not be able to enter the square.
After 1. g6 we have to draw a new square.
Do you see? The king can't enter the square, so he can't capture the pawn. After 1...Kd5; 2.g7, Ke6; 3. g8Q, the king is too late.
Back to the original position.
If black is to move first, he can enter the square (1...Kd5).
This tells us, the king will capture the pawn. (2.g6, Ke6; 3. g7, Kf7; 4. g8Q+, Kxg8;)
You may check this using your chessboard.
The rule of the square is very useful in practice, but I want to warn you for some surprises.
Black to move, can he stop the white pawn from promoting?
Before scrolling down, try to solve this position.
The answer is.....
If you have drawn the square as before, you were tricked.
The pawn may take a double step on its first move. Therefore we need to draw a square as if the pawn was already one step further.
If you have done this, you can clearly see that the black king can't enter the square.
Now solve the next position. It's white's turn, can he promote the pawn?
This should be very easy for you now.
It's an exception because of the pawn's first move. It will ofcourse move forward two steps.
Before the pawn move, our square has to be properly constructed as if the pawn had already advanced one step.
We can see white to move wins (and black to move steps in the square and draws).
You can check the drawing of the square after white's first move. Black can't reach the square.
And here is another exception. White to move, will the pawn promote?
The shortest path to the queening square is blocked. The black king will have to take a detour to get there.
If white is to move first, black will be too late.
Although the black king is already in the square, he can't stay in the declining square after 1.f5, Kc5; 2. f6. The black king needs an extra move to walk around the pawn, and therfore white wins.
Do you see that after 2... Kc6; 3. f7 the king is too late?
I hope you now understand the rule of the square. It's most helpful in positions where the king isn't able to support his pawn. If the king can support the pawn things are very different.