The knowledge of this basic king and pawn vs. king ending will help you save games.
It's easy to apply. Once you've mastered it, you'll never forget it.
In this ending white has the extra pawn.
White would like to promote his pawn to a queen and win the game.
If you're black, and you know what to do, you'll be able to prevent this and drawn the game.
Now what do you have to do if you have to retreat?
I'll tell you: when you have to go back one step, stay in front of the pawn.
If you follow this advice, you'll draw the game.
Why is this important? Well, for one, it's easy to remember. But it has some real importance when you have to retreat for the last time, to the eighth rank.
If you follow my advice, you can't go wrong. But if you don't know this or created a wrong habit, you might retreat diagonally (as this isn't a problem on the other ranks).
We'll look at this "wrong" move now.
Black had to retreat for the last time. And now he thought it didn't make a difference which square to retreat to. So he went to c8.
Now white can play
And here black to move has a problem. He wants to stay in front of the pawn, because 1... kb8; simply loses (after 2. d7 the pawn will promote).
So he plays 1... Kd8;
But now after 2.d7, the king can't stay in front of the pawn. So it moves away with 2...Ke7.
And now, after 3.Kc7, the square for promotion is available for white only, so he will promote his pawn and win the game.
How did this happen? The black player didn't know the rule in this ending to "always retreat in front of the pawn".
Now you know how things can go wrong, let's look at the right way to play this king and rook vs king ending.
As I mentioned before, black has to stay in front of the pawn, especially when moving to the eigtht rank.
So he has to play 1....Kd8!
White will try to make progress. So he plays 2. Kc6 (or ke6).
Now is the time to play the right (and only) move again. If the black king moves away to e8, white can play Kc7, taking control over the d8-square so the pawn will promote.
To prevent this, it's necessary to stay in front of the king. Therefore the only move that draws is 2...Kc8!
Now, if white wants to make progress again, he has to play 3. d7+, after which black can stay in front of the pawn without any problems with 3....Kd8.
In the next diagram you can see the result.
If the white king moves away, black can capture the pawn.
So, the white king has to protect the pawn, but has access to only one square where this can be achieved.
Now it's black's move, but black can't move!
It's a stalemate and a draw. Can you imagine how happy black will be?! He saved a game while he was a pawn down.
And so can you!
I advice you to practice this endgame of king and pawn vs king. You can try to win with a pawn up. And you can try to defend with a pawn down. If you practice this with your chess-friends, you may be able to teach them something and have fun at the same time.
And you'll soon be able to draw this endgame on autopilot.