Key Squares

I've decided to write a bit about endgames because I am not very good at them, have never been very good at them, and have never much liked them either. I'm not sure why. I think it's because if you blunder in the middlegame, you are often still in with a shot, even if you are a piece down. But in the endgame, if you blunder then you are done. This brutal reality is actually one of my least favourite aspects of chess, and one of the reasons why I prefer other games such as backgammon.

About 10 years ago, I read Silman's Complete Endgame Course up to the point where I got stuck, and really enjoyed it. I thought I had a few fundamental positions such as king + pawn versus king, the Lucena, and the Philidor, down pat. But when someone asked me a basic question about what to do in the following position, I actually managed to answer incorrectly.

I had the drawing technique right. For Black here, all you have to know is that you should step straight back with the king if forced to move away from the square in front of the pawn. That way, it can never queen.

You can also draw without following this "straight back" method, but "straight back" is the easiest for me to remember.

But then, someone asked me how to win this position as White, and I confidently explained that you need to reach one of three key squares, which are the three squares directly in front of the pawn, so d5, e5 and f5 if the pawn is on e5.

However, this is not correct! The key squares are actually the ones two ranks in front. That is, d6, e6 and f6.

The rule is: if White can reach a key square, he wins. If Black can prevent this, then it's a draw.

And, if Black does manage to prevent it, then we already know the drawing technique. So the whole battle is whether White can reach a key square or not.

Here, white wins. Even with a heroic effort, Black can't prevent white from reaching one of the key squares, namely f6. Notice that this is the key square which is furthest from the Black king.

Now you should have no problem deciding the result of this position, with White to move.

Black just runs the king to e6 and guards all the key squares. From this point, we already know how to draw.

There's one slight subtlety in these endings though. How about this position?

If white takes the direct route, via Kd2-d3-d4, Black blocks with Kb7-c6-d6 and it's a draw. But there's another key square which, despite appearances, is the same distance away, namely f6! White needs 5 moves to reach any of d6, e6 or f6. But Black needs at least 5 moves to reach f6. So White's winning try is Kd2-e3-f4-f5-f6. And it turns out that there's no way to stop it!

Isn't that beautiful? Doesn't it remind you of the Reti study? The trick is that two squares are the same distance away for one player, but not for the other, because of the peculiar geometry of king moves in chess; it takes exactly the same amount of time for the king to move a distance of √2 as it does to move a distance of 1, so our eyes deceive us.