King vs king & rook-pawn position?

Hello, everybody! I am trying to learn the theory of king vs king & pawn endgame. For the purpose of clarity, in this post, I will refer to the white king as the one with the pawn.

The first thing I have learned is the "rule of the square": If the black king cannot step inside the square, then the pawn can queen without its king help.

However, if the black king can step inside the square, the pawn will need the help of its king.

In Wikipedia [1], I have learned the concept of key squares: "A square such that if White's king occupies it, White can force the pawn to promotion, regardless of where the black king is and regardless of which side is to move, and against any defense."

Wikipedia suggests that the key squares of White when the pawn is an h-file pawn are g8 and g7. But how is it possible? In the following position, white cannot, of course, force a draw:
lichess.org/9ektIBpl

So how is it possible that those are key squares?

Thanks!

[1]en.wikipedia.org/wiki/King_and_pawn_versus_king_endgame#Key_squares

@Sipo #1 In your example the white king has indeed reached a key square, but the position of the defending black king is too good regarding the backward white h pawn. The white h pawn is simply too far away from the promotion square h8.

Does that answer your question ?
Maybe useful for futher reading :
en.wikibooks.org/wiki/Chess/The_Endgame/Pawn_Endings

@achja - Thanks! Well, that is precisely my question. A key square is *defined* as "such that if White's king occupies it, White can force the pawn to promotion, *regardless* of where the black king is". So if it does matter where the black king is, it is not a key square...

@Sipo #3
You are right that the definition on Wikipedia could be much better, because it does actually matter where the white pawn is.
And the sentence in the article "The key squares are relative to the position of the pawn." seems ambigious to me, as I assume that they meant that the key squares are different for e.g. the h pawn vs. the e pawn, and I assumed that they didn't mean that the pawn has to be close enough to the king on the key square to actually have a won position.

@achja
Thanks again. So let's assume I have a rook-pawn. How can I determine whether or not its a win and how to accomplish it?

@Sipo #5
I've made a study with a few chapters with examples.

Hopefully that is helpful.

@achja Thanks a lot, those are great examples.

I will be grateful if you could also explain the *principles* behind this ending: Given that the black king is inside the pawn's square, how can I determine whether the white king can secure his pawn and how? Is there any "algorithm"? Some guidelines? Do I have to calculate each and every move?

Thanks again!

@sipo #7
Sorry. Hopefully someone else can provide you with a bright and clear answer on this one.

@achja
Thank you so much for your taking the time to answer my questions...

Do you, personally, just calculate in such positions?

In chapter 4 the black king is NOT inside the pawns square. If the pawn is in the starting position its square is one rank and one column smaller.

A better example would have been to put the black king on c3, d3 or e3. Then it is won for white even if the black king is inside the square of the pawn (which is h3-c3-c8-h8). On e3, because the black king can not enter g5, on d3 he can not enter f5 and g6 and on c3 he he can not enter e5 and g7. All these squares are controlled by the white king.

If the black king is on f3 black also loses because white plays 1.Kg5!

The only cases which are draw are Black king on h-file or on f4 or g4 or f8 or g8.

In such simple cases you can also count. The white pawn needs five moves to reach h8, if the black king can also reach h8 in five (or less) moves then he draws. The black king on c3 needs eight moves, on d3 seven moves, on e3 six.

However, this can also be misleading. For example if the black king is on e8, he seems to just need three moves and therefore stop the pawn, but in fact the white king will go to g7 (a key square) on move 1 and the route is closed.

So, these tools help when calculating (they can help very much indeed with complex key square cases) but they can not replace calculation.