lichess.org/training/efQQOI saw the solution, and while I "see" why it's winning after going through several moves and seeing engine lines, I don't get two things:
1. How I should "see" that exchanging everything is winning?
2. What is the key idea which can be applied to actual games, that can be learned from this puzzle (other than, you know, brute force calculation for a whole host of pawn and king moves, to see that it's a winning KP endgame)?
TIA
Strategy. When you enter the endgame (or the endgame is reduced to a different type) a thing you do is understand the winning plans for both sides. Then figure out if they can be stopped and how, and also how fast they are according to the steps they require. White's winning plan in a pawn endgame would be to create a passed pawn in the 2 vs 1 on the queenside, and it requires to advance the pawns to force some trade, but even then the black king is close enough to stop it.
White has another plan that involves creating a passed pawn on the opposite side of the board, and the steps involve deflecting the pawn on g5 by playing f4, but this is currently made impossible by the black king. So white would imagine that in a pawn endgame he first would create the passed pawn on b or a, and then when the king has to go stop it, he would follow by creating the other passed pawn on h or g, and the black king can't stop both at the same time. That's the principle of two weaknesses, and it wins many endgames.
What about black's winning plans though? Well, black just has to push the d pawn. He can't do it right now because white would stop it, but the king (not a pawn) is the one doing it. This means that while the white king is busy there (defending that weakness) black's king can go elsewhere and attack other pawns (the second weakness); so now the principle of two weaknesses is making white lose.
White has winning plans, but they happen to be way slower than black's. So what white should think is that he's playing for a draw, and you do this by stopping the other guy's winning plan, but in this case it can't be done: White is either gonna grab the pawns on the queenside and get a second passed pawn on a while the black king is busy defending, or he's getting a second passed pawn on f when his guy on g5 gets deflected.
But do notice that all of this starts with a tactical point, which is that the rook trade can't be refused. Otherwise you couldn't even reduce to a pawn endgame to begin with. Read books about endgames and they tell you how to think.
