Trouble understanding the solution to this problem

White to play and draw.

I have provided the solution but the reason I'm posting it is that I don't understand the solution.

Apparently, White's only drawing move is 1. Kg3. I don't see that. I don't understand why Kg3 draws and Kg2 or Kg4 loses.

There must be a thought process, a way of approaching problems like this that let you find the right move, but I have never learned that.

Could someone explain to me what the corect way of thinking is that lets you solve a problem like this?

It has to do with keeping the opposition and preventing black from getting his king in front of his pawn if he trades a pair of pawns. There is also the complication that the g pawn can lose a move (since it can move 1 or 2 squares.)

If this comes from the Tactics Trainer, there are normally comments and explanations.

What problem number is it?

That is a Richard Réti and Artur Mandler composition from 1921 and can be found here (with no additional explanation, unfortunately): http://www.arves.org/arves/index.php/en/halloffame/134-reti-richard-1889-1929

I am not at all sure, but I think part of the idea is that White wants to be able to reply to 1...Kf7 with 2 Kg4. After 1 Kg4 or 1 Kg2, 2 Kg4 will not be possible.

It is all about getting opposition and remote opposition. This study is explained as #1-176 in Dvoretsky:  Dvoretsky's Endgame Manual (at least in the German edition),

It is 1-181 on page 65 of the 4th English edition.

"... Note that with Black's pawn at g6, the opposition is important for both sides; with the pawn at g7, it is the anti-opposition that is important. This generalization is the mainspring driving this particular endgame. …" - Dvoretsky

I've found the problem in Dvoretsky's book and read his analysis, but I must admit defeat. I still don't understand it. I'm just not good enough to grasp all the concepts and variations.

It's a surprisingly complicated problem (at least for me). One has to keep track of the analysis of the positions that can result from a pawn advance. I think I have somewhat grasped what Dvoretsky was saying. If you want to ask a very specific question, I could maybe take a stab at trying to answer it. Sometimes, I think it helps to just experiment a bit. After 1 Kg4 Kf7, what would you want to do?

I appreciate your help, but I think I'll give up one this one. It's too advanced for me at this time.

I'm studying the end game, pawn endings specifically, and I still don't fully understand the various types of opposition, corresponding squares, waiting moves etc. I need to do a lot more work on the basics before I have another stab at this one.

One small consolation for me is that it does seem to be a very complicated problem, and not something basic that I just don't see.

Sometimes its is a good idea to start at the end-position, and work your way back.

Black wants to promote the pawn to a queen and deliver checkmate. Therefor, black bust achieve a position in which the king can push white out of the way.

After h5 - the move in which black puts white in zugzwang - white is eventually forced to give up defense of g4, and thereby the pawn,

The point in this position is to give away a move at the right time, and force white out of defense of the key square g4. By playing Kg3 rather than advancing to Kg4, white prevents black from giving that key move away. White is in time to exchange the pawns, and get in front of the pawn thats left (black is not able to push white out of the blocking square).

The analysis button under the problem was a huge help in figurering this out - I would have never gotten there on my own.

It's actually not as complex as you think. The theme of this puzzle is zugzwang. Our goal is to reach this position where it is black's turn to move:

Once you understand why this position is a draw, provided that it is black's turn to move, then it's simply a matter of asking yourself: how can I achieve this position?

Here's why I'm struggling:

1. I don't see that the position Deranged gives, is a draw.

2. I don't see why that, and only that position is a draw, so I have no idea that I should be working towards achieving that position in the first place.

3. I hope that once I know how to figure out 1 and 2, I'll know how to force Black to reach that position, but I'm not at all sure.

I appreciate all your help, guys, but I'm going to leave it at this. I'm going back to studying the end game basics and maybe in a few weeks have another look at this.

This isn't the hardest pawn endgame in the world, but it is harder than a good many of them because of the potential for a so-to-speak game-changing pawn advance. I think we could talk you through it if you wanted to experiment for a bit (starting with White's problems after 1 Kg4 Kf7), but I think it is entirely understandable if one would rather postpone the undertaking. If my color perception is working, we are discussing an example that appears in nonblue ink on the 49th page of Dvoretsky's pawn endgame discussion.

The idea is to practice thinking techniques, but I agree that this particular example is somewhat over-the-top for many of us. Again, if my color perception is working, we are discussing an example that appears in nonblue ink on the 49th page of Dvoretsky's pawn endgame discussion. Seems to me to be worthwhile to consider things like the problem at

https://www.chess.com/forum/view/endgames/triangulation-troubles