Tricky pawn endgame

White to move and win

Hey FancyKnight. Lets see.  I think 1.- Kg2 wins.  Black needs to capture a and b pawns while in the meantime White captures h and g pawns.  Then the double pawns actually help White to promote.  Cheers.

1.Kg2 Kb5 2.b4 1-0

1.Kg2 h5!? 2.Kg3 h4+ 3.Kg4 Kb5 4.b4! e6 5.F4! 1-0

1-0

1.b4 also wins

It's a bit deeper than that. Try to see what black can do if white just runs towards the pawns

White's connected passers keep the black king occupied.

The question is... can white capture/trade all the pawns on the kingside?

It's not as simple as it looks. Roeczak is getting white's basic winning idea in his second line, but misses black's refuting reply.

My psychology makes me feel I have lost this endgame as white, though I continue to play and my psychology finally gets the better of me. 

This is what happens to me in every endgame that requires a lot of thinking. 

I think the refutation you're hinting at is black playing ..e5 instead of ..e6 in Roeczak's line. Then playing f4 is a bit more problematic because after exf4, the white king can never capture the h-pawn, nor leave it.

I think white has to play f4 before black can get in ..e5 and keep black's pawns separated into 2 pawn islands. After f4 gxf4 then the white king has time to capture the h-pawn (or the e-pawn, depending on how black tries to advance them).

1. Kg2 e5, clapping down on the f4 square followed by h5 and h4 draws, both kings are stuck guarding connected passed pawns.

1. f4 is the only winning attempt. 1...gxf4 2. Kg2 e5 3. Kf3 h5 4. Ke4 h4 5. Kf3 (5. Kxe5 steps outside of the square of the h pawn) 5...Kb5 6. b4 Ka6 7. Kg4 and White wins the h pawn without allowing the e pawn to advance far enough to queen.

Actually that loses to 6...h3, still without sight of a board here.

Yawn.  Buy some of Nunn's books instead.

That position will never happen over the board.

I got it from my own game

You're special, but too young for that Saturday Night Live skit. 

1) f4 looks like a quick win, if you then go after black's h-pawn.

That comment was a bit moronic, @Vedras.  Sorry.

Didn't you even read the earlier posts?  1) b4, e5 puts white in a pickle.

I don't see what's wrong with 1.b4 e5 2.Kg2.

 1. f4 gxf4 2. Kg2 e5 3. f3 Kb5 4. b4 Ka6 5. Kh3 h5 (otherwise White's king has access to the g4 square and can win the e pawn without giving the h pawn a chance to run) 6. Kh4 Kb5 7. Kg5 (7. Kxh5?? e4 8. Kg4 e3) 7...Ka6 8. Kf5 and wins. I would call 7. Kg5 the key move.

 2.Kg2 e5 3. Kh3 h5 4. Kh4 e4 = would be rather embarrassing over the board. White can't take the h pawn and no longer has any way to make progress. 5. Kh3 Kb6 6. b4 Ka6 7. Kg2 Kb6 ect. 3. Kf3  h5 4. Kg2 e4 is the same friggin fortress, 5. Ke4?? h4 should make White cry.

EDIT Great I posted this wrong, but I think I fixed it.

Titan the passed pawn on the h file. 1. b4 e5 2. Kb2 Kb6 3. Kg3 h5 4. Kh3 Ka6 White cannot make progress.

Thanks kindly for the clarification, @MrAggressive.  Very thorough.

Crying is a bit much... But yeah that is unfortunate.