Sharp pawn endgame - can it be calculated to the end? With Computer engine?

Question

White to move, here is a brief summary of my analysis where I attempted to determine exact evaluation. Number of pawns is equal but White's 2 pawns on the queenside are held by one Black's pawn, so in a sense Black has an extra pawn on the rest of the board.
1. a4 with pawn breaks on both sides of the board by both White and Black (!) leads to a difficult queen endgame for White.
1. Kc3 (played by me in the game) is a blunder that should lose after 1...f4! since then Black puts pawns on e4 and f4 and goes to the kingside with his king to pickup White's pawns.
1. Kd3 is possibly best as now 1...f4 is met with 2.Ke4. But Black instead plays 1...Kf7 and manoeuvres, waiting for zugzwang. Can Black win? Can a computer engine be used in this day and age to determine exactly if this position is a draw or win for Black?

This is a pawn endgame - which are supposed to be evaluated precisely... I feel this is likely a draw, but can't prove exactly. Is there Mr. Grigoriev in the audience?

8/7p/4k3/1p2ppP1/1P5P/8/P1K5/8 w - - 0 38

Answer 1

It's clear that Black has the following advantages:

1) His king is better centralized.

2) He has two connected passed pawns.

3) White has no passed pawns because one Black pawn holds up two White ones on both the queen and king sides.

White's main advantage is that he has two rook pawns, which could lead to "outside" passed pawns. Even so, it might take the sacrifice of a pawn for White to get a passed pawn.

So I would give Black the advantage overall, and say that he should win with proper play. White should draw with great difficulty if at all.

I'm basing this judgment on "pattern recognition," because I am a only a 1500 player.

Answer 2

This is actually a drawn position with correct play. As expected, the two sides with pawns are actually more important in the end-game than the center pawns (because the center pawns can be effectively barricaded.) Here is a full analysis done GNU chess (your move kd3 is correct, however, the difficult moves come later on in the game when there are two queens on the board.)

GNU Chess comes up with this:

[fen "8/7p/4k3/1p2ppP1/1P5P/8/P1K5/8 w - - 0 38"]

1. Kd3 f4 2. h5 f3 3. Ke3 e4 4. g6 hxg6 5. h6 Kf7 6. a4 bxa4 7. b5 a3 8. b6 a2 9. b7 a1=Q 10. b8=Q Qe1+ 11. Kf4 Qh4+ 12. Ke3 g5 13. h7 Qxh7 14. Qb7+ Kg8 15. Qc8+ Kf7 16. Qd7+ Kg6 17. Qe6+ Kh5 18. Qh3+ Kg6 19. Qe6+ Kh5 20. Qh3+ Kg6 21. Qe6+ 1/2-1/2