Yes, 1.Kg4 is the only winning move- the white king must reach h6 before the black king reaches g7. For example:
1. Kf4? Ke7 (any move to the e-file draws for black now)
2. Ke5
For purposes of explication, I show only the line where white takes the opposition, but if white played 2.Kf5, black just draws with 2. …Kf7. Continuing:
2. ………….Kf7
3. Kf5 Kg7
A typical finish in this situation- white had the opposition, but it is worthless in this case because his king isn’t out in front of the pawn which hinders the white king. From this position after black’s third move, white can’t go to e6 without losing the pawn to black’s Kg6. The only hope for progress forward is to push the pawn, but…..
4. g6 Kg8! (the only draw)
5. Kf6 Kf8 (or Kh8 is equal)
6. g7 Kg8
And white either stalemates with Kg6, or loses the pawn. A fundamental K+P vs K ending.
1. Kg4 Ke6
2. Kh5 Kf7
3. Kh6 Kg8
4. Kg6 Kf8
5. Kh7 Ke7
6. g6 Kd6
White wins
Yes, 1.Kg4 is the only winning move- the white king must reach h6 before the black king reaches g7. For example:
1. Kf4? Ke7 (any move to the e-file draws for black now)
2. Ke5
For purposes of explication, I show only the line where white takes the opposition, but if white played 2.Kf5, black just draws with 2. …Kf7. Continuing:
2. ………….Kf7
3. Kf5 Kg7
A typical finish in this situation- white had the opposition, but it is worthless in this case because his king isn’t out in front of the pawn which hinders the white king. From this position after black’s third move, white can’t go to e6 without losing the pawn to black’s Kg6. The only hope for progress forward is to push the pawn, but…..
4. g6 Kg8! (the only draw)
5. Kf6 Kf8 (or Kh8 is equal)
6. g7 Kg8
And white either stalemates with Kg6, or loses the pawn. A fundamental K+P vs K ending.