White to move. How should white proceed?
On first principles, you take the direct opposition across 3 squares- so you should always look at 1.Kh3 first. Dave outlines the main variation well- the key point is reached after 4......Kd7 in that line- white then plays 5.Kf4! and it does black no good to take the diagonal opposition with 5.....Kd6 because after 6.Kf5!, black can't play 6.....Kd5 because the white pawn controls the square.
- Kh3! Kg7, 2. Kg3 Kf7, 3. Kf3 Ke7!, 4. Ke3! Kd7, 5. Kf4! Kd6, 6. Kf5 and White wins
I tried to get it with Kh1-g1-f1-e1-d1-d2-e2. I think I could see forced wins for white after that. First I looked for the variation where black rushes to d4 and gets squeezed back by Kd2. Now I am looking again at it to figure out if it's necessary to go all the way to d1. This is the first time I try to calculate a pawn endgame seriously.