Never mind... I see what I was missing.... every time the black king goes to g1, white can move the king.

Thanks Alena. ... I know I’m missing something ... but in your sequence, how would white proceed if on the 8th move, black played Kg1, trying to use its pawn as a shield.

1. Kf5 Kf3
2. g6 g3
3. g7 g2
4. g8=Q Kf2
5. Qa2+ Kf1
6. Qa1+ Kf2
7. Qd4+ Kf1
8. Qf4+ Ke1
9. Qe3+ Kd1
10. Qg1+
    It's a win for white.

Actually, there is a check after white queens.... white can play Qa2+ ... but can white stop the black pawn from queening?

...

By opposition

Draw

Yes. But if black plays Kf3 in response, I don’t see how white stops the black pawn from queening. I think after white plays g8=Q, black plays Kf2, and black’s pawn is on g2. With white’s king on g5, white can’t immediately check the black king. So, whatever white does (except for qxg2, which draws), black queens on the next move. So, I think this is a draw

Hi Yancey...looks like Kf5 is the way to go giving white an extra tempo because the black king will have to stay on the third rank the next move to protect the pawn.