1. Kf4 1.Kg(e)7 2. Kf5 2.Kf7 3. g3 3.Kg7 4. Ke6 4.Kg6 5. Kd6! 5.Kf5 (if black is trying Kh6 to hold the oppsition than white can go after the a pawn, and win easily, as the black king is far away from white’s pawns) 6. Ke7 6.Kg4 7. Kxf6 7.Kxg3 8. Kg5
if
1.Kf4 1.Ke6 2.Ke4 2.Ke7 (2. f5 losing immediately after 3. Kf4 3. Kf6 4. g3 because either the f or h pawn will be lost) 3.Kf5 3.Kf7 4.g3…
or: 1.Kf4 1.Kg6 2.Ke4 2.Kg7 (f5 is losing here as well after Ke5 and the f pawn will be lost soon) 3.Kf5 3.Kf7 4.g3…
If I my calculation is good, white wins by : 1.Kf4 Ke7! (1… Ke6 2.Ke4 Kf7 (2…f5+? 3.Kf4 Kf6 4.g3 , 2…Ke7 3.Kd5 is the same) 3.Kd5 Ke7 4.Kc5 Ke6 5.Kb4 Kf5 6.Kxa4 Kg4 7.Kb5 Kg3 8.a4 Kxg2 9.a5 f5 10.a6 f4 11.a7 f3 12. a8=Q and white wins)
2.Ke3! (loong opposition) Kf7 3.Kd4! Kg6 3.Ke4 Kg7 4.Kd5 Kg6 (Kf7 5.Kc5 is won as in prev. line) 5.Ke6 Kg7 6.Kd6 Kg6 7.g3! Kf5 8.Ke7 Kg6 9.Kf8 Kf5 10.Kf7 winning.
First things first: If white moves to the queen side, it takes him 11 moves to queen the a-pawn, while black can queen his f-pawn in 10. At best, this strategy is a draw for white.
1. g3 f5 2. Kf4 Kf6 and this might be zugzwang for white:
3. Ke3 Ke5 4. Kf3 Kd4 going after the queenside, where black can queen the a-pawn in 7 more moves, while it will take white 9 moves to clear the way for either pawn on the kingside. So, white must follow to the queen side:
5. Kf4 Kc4 6. Ke3 Kb3 7. Kd3 Ka3 8. Kc3 Ka2 9. Kc2 a3 10.Kc1 Kb3 and white is probably doomed as he must capture the a-pawn while black skedaddles back to pick up both white pawns on the kingside, if necessary:
11.Kb1 Kc3 12.Kb2 Kd3 13.Ka3 Ke3 14.Kb3 Kf3 15.Kc3 Kg3 16.Kd4 f4 and it is all over for white in this line.
Looking at other options for white in the above line:
1. g3 f5 2. Kf4 Kf6 3. Ke3 Ke5 4. Kd3 Kd5 5. Ke3 Kc4 and, again, black will queen 2 or 3 moves ahead of white in the race a-pawn vs g-pawn. So, at move 5 in this sub-line, white must play
5. Kc3 Kc5 6. Kc2 Kc4 7. Kb2 Kd3 8. Kb1 Kc3 9. Ka2 Kc2 and white again loses the a-pawn and the game.
After 1. g3, there seems to be one other major continuation for white that looks the best:
The other main continuation for black in this line is 1. …Kg6:
1. g3 Kg6 2. Kf4 f5 3. Ke3 Kf6 4. Kf4 Ke6 5. Kg5 Ke5 6. Kh5 Kf6 7. g4 fg4 8. Kg4 Kg6 9. Kf4 Kh5 10.Ke4 Kh4 11.Kd4 Kg5 12.Kc4 Kf6 13.Kb4 Ke6 14.Ka4 Kd6 15.Kb5 Kc7 16.Ka6 Kb8 and white will have to give up the corner to black allowing a draw.
All in all, I don’t see anything more than a draw for white after 1. g3, and plenty of opportunity to lose the game.
1. Ke4 Ke6 2. Kf4 Kd5 3. Kf5 Kc4 4. Kg6 Kb3 5. Kh5 Ka3 6. Kg6 Kb3 7. h5 a3 8. h6 a2 9. h7 a1(Q) 10.h1(Q)and this should be a draw.
Other variations in this main line:
1. Ke4 Ke6 2. g3 f5 looks like an interpolation of one of the lines I discussed in the previous comment.
1. Ke4 Ke6 2. g4 hg4 3. Kf4 f5 4. h5 Kf6 will win for black as the h-pawn will be stopped and white’s king is forever caught holding up connected passed pawns.
1. Kf4 Ke6 2. g4 hg4 3. Kg4 f5 4. Kf4 Kf6 5. h5 and now black must give way 5. …..Kg7 6. Kf5 Kh6 7. Ke5 Kh5 8. Kd5 Kg5 9. Kc4 Kf6 10.Kb4 Ke6 11.Ka4 Kd6 12.Kb5 Kc7 13.Ka6 Kb8 and this is still a draw.
Other variations:
1. Kf4 Ke6 2. g3 f5 3. Kg5 Ke5 4. Kh5 Kf6 and I think I covered this line as an earlier interpolation- black eventually picks up the h-pawn and makes it to the a8 corner in time to hold the draw.
White has to reach a point where he is closer to a file and black is just as far away. The pawns will queen on the a8-h1 diagonal with white queening first. So he sort of triangulates looking for a tempo.
1. Ke3 Kg6 2. Ke4
pushing back the black king.
f5+ loses because of the tempo g3, black will lose the pawn on f5.
After more thinking, in my main variation, 1.Kf4 Ke7 2.Ke3 Kf7 3.Kd4! Kg6 3.Ke4 Kg7 4.Kd5 Kg6 5.Ke6 Kg7 6.Kd6 Kg6 7.g3 black has Kh6! and I don’t see a win, if white goes to queen side, black has enough time.
If white plays 1.Ke3 . on 1…Ke7 (1…Ke6 2.Ke4 – as my previous line) 2.Kd3! Kd6 3.Kd4 Ke6 4.Ke4 Kf7 5.Kd5 as main line.
But black has 1…Kg6 – then 2.Ke4 Kg7 3.Kd5 Kg6 4.Ke6 Kg7 as previous line.
White needs to capture the a pawn and promote before the black h-pawn. To win this pawn race (bearing in mind that with black king on g2 after capturing white pawn, a8=Q is check), the white king quite simply needs to reach the d-file before the black king comes to the 6th rank. So the win is easily achieved with 1.Ke3!, threatening Kd4. If 1…Kg6 or 1…Ke6, then 2.Ke4 forces the king to retreat to the 7th rank, allowing the king to the d-file. From there you just have to count moves to see the win
The corresponding squares for which white and black are: f5 vs f7 e4 vs e6 or g6 and this also f4 vs e7 or g7
If white is on one of the first mentioned squares, black on the latter, with black having the move, white wins. e.g. with white’s king on f5 nad black’s king on f7, with black having the move: 1. .. Ke7 2. Kg6 and 3. Kxh5 1. .. Kg7 2. Ke6 Kg6 3. g3 and 4. Kd5 reaching for the a pawn
This means that those squares are only to be entered _after_ black has entered one fo them.
I would play: 1. Ke3 .. Ke6? 2. Ke4, and white will reach f5 and win. .. Ke7? 2. Kf4, and white will reach f5 and win. .. Kg7? 2. .. Kg6? 2. Kf4, and white will reach f5 and win. 1. .. Ke8 2. Kd4 reaching for the a pawn
Black might also play f5, but that opens field g5 for white and makes it even easier for white to win.
I believe the position with the White king at e4 and the Black king at g6 is a zuzwang position for Black. For example:
1. Kf4 Kg6(?) 2. Ke4 Kh6 3. Kd4 Kg6 4. Kc4 Kf5 5. Kb4 Kg4 6. Kxa4 Kxh4 7. Kb4 Kg3 8. a4 Kxg2 9. a5 h4 10. a6 h3 11. a7 h2 12. a8=Q+ and without the f-pawn this would be a draw, but (I’m not absolutely sure about this) in this position the White king may have enough time to approach without stalemating since the f-pawn can advance.
This also fixes M. Pasman’s main line, as after 1. Kf4 Ke7 2. Ke3 Kf7 3. Kd4 Kg6 White just plays 4. Kc4 going into the above line.
I believe Anonymous has shown the correct response to 1. Kf4 Kg(e)7 2. Kf5.
To anonimous note: your variation is drawn : 1. Kf4 Kg6 2. Ke4 Kh6 3. Kd4 Kg6 4. Kc4 Kf5 5. Kb4 Kg4 6. Kxa4 black, of course, plays 6…Kxg2 and not Kxh4 and the ending with white queen and black pawn on f2 is drawn also with points h4,h5
best what white can get is Q+pawn h4 ending against queen.
White has to take the opposition. Ke3 wins. If Kg6 then Ke4 takes the opposition and black must move back.
If black tries f5+ then Kf4 and after Kf6 white has g3 to get the opposition back and wins the pawn on f5. So black can not play f5 and must go back to f7 or g7.
Essentially, white needs to win black’s h pawn, then trade his h pawn for the black f pawn. With the g pawn where it is, white’s king will have time to go to the queen side and queen his a pawn. The question is, how to effect this?
I think, if white can get his king to e6 with the black king on g7 (defending the f pawn, and it is essential that the g pawn remain where it is, noticing the potential check on the diagonal also), he can lunge at the queenside. The a pawn should win a race in these circumstances against the f pawn.
The problem is achieving this position. There is no problem in getting the diagram position with the white king on f5, however, white must then have the opposition. I cannot see how this could be achieved.
So, I think white must start with e3, continue toward the queenside, threatening at the same time to attack the black a pawn and to take an opposition that allows him to reach either the position I described earlier or attack the black f pawn.
Unfortunately, I cannot calculate all this, but I think this is what should be done.
Actually, adding to the last, as an example, 1. Ke3 Ke7 2. Kd3 (it will not avail black to continue further) Ke6 3. Ke4 Ke7(or Kf7) 4. Kd5 should yield the desired result. From this position, white can lunge at the queenside and win the race between a and f pawns. If black follows, of course, white can do as usual and return winning both the black f and h pawns.
I cannot write all the possible variations, but the idea is presented there.
Black does no want to advance his f pawn since that allows white to attack the h pawn, and black is also tied to defending the f pawn.
I don’t know if it will help anyone solve this, but I repeatedly ran into the problem that white cannot win with the a pawn- he either loses/draws the race with the f-pawn of black, or, if the kingside is liquidated, the distance of his a-pawn from a8 always allowed the black king to recover to corner.
Also, because his a-pawn is closer to the queening square, and the kings are equidistant from the opponent’s a-pawn, black is always threatening to move queenside and force a win. To win, I believe white must queen a kingside pawn, but he must not allow black to break to queenside. This thinking argues for g4 at some point to create a passed h-pawn for white, but this also means the white king must remain kingside to pick up new black g-pawn.
I want to point out few important things about this endgame: white always has a tempo with g3, so in position with g3 black has to keep the opposition, as I pointed before in variation 1.Kf4 Ke7 2.Ke3 Kf7 3.Kd4 Kg6 3.Ke4 Kg7 4.Kd5 Kg6 5.Ke6 Kg7 6.Kd6 Kg6 7.g3 Kh6! on Kd7 black has to play Kh7! on Kd5 – Kg7! and on Ke6 – Kg6.
Before g3 black has to ignore the opposition when the white king is from the side : on Ke6 black has to answer Kg7 , on Ke7-Kg6.
but if white goes from the front – on Kf5 black has to play Kf7! , because if on Kf5 black answers Kg7, white wins by 1.Ke6 Kg6 2.g3 Kg7 3.Ke7 Kg6 4.Kf8
So, if white starts with 1.Kf4 Kg6 2.Ke4, black plays 2…Kg7! 3.Kd5 Kg6 (no Kf7 , then white wins taking a pawn) Now on Kd6 black has Kf5, on 4.Ke6 Kg7 and if 5.g3, then 5…Kg6 – drawing as I noted before.
So, I will be very surpised if there is a win for white.
the move will be Ke4.
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White will win after:
1. Kf4 1.Kg(e)7
2. Kf5 2.Kf7
3. g3 3.Kg7
4. Ke6 4.Kg6
5. Kd6! 5.Kf5 (if black is trying Kh6 to hold the oppsition than white can go after the a pawn, and win easily, as the black king is far away from white’s pawns)
6. Ke7 6.Kg4
7. Kxf6 7.Kxg3
8. Kg5
if
1.Kf4 1.Ke6
2.Ke4 2.Ke7 (2. f5 losing immediately after 3. Kf4 3. Kf6
4. g3 because either the f or h pawn will be lost)
3.Kf5 3.Kf7
4.g3…
or:
1.Kf4 1.Kg6
2.Ke4 2.Kg7 (f5 is losing here as well after Ke5 and the f pawn will be lost soon)
3.Kf5 3.Kf7
4.g3…
If I my calculation is good, white wins by :
1.Kf4 Ke7!
(1… Ke6 2.Ke4 Kf7 (2…f5+? 3.Kf4 Kf6 4.g3 , 2…Ke7 3.Kd5 is the same)
3.Kd5 Ke7 4.Kc5 Ke6 5.Kb4 Kf5 6.Kxa4 Kg4 7.Kb5 Kg3 8.a4 Kxg2 9.a5 f5 10.a6 f4 11.a7 f3 12. a8=Q
and white wins)
2.Ke3! (loong opposition) Kf7 3.Kd4! Kg6 3.Ke4 Kg7 4.Kd5 Kg6 (Kf7 5.Kc5 is won as in prev. line) 5.Ke6 Kg7 6.Kd6 Kg6 7.g3! Kf5 8.Ke7 Kg6 9.Kf8 Kf5 10.Kf7 winning.
May be there is some mistake, I am not sure.
g4 shoudl win as white gets h passed pawn – if king goes to stop that, white king will pick the a pawn and promote (or vice versa).
First things first: If white moves to the queen side, it takes him 11 moves to queen the a-pawn, while black can queen his f-pawn in 10. At best, this strategy is a draw for white.
As for playing g4:
1. g4 Kg6
2. gh5 Kh5
3. Kf4 Kh4
4. Kf5 Kh3
5. Kf6 Kg3
6. Ke5 Kf3
7. Kd4 Kf4
8. Kc4 Ke4
9. Kb4 Kd4
10.Ka4 Kc4
11.Ka5 Kc5
12.a4 Kc6
13.Ka6 Kc5
14.a5 Kc6
15.Ka7 Kc7
16.a6 Kc8
17.Kb6 Kb8
18.a7 Ka8 with a draw.
kf4
h
ooops, ke4
h
get the wh ke6 and blk kg7 before running for the a pawn
h
Continuing with 1. g3:
1. g3 f5
2. Kf4 Kf6 and this might be zugzwang for white:
3. Ke3 Ke5
4. Kf3 Kd4 going after the queenside, where black can queen the a-pawn in 7 more moves, while it will take white 9 moves to clear the way for either pawn on the kingside. So, white must follow to the queen side:
5. Kf4 Kc4
6. Ke3 Kb3
7. Kd3 Ka3
8. Kc3 Ka2
9. Kc2 a3
10.Kc1 Kb3 and white is probably doomed as he must capture the a-pawn while black skedaddles back to pick up both white pawns on the kingside, if necessary:
11.Kb1 Kc3
12.Kb2 Kd3
13.Ka3 Ke3
14.Kb3 Kf3
15.Kc3 Kg3
16.Kd4 f4 and it is all over for white in this line.
Looking at other options for white in the above line:
1. g3 f5
2. Kf4 Kf6
3. Ke3 Ke5
4. Kd3 Kd5
5. Ke3 Kc4 and, again, black will queen 2 or 3 moves ahead of white in the race a-pawn vs g-pawn. So, at move 5 in this sub-line, white must play
5. Kc3 Kc5
6. Kc2 Kc4
7. Kb2 Kd3
8. Kb1 Kc3
9. Ka2 Kc2 and white again loses the a-pawn and the game.
After 1. g3, there seems to be one other major continuation for white that looks the best:
1. g3 f5
2. Ke3 Ke6
3. Kd4 Kd6
4. Kc4 Ke5
5. Kb4 Ke4
6. Ka4 Kf3
7. Ka3 Kg3
8. a4 f4
9. a5 f3
10.a6 f2
11.a7 f1(Q)
12.a9(Q) with a draw.
The other main continuation for black in this line is 1. …Kg6:
1. g3 Kg6
2. Kf4 f5
3. Ke3 Kf6
4. Kf4 Ke6
5. Kg5 Ke5
6. Kh5 Kf6
7. g4 fg4
8. Kg4 Kg6
9. Kf4 Kh5
10.Ke4 Kh4
11.Kd4 Kg5
12.Kc4 Kf6
13.Kb4 Ke6
14.Ka4 Kd6
15.Kb5 Kc7
16.Ka6 Kb8 and white will have to give up the corner to black allowing a draw.
All in all, I don’t see anything more than a draw for white after
1. g3, and plenty of opportunity to lose the game.
Continuing with 1. Ke4:
1. Ke4 Ke6
2. Kf4 Kd5
3. Kf5 Kc4
4. Kg6 Kb3
5. Kh5 Ka3
6. Kg6 Kb3
7. h5 a3
8. h6 a2
9. h7 a1(Q)
10.h1(Q)and this should be a draw.
Other variations in this main line:
1. Ke4 Ke6
2. g3 f5 looks like an interpolation of one of the lines I discussed in the previous comment.
1. Ke4 Ke6
2. g4 hg4
3. Kf4 f5
4. h5 Kf6 will win for black as the h-pawn will be stopped and white’s king is forever caught holding up connected passed pawns.
Continuing with 1. Kf4:
1. Kf4 Ke6
2. g4 hg4
3. Kg4 f5
4. Kf4 Kf6
5. h5 and now black must give way
5. …..Kg7
6. Kf5 Kh6
7. Ke5 Kh5
8. Kd5 Kg5
9. Kc4 Kf6
10.Kb4 Ke6
11.Ka4 Kd6
12.Kb5 Kc7
13.Ka6 Kb8 and this is still a draw.
Other variations:
1. Kf4 Ke6
2. g3 f5
3. Kg5 Ke5
4. Kh5 Kf6 and I think I covered this line as an earlier interpolation- black eventually picks up the h-pawn and makes it to the a8 corner in time to hold the draw.
White wins.
White has to reach a point where he is closer to a file and black is just as far away. The pawns will queen on the a8-h1 diagonal with white queening first. So he sort of triangulates looking for a tempo.
1. Ke3 Kg6
2. Ke4
pushing back the black king.
f5+ loses because of the tempo g3, black will lose the pawn on f5.
White wins.
After more thinking, in my main variation,
1.Kf4 Ke7 2.Ke3 Kf7 3.Kd4! Kg6 3.Ke4 Kg7 4.Kd5 Kg6 5.Ke6 Kg7 6.Kd6 Kg6 7.g3 black has Kh6!
and I don’t see a win, if white goes to queen side, black has enough time.
If white plays 1.Ke3 .
on 1…Ke7 (1…Ke6 2.Ke4 – as my previous line) 2.Kd3! Kd6 3.Kd4 Ke6 4.Ke4 Kf7 5.Kd5 as main line.
But black has 1…Kg6 – then
2.Ke4 Kg7 3.Kd5 Kg6 4.Ke6 Kg7 as previous line.
so I didn’t find a win yet.
White needs to capture the a pawn and promote before the black h-pawn. To win this pawn race (bearing in mind that with black king on g2 after capturing white pawn, a8=Q is check), the white king quite simply needs to reach the d-file before the black king comes to the 6th rank. So the win is easily achieved with 1.Ke3!, threatening Kd4. If 1…Kg6 or 1…Ke6, then 2.Ke4 forces the king to retreat to the 7th rank, allowing the king to the d-file. From there you just have to count moves to see the win
The corresponding squares for which white and black are:
f5 vs f7
e4 vs e6 or g6
and this also
f4 vs e7 or g7
If white is on one of the first mentioned squares, black on the latter, with black having the move, white wins.
e.g. with white’s king on f5 nad black’s king on f7, with black having the move:
1. .. Ke7 2. Kg6 and 3. Kxh5
1. .. Kg7 2. Ke6 Kg6 3. g3 and 4. Kd5 reaching for the a pawn
This means that those squares are only to be entered _after_ black has entered one fo them.
I would play:
1. Ke3
.. Ke6? 2. Ke4, and white will reach f5 and win.
.. Ke7? 2. Kf4, and white will reach f5 and win.
.. Kg7? 2.
.. Kg6? 2. Kf4, and white will reach f5 and win.
1. .. Ke8 2. Kd4 reaching for the a pawn
Black might also play f5, but that opens field g5 for white and makes it even easier for white to win.
I believe the position with the White king at e4 and the Black king at g6 is a zuzwang position for Black. For example:
1. Kf4 Kg6(?) 2. Ke4 Kh6 3. Kd4 Kg6 4. Kc4 Kf5 5. Kb4 Kg4 6. Kxa4 Kxh4 7. Kb4 Kg3 8. a4 Kxg2 9. a5 h4 10. a6 h3 11. a7 h2 12. a8=Q+ and without the f-pawn this would be a draw, but (I’m not absolutely sure about this) in this position the White king may have enough time to approach without stalemating since the f-pawn can advance.
This also fixes M. Pasman’s main line, as after 1. Kf4 Ke7 2. Ke3 Kf7 3. Kd4 Kg6 White just plays 4. Kc4 going into the above line.
I believe Anonymous has shown the correct response to 1. Kf4 Kg(e)7 2. Kf5.
To anonimous note:
your variation is drawn :
1. Kf4 Kg6 2. Ke4 Kh6 3. Kd4 Kg6 4. Kc4 Kf5 5. Kb4 Kg4 6. Kxa4
black, of course, plays 6…Kxg2 and not Kxh4
and the ending with white queen and black pawn on f2 is drawn also with points h4,h5
best what white can get is Q+pawn h4 ending against queen.
So I still believe that the position is drawn.
White has to take the opposition. Ke3 wins. If Kg6 then Ke4 takes the opposition and black must move back.
If black tries f5+ then Kf4 and after Kf6 white has g3 to get the opposition back and wins the pawn on f5. So black can not play f5 and must go back to f7 or g7.
Essentially, white needs to win black’s h pawn, then trade his h pawn for the black f pawn. With the g pawn where it is, white’s king will have time to go to the queen side and queen his a pawn. The question is, how to effect this?
I think, if white can get his king to e6 with the black king on g7 (defending the f pawn, and it is essential that the g pawn remain where it is, noticing the potential check on the diagonal also), he can lunge at the queenside. The a pawn should win a race in these circumstances against the f pawn.
The problem is achieving this position. There is no problem in getting the diagram position with the white king on f5, however, white must then have the opposition. I cannot see how this could be achieved.
So, I think white must start with e3, continue toward the queenside, threatening at the same time to attack the black a pawn and to take an opposition that allows him to reach either the position I described earlier or attack the black f pawn.
Unfortunately, I cannot calculate all this, but I think this is what should be done.
Actually, adding to the last, as an example, 1. Ke3 Ke7 2. Kd3 (it will not avail black to continue further) Ke6 3. Ke4 Ke7(or Kf7) 4. Kd5 should yield the desired result. From this position, white can lunge at the queenside and win the race between a and f pawns. If black follows, of course, white can do as usual and return winning both the black f and h pawns.
I cannot write all the possible variations, but the idea is presented there.
Black does no want to advance his f pawn since that allows white to attack the h pawn, and black is also tied to defending the f pawn.
I don’t know if it will help anyone solve this, but I repeatedly ran into the problem that white cannot win with the a pawn- he either loses/draws the race with the f-pawn of black, or, if the kingside is liquidated, the distance of his a-pawn from a8 always allowed the black king to recover to corner.
Also, because his a-pawn is closer to the queening square, and the kings are equidistant from the opponent’s a-pawn, black is always threatening to move queenside and force a win. To win, I believe white must queen a kingside pawn, but he must not allow black to break to queenside. This thinking argues for g4 at some point to create a passed h-pawn for white, but this also means the white king must remain kingside to pick up new black g-pawn.
I want to point out few important things about this endgame:
white always has a tempo with g3,
so in position with g3 black has to keep the opposition, as I pointed before in variation
1.Kf4 Ke7 2.Ke3 Kf7 3.Kd4 Kg6 3.Ke4 Kg7 4.Kd5 Kg6 5.Ke6 Kg7 6.Kd6 Kg6 7.g3 Kh6!
on Kd7 black has to play Kh7!
on Kd5 – Kg7! and on Ke6 – Kg6.
Before g3 black has to ignore the opposition when the white king is from the side : on Ke6 black has to answer Kg7 , on Ke7-Kg6.
but if white goes from the front – on Kf5 black has to play Kf7! , because if on Kf5 black answers Kg7, white wins by 1.Ke6 Kg6 2.g3 Kg7 3.Ke7 Kg6 4.Kf8
So, if white starts with 1.Kf4 Kg6 2.Ke4, black plays 2…Kg7!
3.Kd5 Kg6 (no Kf7 , then white wins taking a pawn)
Now on Kd6 black has Kf5, on 4.Ke6 Kg7 and if 5.g3, then 5…Kg6 – drawing as I noted before.
So, I will be very surpised if there is a win for white.
Pasman: in your line with Kings on f5 and g7 with white to move — after 1. Ke6 Kg6 2. g3 Kg7 3. Ke7 Kg6 4. Kf8
Black wins with 4 … f5 5. Ke7 f4 6. gxf Kf5 7. Kf7 Kxf4 8. Kg6 Kg4, right?
Tom, you are right, so white can not play Kf8 and that is draw too.