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1) Kg6; R:g4
2) a7; Ra4
3) f7; Ke7
4) Kg7; +-
1.Kg6 Ra2 2.Be2! Rxe2 3.a7 Ra2 4.f7 Ke7 5.Kg7 and white must win
A few options of Bh3 as the first move:
1. Bh3 Rg3
2. Bf1 Rf3
3. Kg5 Rf1
4. a7 Ra1
5. f7 Ke7 and black stops both pawns. Can white do better in this line?
1. Bh3 Rg3
2. f7 Ke7
3. Kg6 Rh3
4. Kg7 Rf3
5. a7 Rf7
6. Kg8 Rg8 wins for black. At move 2, white can try pushing the other pawn:
1. Bh3 Rg3
2. a7 Ra3
3. f7 Ke7 (forced)
4. Kg5 Kf7
5. Kh4 should draw for white, at least, but I don’t see a win starting with Bh3.
1. Kg6 Rf2
2. a7 Ra2
3. f7 Ke7
4. Kg7 Rxa2
5. f8=Q+
1. Kg6 Ra2
2. Be2 Rxe2
3. a7 Ra2
4. f7 Ke7
5. Kg7 Rxa7
6. f8=Q+
1. Kg6 Ra2
2. Be2 h3
3. f7 h2
4. f8=Q+ Kc7
5. Bf3
Options starting with Bf3:
1. Bf3 Rf2
2. Kg4 Ra2 (a7 is the threat)
3. Bb7 Ra5 (to protect g5)
4. Kh5 Ke8 (threatens the f-pawn)
5. Kg6 Kf8 (white’s threat is Kg7)
6. Bc8 Rc5
7. Bg4 Ra5
8. Bc8 Ra6 (Rc5=, I am not sure)
9. Ba6 g4
10.Kg5 g3
11.Bf1 Kf7
12.Kf5 and white will win, so at move 8, black cannot sacrifice the rook at a6, as I suspected. Black may have a win in this line after move 5, but it isn’t obvious to me what it is.
Since the recurrent theme of these “classic” studies is the least obvious moves being the correct ones, lets analyze Kg6 and Ke6:
1. Kg6 Rg4
2. f7 Ke7
3. Kg7 Rf4
4. a7 Rf7+ wins both pawns and the game. Interpolating moves 2 and 3 doesn’t make any difference that I can see.
The more interesting Ke6, which stops 2. ….Ke7:
1. Ke6 Rg4
2. f7 Rf4
3. a7 Re4
4. Kd5 wins for white.
Also,
1. Ke6 Rg4
2. f7 Re4
3. Kd5 Rf4
4. a7 Rf7
5. a8(Q)Ke7
6. Qg8 should be a win for white, but this needs deeper analysis than I have given it here, and move six might not be the best option for white.
Do other first move replies save black? One doesn’t, but the other might.
1. Ke6 Ke8
2. Bf3 h3 (trying a ruse on white)
3. a7?? Ra2 (threat is a8(Q)#)
4. a8(Q)Ra8
5. Ba8 g4
6. Be4 g3 and one of the pawns will queen. However, at move 3, white can just take the rook:
1. Ke6 Ke8
2. Bf3 h3
3. Bg2 hg2
4. a7! wins.
The main and best option for black, I think, is:
1. Ke6 Ra2
2. a7 Ra7
3. f7 Ra6
4. Kf5 Ke7
5. Kg5 and this looks like a draw to me.
Options for Kg5/Ke5:
Of all the moves, the one I actually looked at first is Kg5, but I don’t see anything more than draw for white:
1. Kg5 h3
2. a7 Ra2
3. Bh3 Ra7 and this looks like a draw to me.
As for Ke5:
1. Ke5 Rg4
2. f7 Ke7 and black should win.
After Kg6, Black cannot stop both pawns.
1. Kg6! Rxg4
2. Kg7 Rf4
3. a7
Black is unable to stop both pawns.
Other defenses also fail, for example:
1…Rf2
2. Kg7 and 3.a7
1…Ra2
2. Kg7 Rf2
3. a7
1…h3
2. Bxh3 only delays inevitable.
I like Ke6:
1. Ke6 Rg4
2. f7 Rf4
3. a7
wins for White
1. Ke6 Rg4
2. f7 Re4
3. Kf6 Rf4
4. Kg7 Ke7
5. a7
wins for White
1. Ke6 Ke8
2. Bf3 Ra2
3. Bc6+
wins for White
1.Kg6 Ra2 2.Be2 Re2 3.a7 Ra2 4.f7 Ke7 5.Kg7 Ra7 6.f8Q+ Ke6+ 7.Kg6+- (black cannot build a fortress, I think).
the best i can think of is
1. Kg6, Rxg4
2. a7, Ra4
3. f7, Ke7
4. Kg7, Rxa7
5. f8Q+, Ke6+
6. Kg6 and i don`t know if white can win with queen against rook and two pawns.
Everyone has move order wrong.
Both in 1.Kg6 Rxg4 and 1.Kg6 Ra2 Be2 Rxe2 -lines white has to play f7 first and not rush with a7.
1. Kg6 Rxg4 2.a7?? (f7!+-) Ra2 3.f7 Ra6+! -+
and 1.Kg6 Ra2 2.Be2 Rxe2 3.a7?? (f7!+-) Ra2 3.f7 Ra6+! -+