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I think White will lose on time 🙂
I think White wins after f4!
The rest is a matter of technique!
1. Rb7+ looks like a win
I sort of like Rb7+, but I can’t be sure if this is best (I’m terrible at these sort of endgames). My thought is that there is a threat of a back-rank mate if black retreats, giving white a tempo, with which he can snatch two pawns for one.
So if …Kg8 2 Kf6 and black is in big trouble because the b-pawn keeps the black rook from checking and if 2…h4 3 Kxg6 and black is lost.
So 1 Rb7+ Ke6 looks like black’s only defense. And now 2 Rxh7 Rxb5 3 Kxg6 seems to give white an extra passed pawn and hence a winning game.
Tentatively (as a patzer) I would proceed Kh6, Black would then defend by Kg8, Rb8+ forcing K away from pawn, then Kxh7 and this is then a winning position. Hopefully I am right but look forward to seeing other, more informed, comments.
After 1.Kh6 I would simply play Rc4.(2.Kxh7 Rh4++)
I am not sure if after 1 Rb7+ Ke6 2 Rxh7 Rxb5 3 Kxg6 f4 it is an easy win for white.
What about 1 h5 gxh 2 Rf6+ K… 3 Rxf5 Rc… 4 Kxh5 keeping the b-pawn and making another passed pawn on the f-file?
if h5, i would play f4+ Kxf4 Rxh5.
1 Rb7+ Ke6 2 Rxh7 Rxb5 3 Kxg6 f4 4 Rf7 and now black king is cut from the h pawn, and black have to protect f4. White must win this.
No real solution thus far? So i feel free to present my 4 hours workout (with pieces and with silicon help). The given position is FAR away from being easy. I think white can win this, but it is a titanic task and worth a grandmasters mind… so – my humble efforts might be proven wrong (and i liked the comment of anonymous Nr.1 1:28:00 AM very much…!)
1.Rb7+ Ke6
2.b6!
[2.Rxh7? Rxb5 3.Kxg6 Rb3! 4.f4 Rg3+ 5.Kh5 Rg4=; 2.Kh6? Rc4 3.Kxh7 (3.Rxh7?? Kf6! 4.h5 Rh4–+) 3…Rxh4+ 4.Kxg6 Rf4 5.b6 Rxf3 6.Ra7 Rb3 7.b7 f4=]
2…f4+
3.Kh6 Rc3
[3…Rh5+ 4.Kg7 Rxh4 (4…Rb5 5.Rb8! (5.Kxh7 g5 6.hxg5) ) 5.Re7+! Kxe7 6.b7+-; 3…Rb5 4.Kxh7 g5 (4…Rb3 5.Kg7 Rxf3 6.Rf7 Rb3 7.Rxf4 Ke5 (7…Rxb6 8.Rf6+) 8.Rf6 Rb4 9.Rxg6+-) 5.hxg5 (5.h5? g4! 6.fxg4 f3! 7.Kg8 Rb4 8.g5 Rf4! 9.Rg7) 5…Rxg5 6.Rb8 Kd6 (6…Kf7 7.Kh6 Rg6+ (7…Rg3 8.b7 Rxf3 9.Rf8+ Kxf8 10.b8Q+ Kf7 11.Qb7+) 8.Kh5 Rg1 9.b7 Rb1 10.Kg4 Kg7 11.Kxf4+-) 7.Rf8 Rb5 8.Kg6 Rb4 (8…Rxb6 9.Rf6+ Kc5 10.Rxb6 Kxb6 11.Kf5+-) 9.Rf7 Rb1 10.Rxf4+-]
4.Rb8!
[4.Rxh7? Rxf3 5.b7 Rb3 6.Kxg6 Rg3+ 7.Kh5 Rb3 8.Kg4 f3 9.Kg3 Kf6 10.Rc7 Kg6 11.Rd7 Kh5=]
4…Kf7
[4…Rb3 5.Kxh7 Kf7 6.Rb7+ Kf6 7.Rg7 Rxf3 8.Rxg6+ Kf7 9.Rg4! Rb3 10.Rxf4+ Ke6 11.h5 Rxb6 12.Kg7™ Rb7+ 13.Kg6 Rb2 14.Re4+ (14.h6? Rg2+ 15.Kh5 Rh2+ 16.Rh4 Rxh4+ 17.Kxh4 Kf7=) 14…Kd5 15.Rg4 Rb6+ 16.Kf5 Ra6 17.Rh4 Ra8 18.h6 Rg8 19.Kf6 Kd6 20.h7 Rf8+ 21.Kg7+-]
5.Ra8
[5.Kxh7? Rxf3 6.b7 Rb3=]
5…Rb3
6.Ra7+ Ke6
[6…Kg8? 7.Rg7+ Kf8 8.b7 Rb5 9.Kxh7 Rb2 10.b8Q+ Rxb8 11.Rg8++-]
7.b7 Kf6
[7…Kd6 8.Kxh7 Kc7 9.Kxg6 Rxf3 10.Kg5 Rd3 (10…Rh3 11.Ra4 f3 12.b8Q+! Kxb8 13.Kg4 f2 14.Rf4 Rh1 15.Rxf2+-) ]
8.Kxh7 g5
[8…Rb1 9.Kh6 Rb2 10.Ra6+ Kf5 11.Ra8 Rxb7 12.Rf8+ Ke5 13.Kxg6 Rb6+ 14.Kg5 Rb3 (14…Rb7 15.Re8+ Kd4 16.h5 Rg7+ 17.Kxf4 Rb7 18.h6 Rc7 19.h7 Rxh7 20.Kg5 Rg7+ 21.Kf6 Rg1 22.f4 Kd5 23.f5 Rf1 24.Kg6 Rg1+ 25.Kf7 Rf1 26.f6 Rf2 27.Kg7 Rg2+ 28.Kf8 Rf2 29.f7 Kd6 30.Re7 Ra2 31.Re4 Kd7 32.Rg4 Rf2 33.Kg7 Ke7 34.Re4+ Kd6 35.f8Q++-) 15.Rf5+ Kd6 16.Rxf4+-]
9.Ra6+ Ke5
[9…Kf5 10.Ra5+ Ke6 11.hxg5 Rxb7+ 12.Kg6 Rb3 13.Ra4 Rxf3 14.Re4+ Kd5 15.Kf5 Kd6 16.Kf6! Kd5 17.Ra4 Kc5 18.g6 Kd5 19.g7 Rg3 20.Rxf4 Kd6 21.Rf5 Kd7 22.Rg5 Rf3+ 23.Kg6+-]
10.hxg5 Rxb7+
11.Kg6!
[11.Kh6? Rb3 12.Ra5+ Ke6 13.g6 Rxf3 14.g7 Rh3+ 15.Kg6 Rg3+ 16.Kh7 Kf6 17.g8N+ (17.g8Q? Rh3+ 18.Rh5 Rxh5#) 17…Ke6=]
11…Rb3
[11…Rb5 12.Ra4 Rb6+ 13.Kh5 Rb1 14.Ra5+ Ke6 15.Kg4 Kf7 16.Kxf4 Kg6+-]
12.Ra5+ Ke6
[12…Kd4 13.Kf5 Ke3 14.g6 Rb7 (14…Rb1) 15.Ra3+ Kd2 16.Kxf4 Kc2 17.Kg5 Rb5+ 18.Kh6 Rb1 19.g7 Rh1+ 20.Kg6 Rd1 21.g8Q Rg1+ 22.Kf7+-]
13.Ra4
[13.Rf5? Rxf3 14.Rf8=]
13…Rxf3
14.Re4+ Kd5
15.Kf5 Kd6
16.Kf6 Rf2
17.g6 f3
18.Rf4 Kd5
19.g7 Rg2
20.Rxf3 Ke4
21.Rf1 Rg3
22.Kf7+-
“1.Rb7+ Ke6
2.b6!
[2.Rxh7? Rxb5 3.Kxg6 Rb3! 4.f4 Rg3+ 5.Kh5 Rg4=”
Well done! I got the first move, but totally missed 2 b6! What a tough problem.
“I think white can win this, but it is a titanic task and worth a grandmasters mind… ”
Good — then I don’t feel bad that I was in a fog and couldn’t see the second move.