Originally posted by Mephisto2
Maybe not difficult, but not quite as easy as you make it sound. Probably both 1.Bd7+ and 1.Bb7 win, but I think that 1.Bd7 leads to a slightly easier winning endgame K+R+pvs.K+R. For instance:
1.Bd7+ Kxc7 (Kxd7 is similar) 2.Rc8+ Kd6 (Kxd7 loses much faster) 3.Rc6+ Kxd7 4.Rd8+ (the crucial clearing move to free the king) Kxc6 5.g8=Q Nf8+ 6.Kg7 Rxg6 7.Kxf8 Ne6+ 8.Qxe6 Rxe6 9.Kf7 and wins.
Or what do I miss?
Almost right, only 1.Bb7+! wins
Black threatens mate. In order to win, White must vacate g7. This calls for a check by the Rg8, which calls for a check by Rf8 - which calls for a line-opening bishop sacrifice.
Why 1.Bd7+ doesn't work will be explained later. If Black does not capture a bishop now, White will have less trouble liberating the North-East corner. There are two variations.
a) 1...Kxc7 2.Rc8+ Kb6 3.Rc6+
After 3...Kxb7 4.Rb8+ Kxc6 5.g8Q Nf8+ 6.Kg7 Rxg6+ 7.Kxf8 Ne6+ 8.Qxe6+ Rxe6 9.Kf7 White wins the rook ending. The thematic defence is
when Black hides behind the white pieces. A strange hunt develops:
4.Ba6+ Ka5 5.Rc5+ Ka4 6.Bb5+ Kb4 7.Rc4+ Kb3 8.Ba4+ Ka3 9.Rc3+ Ka2 10.Bb3+ Kb2 11.Rc2+ Kb1 12.Ba2+ Ka1 13.Rc1+
This could go on forever, if not for the edge of the board:
13...Kxa2 14.Ra8+ followed by 15.g8Q, and White wins.
b) 1...Kxb7 2.Rb8+ Kc6 3.Rb6+
and now the dark-squared bishop joins the hunt:
(or 3...Kxc7 4.Rc8+ Kxb6 5.g8Q and White wins)
4.Bd6+ Kd5 5.Rb5+ Kd4 6.Bc5+ Kc4 7.Rb4+ Kc3 8.Bd4+ Kd3 9.Rb3+ Kd2 10.Bc3+ Kc2 11.Rb2+ Kc1 12.Bd2+ Kd1 13.Rb1+ and Rg8 finally gets its check.
The thematical try
1.Bd7+? does not work, because after
the black king gets too close:
2.Rd8+ Kc6 3.Rd6+
If Black tries to hide now, White wins as above, but Black draws with
3...Kxc7! 4.Rc8+ Kxd6 5.g8Q
After 5.Rd8+ Ke7! both promotions only draw; 6.g8Q Nf8+ 7.Kg7 Rxg6+ etc., or 6.g8N+ Kxd8 7.Nxh6 Nf8
5...Nf8+ 6.Kg7 Rxg6+ 7.Kxf8 Ne6+ 8.Qxe6+ Kxe6 and now the rook ending is a draw.