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As I understand it from "Pandolfini's Endgame Course," it's a draw if the defending king can get into the corner with his bishop next to him at N1. However, if the defending king is unfortunate enough to get into the wrong corner where his king cannot be shielded with his bishop at N1, but rather at B1, then by the superior side losing a tempo at the right moment by a rook shift along the back rank aimed toward the defending king, the defending king must step into the corner (R1) due to Zugzwang, whereupon mate follows on the next move with RxB (at B1) #. There are also further nuances where the rook prevents the bishop from finding a safe spot to hide, before that ending position occurs.
You're welcome. I'm surprised nobody else volunteered any more comments. Below is one page of several on this topic in Pandolfini's book.
----------
(p. 59)
ENDGAME 36
W: Kb6, Rb2 B: Kb8, Bf7
White moves and wins
Pin and Win
1k6/5b2/1K6/8/8/8/1R6/8 w - -
Black's Bishop controls the corner square closest to his King
(a8), therefore it's the wrong Bishop. To engineer a draw, the
Bishop must be able to occupy the square next to the corner
(here, b8). The actual corner square (a8) is reserved for Black's
King. If White's Rook attacks along the back row, Black's light-
square Bishop won't be a reliable shield for his King. The White
Rook conquers by starting with double attack, threatening the
Bishop and mate. After the x-ray assault 1. Rf2, White stam-
pedes the Bishop and the back-rank square immediately be-
hind (f8). When the Rook reaches the last row, a delaying move
forces mate.
1. Rf2 Be6
2. Rf8+ Bc8
3. Rh8 Ka8
4. Rxc8 mate
(1-0)
Pandolfini, Bruce. 1988. Pandolfini's Endgame Course. New York, New York: Simon & Schuster.
How to win?
Thanks much. It's been about 40 years since I seriously studied Reuben Fine's book. I can still do the N & B mate, but had forgotten this one.
You're welcome. For contrast, below is what happens if the defending player has his king in the *correct* corner: stalemate!
----------
(p. 58)
ENDGAME 35
W: Kh1, Bh8 B: Kg3, Re7
White moves and draws
The Right-Corner Mate
7B/4r3/8/8/8/6k1/8/7K w - -
Black threatens mate at e1 and a Bishop-King fork at h7--a
double attack. If White had a light-square Bishop, his cause
would be hopeless. But White has the dark-square Bishop, the
right Bishop for the corner his King already occupies. To draw,
the Bishop must move on squares of different color from the
King's corner. Then it can block the Rook's check on a square
contiguous to the King's. After 1. Bd4 Re1+ 2. Bg1, Black has
no way to progress, and carefully must keep White from a
looming stalemate. In the final position, if everything were
moved on square to the left, Black would force mate by
making a tempo Rook move along the back rank. Such a move
would force White's King to the corner and the Bishop (then at
f1) would hang.
1. Bd4 Re1+
2. Bg1 Rd1
Stalemate
Pandolfini, Bruce. 1988. Pandolfini's Endgame Course. New York, New York: Simon & Schuster.