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Kf5 should do the trick:
1. Kf5 a6 2. Rh7 and black is in zugzwang: If the pawn moves, black rook takes is and returns, and black will lose the bishop too; if the king moves, black will have time to take the bishop and return to guard a8.
There is no move after 1. Kf5 a6 2. Rh7 a7 3. Rxa7 that can save the bishop from Rg7 because of the mate threat, pin, and black’s ability to move the rook back and forth on h file.
1. …, Kf5
2. a6, Rh7
3. a7, Rxa7
0-1
win
1. … Kf5 followed by 2. … Rh7
Of course Black draws without any effort…but after edging the king closer…like KF5…white will eventually run out of moves and have to ditch the Bishop as well…its pretty much a no lose situation for black.
Ra8?
tougr me. I will settle with a draw
kf5 Zuggy
Kf5 a6 (otherwise King has to move and B is lost)
Rh7 a7 (otherwise King has to move and B is lost)
Rxa7 and white is mating…
1. Kf5 a6 2. Rh7 a7 3. Rxa7 followed by Rh7 and Rh8?
The endgame rook vs dark squared bishop is a draw, if the defending king can reach h1 or a8 corner. However, in this situation we can prevent this by exploiting zugzwang and win the bishop.
1. … Kf5
2. a6 Rh7
3. a7 Rxa7
Note that white’s moves are forced, otherwise black plays Rxh6+ followed by Ra6.
And now:
4. Kh4 Rh7
5. Kh5 Rh8
6. Kh4 Rxh6+
or if white moves the bishop in move 4:
4. … Rh7+
5. Bh6 Rh8
6. Kh4 Rxh6+
1..Kf5! 2.a6(Zugzwang)Rh7! 3.a7(Zugzwang)Rxa7 4.Kh4 Rh7 5.Kh5(Zugzwang)Rh8! 6.Kh4(Zugzwang)
etc Black wins
…… Kf5
a6 Rh7
a7 Rxa7
A:
Bishop move any Rh7+
Bh6 Rh8
Kh4 Rxh6 black wins
B:
Kh4 Rh7
Kh5 Rh8
Kh4 Rxh6 black wins
This is win for black:
1… Kf5 2. a6 Rh7 3. a7 Rxa7 4. Be3 Rh7+ 5. Bh6 Rh8 6. Kh4 Rxh6+ -/+
It becomes K and B vs K and R. Black K goes to f5, white is in zugzwang and must promote pawn while black king goes to f6 and back to f5. But I don’t know what happens after that..is it a draw?
Oh, I see a little more…after white is forced to promote pawn and black R takes it off, white B could be trapped in lethal pin again, while white king is left on h5 in danger of mate from Rh8. So white must play Bg7…that’s all i got…I’m only a patzer working it out in my head…
Black wins with Kf5!
1. … Kf5
2. a6 Rh7
3. a7 Rh8
not “better” or correct in the sense of a fast win, but it shows the full beauty of this zugzwang position. White has to offer the pawn a second time 🙂
4. a8-Q Rxa8
the rest is already discussed:
5. Kh4 Rh8
6. Kh5 Rh7
7. Kh4 Rxh6+
or
5. Bxx Rh8+
6. Bh6 Rh7
7. Kh4 Rxh6+
Greetings, TG
1. … Kf5
2. a6 Rh7
3. a7 Rh8
not “better” or correct in the sense of a fast win, but it shows the full beauty of this zugzwang position. White has to offer the pawn a second time 🙂
4. a8-Q Rxa8
the rest is already discussed:
5. Kh4 Rh8
6. Kh5 Rh7
7. Kh4 Rxh6+
or
5. Bxx Rh8+
6. Bh6 Rh7
7. Kh4 Rxh6+
Greetings, TG