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Umm… would d6+ do? It closes the 6th rank to guard the h-pawn home (Rxd6 loses the rook to Bc5).
Starts with 1.Bg7. Protect this passed pawn.
If the black king advances to grab the the d-pawn, just advance with h7. Cant stop from queening. White will win the black rook.
1. d6 Kxd6
2. h7 Ra1
3. g3!
allows Bg2, then the white king can march to d4 unopposed. 3.h8 is premature and makes the ending harder to win, as the black king can advance. Later sacrificing the white squared bishop for 2 pawns will leave an opposite coloured bishps position which might be drawn.
It seems the critical idea is to close the 6th rank to prevent the rook from getting behind the pawn with check.
This forces the exchange of a rook for the queen at h8. I’m pretty curious how the rest of the endgame works out. Those are the types of positions I get into in endgames that I often mess up. It seems that white needs to give his light square bishop some room, which could suggest g3. On the other hand, g3 makes it more difficult to get the king into position. However, with bishops of b4 and g2, the king can get up to d4. Yet, white can trade bishops (and the expense of breaking up his connected pawns) – this would seem to be something that needs to be considered in a plan.
How do you calculate this?
1.d3 kd3
2.h7
or
1.d3 Rd3
2.Bc4
Perhaps 1. Bg7 is not so protective.
1. … Kf7
2. h7 Kxg7
3. h8Q Kxh8
1.d6+ Kxd6
2.h7 Ra8
3.h8=Q Rxh8
4.Bxh8 Kc5
5.Bd4+ Kd5 ( or 4…Kd5 without Kc5)
6.g3 Bc2
7.Bg2+ Be4
8.Kg1 Bxg2
9.Kxg2 Ke4
10.Kf2 Kd3
11.Ke1
with the idea of bringing the white king to capture the b pawn.
the black king can try counter attack on the g pawn but the bishop placed on f6 ( keeping an eye on c3 )will protect it via h4 when the black king goes to f3.
i should replace 8.Kg1 by 8.Bh8 because when the bishop stand on d4 and the black king on d3, the b pawn can be push to complicated the endgame for white… 😉
Bc5+/d6+/h7 i think the last is the best but i doubt it will be enough to win, because the whte whte bshp will be treaded whith the bck one, and one bshp might no be enough if the pawns are on hte other color, need to look at it more deeply but i want to keep reading hthis fascinating blog.
try it