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1. Qh8+ Kg5
2. Qg7+ Kxh5
3. Bf7+ Qxf7
4. g4#
1) Qh8+, forces Kg5
2) Qg7+, IF: Qg6, 3) Qxg6#
—, Kxh5
3) Bf7+, and either … Qxf7, 4) g4# OR … Qg6, 4) Qxg6#
Okay, think I got it
Qh8+, Kg5, Qg7+ Kxh5, Bf7+ Qg6, Qxg6#
Qh8+, Kg5, Qg7+ Kxh5, Bf7+ Qxg6 g4#
Of interest is the line that begins with 1.Qf7+, which is a line a lot of players might choose over the board:
1. Qf7?! Ke5
Of course, Kg5 allows 2.Qg7 for a forced mate. However, now white only two palatable options- check from g7 or check from e8. The best of the two looks like….
2. Qg7 Kd6
3. Qh6 Kc7
And the black king is pretty safe now, but white can get the queens off the board now…
4. Qf4 Qf4
5. gf4!?
If white tries 5.Nf4, then 5. …Ne5 creates some counterplay for black on the queenside, and I can’t fully evaluate whether or not white retains a decisive edge. Continuing:
5. ………….Nd8 (what better?)
6. Bg8! Ne6
7. h6 Nf8
8. f5
And I think black will lose a piece. However, the ending is still tough, though likely won for white.
Isn’t 1. Qf7+ Ke5 2. Qg7+ Qf6 better for Black?
No, after 2. …Qf6, white takes at d7 and black’s position collapses;
2. ………..Qf6?
3. Qd7 Qd6 (what is better?)
4. Qg7 Qf6 (forced)
5. Qb7 and this is hopeless for black.