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… B:h2
Q:c7 Bf3+
Bg2 R:g2+
Kf1 R:h2
Bg2
1…Bxg2! 2.Qxc7 Bf3+ 3.Bg2 Rxg2+ 4.Kf1 (4.Kh1 Rg3#) Rxh2 0-1
Bg2 jumps out since it threatens a discovered check on move 2, and has uncovered an attack on the white queen. None of white’s options look palatable:
1. …..Bg2
2. Bg2 Qc4 wins
Or
1. …..Bg2
2. Qc7 Bf3
3. Bg2 Rg2
4. Kf1 Rh2
5. Ne2 Re2
6. Rd8 Bf8
7. Rf8 Kf8
8. Qc5 Re7!
9. Qc8 Re8
10.Qc5 Kg8 and white is out of checks and must give up the queen for a rook just to prevent mate.
Bxg2 Qxc7 Bf3+ Bg2 Rxg2+ Kf1 Rxh2
1. … Bg2: looks like a winner.
2. Qc7: Bf3+
3. Bg2 Rg2:+
4. Kf1 Rh2: and mate at h1.
1. Bxg2 Qxc7 (what else?)
2. Bf3+ Bg2
3. Rxg2+ Kf1 (Kh1 Rg5#)
4. Rxh2!!
This was the hard move to find.
Now the threat Rh1# can’t be defended, since Kg1 doesn’t help, other K moves are impossible, f3 is impossible, f4 guards against the queen, and Bf3 guards:
4. … Ne2
5. Rxe2
and there is only:
5. … Qc8+
6. Bf8! …
7. Rh1#
It’s not at all intuitive that black’s white bishop and g rook can mate that king all alone.
But with the tempo from white’s Qxc7, and because black rook controls the e-file, and the f4 pawn makes queen offside on c7, so the “magic” happens.
Bxg2 looks like the best move for black, as most others already pointed out. But there is no straightforward path to mate initially if white plays correctly.
[FEN “4r1k1/1pq2p1p/2b3pb/6r1/PPQ2p2/2N5/5PPP/1R1R1BK1 b – – 0 0”]
1… Bxg2 {Leaving the black queen vulnerable.}
2. Qxc7? Bf3+ {Discovered check. White king has no exit from 1st rank. White’s only choice is to interpose bishop at g2.}
3. Bg2 Rxg2+
4. Kf1 Rxh2! {Threatening Rh1#.}
5. Ne2 Rxe2 {White hoping to interpose Ng1 to prevent mate.}
6. Rd8+ Bf8
7. Rxf8+ Kxf8 {White has bought some tempo to try to get queen to g5. Pretty hopeless at this point, though, since white will have to sacrifice queen for rook.}
8. Qc5+ Re7
9. Qg5 Rh1+
10. Qg1 Rxg1+
11. Kxg1 Re5 {Black has a descisive advantage. Now black’s goal is to get rook to h1 for a mate threat or, at least, to win the other white rook.}
12. Kf1 Rh5
13. Ke1 Rh1+ {The white king now has an escape route, but black’s rook will take white’s.}
14. Kd2 Rxb1 {An easy win for black from here.}
Analysis of Pht’s Qc8+ move:
6. Qc8+ Bf8
7. Qg4 Rexf2+ {Tempting Bxg4, causing some temporary disturbance to black’s mate attack via Rh1. But Rexf2+ doubles the rooks, so the white king is no danger to the rook at h2. Also, this adds a new mate threat Rfg2#. White has no adequate answer to this threat or, alternatively, to Rh1#.}
8. Kg1 Bxg4
9. Rf1
(9. Rd3 Be2
10. Rg3
(10. Rh3 Rfg2#)
10… fxg3
11. Rd1 Rfg2#)
(9. Rd5 Rfg2+
10. Kf1 Bh3
(10… Bf3
11. Rh5 Rxh5
12. Rd1 Rh1#)
11. Rb2 Rh1#)
9… Rfg2# {Conclusion: early Qc8+ move by white leads to mate by black within six moves.}