johnlspouge: Out of deference to those who dislike long posts, I am going to write a prolog. I went for
18.Bh5 hxg5 19.Bxf7+ Kxf7 20.fxg5+
Upon analysis, my lines appear adequate to win (although rarely with the mates I "foresaw"). In particular, however, the computer needed a lot of coaxing to show my line
yields a win and not a perpetual check, and it preferred 20...Kg8 for Black and 20...Kg6 21.Rxf8 for White. I note that <MostlyAverageJoe> found at least one line where the White advantage sputtered. I will report back with computer-aided analysis, after I absorb the kibitzing.
Sunday (Insane): White to play and win.
Material: Even. White has a typical K-side attack in the Sicilian defense. The particular features of this attack include: the White Qg3 on the same file as the Black Kg8, separated by the White Ng5 and Black Pg7; the White Bd4 focused on Pg7, like Qg3; and the White Rd1 and Rf1, which will be active against Pd6 and Pf7, after the obscuring White pieces move. Only the White Nc3 and Be2 require activation. Black has two threats: Nxc2 and hxg5 (the latter apparently forcing the retreat of Ng5). The Ng5 is almost immune to capture, however, because after its capture, fxg5 opens the f-file for attack against Pf7.
Candidates (18.): Nxf7, Bh5
18.Bh5 (threatening 19.Bxf7+ 20.Nxe6)
To avoid outright loss of a P, Black must capture or threaten at least a piece, because the original Black threat
18…Nxc2 19.Bxf7+ Kh1 20.Nxe6 Bxe6 21.Bxe6
leaves Black a P down and cramped in a dangerous position. The response
18…g6 19.Nxf7 (threatening 20.Qxg6+)
is also inadequate, so Black must accept the sacrifice of Ng5.
18…hxg5 19.Bxf7+ Kxf7 [else, 20.Qh3#] 20.fxg5+
Black has 3 flight squares for Kf7 and 1 interposition. Black's most serious try 20…Kg6 seems to require White to throw Rf1 onto the fire.
(1) 20…Kg6 21.Rf6+
Black has 4 legal moves, of which 3 can be rapidly disposed of.
(1.1) 21…Kh5 22.Qf3+ and mate soon, with the aid of Bd4
(1.2) 21…Kh7 22.g6+ 23.Qh4 and mate soon
(1.3) 21…Nxf6 22.gxf6+ (threatening 23.fxg7 then 24.g8=Q or 24.Qxg7+ 25.Rf1)
Black is mated if Rd1 enters the K hunt with tempo at f1. The Bd4 and Qg3 can check Kg3 to either f7 or g8, however, at which point Pf6 disappears with f7+ or fxg7 and Rd1 enters with tempo at f1.
(1.4) 21…gxf6 22.gxf6+ (threatening 23.Qg5 24.Qh5+)
The same pattern prevails as in line (1.3), so Black is mated.
Any response to 20.fxg5+ other than 20…Kg6 rapidly undermines the Black position. White does not need to invest Rf1, which then supports the infiltration of Qg3 and blocks the Black K's flight at the f-file.
(2) 20…Kg8 21.Qf4 (threatening 22.Qf7+ 23.Qh4+ 24.g6 and mate soon)
21…Bc6 [Nf6 22.gxf6 (threatening 23.f7+) wins]
22.Qxf8+ Kh7 23.Rf7 (threatening 24.Rxg7+ Nxg7 25.Qxg7#)
Black must lose material and still face a potent mating attack.
(3) 20…Ke7 21.Qf4 Nf6 22.gxf6+
and as above, a massacre ensues.
(4) 20…Nf6 21.gxf6 g6 [else, 22.fxg7] 22.Qh4 (threatening 23.Qh7+)
and the Black position collapses.