johnlspouge: Sunday (Insane): Black to play and win.
Material: Even. Black has a spatial advantage on the K-side, with a battery Rg7 and Qg6 opposite Kg1. White has a battery Rf1 and Rf3 opposite Rf5, which Pe6 protects. Black must take action, because the White Q-side majority already threatens and certainly wins the endgame. Black has 2 mobile Ps, Pd5 to deflect Qe3 and Ph4 to remove Pg3. Positionally, Black should maintain the wedge Pg3, to impede the flight of Kg1, and advance Ph4 to open the h-file. The Rf5 blockade of Pf4 should be maintained to prevent counterplay with the move f5 as long as necessary. The position of Qg6 is a liability should such counterplay occur. The Rg7 provides critical shelter for Kh8 if Qe3 checks on the back rank.
Candidates (43…): h3, Qg4, Rh5, Rh2, d4
43…d4 (threatening 44…d3)
<As Toga shows below, my candidate draws>, but I did not delete my (today mostly verbal) processes, in case anyone is interested. Black's K-side attack was more autonomous than I expected, so most of my concern about the Q-side was unfounded.
If White does not capture, Pd4 deflects the White Qe3 from the a7-g1 diagonal and slows Q-side counterplay based on the move b6. At the mere cost of surrendering e4 and with no loss of tempo, the placement of Pd4 at d3 instead of d5 improves resources for the Black attack. White has 2 feasible captures. The first, 44.cxd4, slows the White Q-side counterplay and creates a passer Pc4. Thus,
44.Qxd4 h3, threatening
45…hxg2 46.Kxg2 Rh4 47.Rh1 [else, Rh2+] Rxh1 48.Kxh1 Qh4+ etc.
Because closing the White K-side with …h2+ loses to the White Q-side majority, Black must capture …hxg2, to open the K-side. Black can force Kg1 into the open by invading at either h2 or h1. White has lost an essential tempo for defense and has 2 feasible moves.
(1) 45.Qe3 hxg2, and
(2) 45.Qd8+ (making Kh8 block Rg7) Kh7 46.Qd2 Qh3,
both followed by 46…Rh4 and invasion on the h-file, with collapse of the White position.
Toga II 1.3.1 evaluates the position (with minus scores favoring Black):
[ply 15/45, time 00:45, value -1.18]
43...h3 44.gxh3 <<>Qh7> 45.Kg2 Rh5 46.Rxg3 Rxh3 47.Rxg7 Rh2+ 48.Kg1 Rh1+ 49.Kf2 <<>Qc2+> 50.<Ke1> Qb1+ 51.Kd2 Rxf1 52.Qxa7 Qd1+ 53.Ke3 d4+ 54.cxd4 Re1+ 55.Kf2 Qe2+ 56.Kg3 Rg1+ 57.Kh4 Rxg7 58.f5
<<>Two critical moves> are required to justify 43…h3. The game line deviates from the best line at 15 plies at the indicated <move>!!! At deeper plies, White's defense improves to
[ply 16/73, time 07:27, value -2.21]
43...h3 44.<Rc1> Rh5 45.f5 exf5 46.e6 Rh4 47.gxh3 Re4 48.Qd2 Qxe6 49.Rd1 Re2 50.Qf4 Re1+ 51.Rxe1 Qxe1+ 52.Rf1 Qxc3 53.Rd1 Qc2 54.Qh4+ Rh7 55.Qd4+ Kg8 56.Qxd5+ Kg7 57.Qb7+ Kg6
According to Toga, with best play 43…d4 yields a perpetual check:
[ply 17/67, time 08:03, value 0.00]
43...d4 44.Qxd4 h3 45.Qd8+ Kh7 46.Rd1 Rh5 47.f5 exf5 48.Rd7 hxg2 49.Rxg7+ Qxg7 50.Qd4 Rh1+ 51.Kxg2 Rh2+ 52.Kg1 Rh1+ 53.Kg2 etc.
although the return 45.Qe3 loses much as I described.
Like <dzechiel>, I take my hat off to anyone who got the winning idea, which is 43...h3 44...<<>Qh7> 49...<<>Qc2+>.