Section A baseline after 3...Nf6 suggests that 4.0-0 is the only move with a chance for white advantage. I am keeping this analysis line active, hoping for a reversal in 4.d3 of some kind... come on, 4.d3! 3000 hours, probably a record run for me...
Stockfish_191017
76/105 2449:30:58 8,842,848,536k 8,188k +0.13 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5 7.Rxe5+ Be7 8.Bf1 0-0 9.Nc3 Bf6 10.Re1 Re8 11.Nd5 Rxe1 12.Qxe1 b6 13.Nxf6+ Qxf6 14.c3 c5 15.d4 cxd4 16.cxd4 Qxd4 17.Bd2 Qd5 18.Bf4 Bb7 19.Rd1 Re8 20.Qxe8+ Nxe8 21.Rxd5 Bxd5 22.Bb8 a5 23.Ba7 Bxa2 24.Bxb6 a4 25.Bb5 Bb3 26.Bxd7 Nd6 27.Bd4 Nc4 28.f3 f6 29.Kf2 Kf7 30.Ke2 a3 31.bxa3 Nxa3 32.Bc6 Ke6 33.g3 Nc4 34.Kf2 Ne5 35.Bb5 Nc4 36.Ba6 Nd6 37.Bd3 h5 38.Bh7 Kf7 39.Bb1 g6 40.Bc5 Nf5 41.f4 Bc4 42.h3 Ng7 43.f5 gxf5 44.Ke3 Be6 45.Kd4 f4 46.gxf4 Bxh3
76/105 2787:41:30 8,842,848,536k 8,207k 0.00 4.d3 Bc5 5.Bxc6 dxc6 6.0-0 Nd7 7.c3 0-0 8.d4 Bb6 9.h3 Re8 10.Re1 h6 11.Qc2 exd4 12.cxd4 Qf6 13.Be3 Nf8 14.Nbd2 Ng6 15.Kh2 Qe6 16.Kh1 Bd7 17.Ng1 f5 18.a4 f4 19.a5 fxe3 20.fxe3 Nh4 21.axb6 axb6 22.Rxa8 Rxa8 23.Rf1 c5 24.Ngf3 Nxf3 25.Rxf3 cxd4 26.exd4 Ra1+ 27.Rf1 Rxf1+ 28.Nxf1 Qf6 29.Qc4+ Kh8 30.Nd2 c5 31.Nf3 Qf4 32.Qd3 cxd4 33.e5 Qc1+ 34.Kh2 Qf4+
76/119 2922:19:22 8,842,848,536k 8,222k 0.00 4.Nc3 Bc5 5.0-0 0-0 6.Bxc6 dxc6 7.d3 Re8 8.Be3 Bxe3 9.fxe3 Qe7 10.a4 Qb4 11.Qd2 a5 12.b3 Nd7 13.h3 f6 14.Ne2 Nc5 15.Qe1 Qxe1 16.Rfxe1 Bd7 17.Rec1 b6 18.Nc3 Be6 19.Kf2 Rad8 20.Ke2 h5 21.Rg1 Nb7 22.Kd2 Nd6 23.Kc1 Kf7 24.Rd1 Kg6 25.Kb2 Bd7 26.Rg1 Rh8 27.Rh1 Rhe8
75/109 2449:30:58 8,842,848,536k 8,188k 0.00 4.Bxc6 dxc6 5.d3 Bd6 6.0-0 Qe7 7.Nbd2 Be6 8.b3 a5 9.Nc4 Nd7 10.Nxd6+ cxd6 11.Ng5 a4 12.Be3 0-0 13.Nxe6 Qxe6 14.c4 axb3 15.axb3 d5 16.exd5 cxd5 17.Re1 h6 18.Rxa8 Rxa8 19.h3 Qd6 20.d4 dxc4 21.bxc4 exd4 22.Bxd4 Nf8 23.Be3 Qxd1 24.Rxd1 Rc8 25.c5 Ne6 26.Rc1 Rc6 27.f4 f5 28.g4 g5 29.gxf5 Nxf4 30.Bxf4 gxf4 31.Kf2 Rf6 32.Kf3 Rxf5 33.Rb1 Rxc5 34.Rb6 Rc6 35.Rxb7 Rc4 36.Rb5 Ra4 37.Rf5 Kg7 38.Rxf4
curious and also worth considering are:
48/36 14:40:22 391,227,892k 7,406k 0.00 4.Qe2 Bc5 5.Bxc6 bxc6 6.Nxe5 0-0 7.0-0 Re8 8.Nxf7 Qe7 9.Ng5 d5 10.d3 Bg4 11.Nf3 dxe4 12.dxe4 Nxe4 13.Nbd2 Nxf2 14.Qxe7 Rxe7 15.b4 Nh3+ 16.Kh1 Nf2+
48/69 15:52:34 423,655,046k 7,412k -0.06 4.d4 exd4 5.0-0 a6 6.Ba4 Be7 7.e5 Ne4 8.Nxd4 0-0 9.Re1 Nxd4 10.Qxd4 Nc5 11.Nc3 d6 12.Bb3 c6 13.exd6 Nxb3 14.axb3 Qxd6 15.Qf4 Qxf4 16.Bxf4 Be6 17.Ne4 Rfe8 18.f3 Bf5 19.Kf2 h6 20.c3 Bxe4 21.Rxe4 Bc5+ 22.Ke2 g5 23.Bd2 Rxe4+ 24.fxe4 Re8 25.Kd3 Rd8+ 26.Kc2 f6 27.c4 Re8 28.Kd3 Kf7 29.Rf1 Bd6 30.Bc3 Be5 31.Bxe5
Section B 4.0-0 Nxe4 5.d4
this popular continuation is apparently drawn on best play...
70/95 22:46:49 809,056,482k 9,865k 0.00 5...Nd6 6.Bxc6 dxc6 7.dxe5 Nf5 8.Qxd8+ Kxd8 9.Rd1+ Ke8 10.Nc3 Ne7 11.h3 Ng6 12.a4 a5 13.Ne2 Be7 14.Be3 h5 15.Rd2 h4 16.Nf4 Nxf4 17.Bxf4 Be6 18.Nd4 g5 19.Be3 Bd7 20.f4 gxf4 21.Bxf4 Rh5 22.e6 Bxe6 23.Nxe6 fxe6 24.Re1 Rd5 25.Rxe6 Kd7 26.Rxd5+ cxd5 27.Rh6 c6 28.Rh7 Ke6 29.b3 b5 30.Kf2 bxa4 31.bxa4 Bf6 32.Kf3 Re8 33.Rh5 Kf7 34.Rh7+
Section C Mainline after 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5 7.Rxe5+ Be7 8.Bf1 0-0
stockfish_191009
75/120 698:04:40 9,181,570,060k 6,958k +0.13 9.Nc3 Bf6 10.Re1 Re8 11.Nd5 Rxe1 12.Qxe1 b6 13.Nxf6+ Qxf6 14.Qe3 Bb7 15.d3 c5 16.Qf4 Qxf4 17.Bxf4 Nf5 18.a4 f6 19.c3 g5 20.Bd2 a5 21.Be2 h6 22.g3 Bc6 23.f4 Kh7 24.d4 Nd6 25.dxc5 bxc5 26.b4 axb4 27.cxb4 Rxa4 28.Rxa4 Bxa4 29.Bd3+ Kg7 30.bxc5 Bb5 31.Bc2 Nc4 32.Bc1 d6 33.cxd6 Nxd6 34.g4 Nb7 35.Be3 Nd6 36.Kf2 Kf7 37.f5 Nc4 38.Bd4 Ne5 39.Bb3+ Kg7 40.Kg3 Bc6 41.h3 Be4 42.Kf2 Bc6 43.Bc2 Bd5 44.Kg3 Kf7 45.Bd1 Nd3 46.h4 Ke7 47.hxg5 hxg5 48.Be2 Nf4
75/114 763:17:12 9,181,570,060k 7,077k +0.13 9.d4 Ne8 10.c4 Bf6 11.Re1 d5 12.cxd5 Qxd5 13.Be3 Be6 14.Nc3 Qd7 15.h3 c6 16.d5 cxd5 17.Bc5 Be7 18.Bxe7 Qxe7 19.Qxd5 Nf6 20.Qd4 Rfe8 21.Rad1 Red8 22.Qe5 Rxd1 23.Rxd1 Rd8 24.Rxd8+ Qxd8 25.b3 h6 26.Nb5 a5 27.Nd4 Bd5 28.Bb5 Be4 29.Nf5 Qd1+ 30.Bf1 Kh7 31.Ne3 Qd2 32.a3 Qa2 33.Qxa5 Qxb3 34.Qb4 Qxb4 35.axb4 Kg6 36.f3 Bf5 37.h4 Ne8 38.g4 Bd7 39.Bd3+ Kf6 40.f4 g6 41.Kf2 Nc7 42.Kf3 Bc6+ 43.Be4 Na6 44.b5 Bxb5 45.Bxb7 Nb4 46.g5+ hxg5 47.hxg5+ Ke7 48.Ke4 Kd6 49.Kd4 Nc6+ 50.Bxc6 Bxc6 51.Nc4+ Ke7
74/100 679:30:17 9,181,570,060k 6,906k 0.00 9.Re1 Nf5 10.d4 d5 11.c3 c6 12.Bf4 Bd6 13.Bxd6 Nxd6 14.a4 Qb6 15.b3 a5 16.Nd2 Bf5 17.Qf3 Bg6 18.Bd3 Bxd3 19.Qxd3 Rae8 20.c4 Rxe1+ 21.Rxe1 Re8 22.Re3 Qd8 23.c5 Rxe3 24.fxe3 Ne8 25.e4 dxe4 26.Nxe4 h5 27.h3 Qd5 28.Qe3 Qe6 29.Kf2 Qf5+ 30.Kg1
Section D Mainline after 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5 7.Rxe5+ Be7 8.Bf1 0-0 9.Nc3
There is no advantage for white in this particular run, but 146 hours is a long time...
stockfish_191026
78/76 146:44:21 5,067,530,182k 9,593k 0.00 9...Bf6 10.Re1 Re8 11.Rxe8+ Nxe8 12.Nd5 Bg5 13.d4 Bxc1 14.Rxc1 c6 15.Ne3 d5 16.c4 dxc4 17.Bxc4 Qf6 18.d5 Qxb2 19.dxc6 bxc6 20.Bb3 Qf6 21.h3 Rb8 22.Ng4 Bxg4 23.Qxg4 Rb7 24.g3 Rc7 25.Ba4 g6 26.Kg2 Ng7 27.Qe4 Ne6 28.Rxc6 Rxc6 29.Bxc6 Kg7 30.Bd5 Qd4 31.Qxd4+ Nxd4 32.f4 Kf6 33.Kf2 h6 34.Bc4 g5 35.fxg5+ hxg5 36.Ke3 Nf5+ 37.Kf3 Nd4+ 38.Kf2 a5 39.Ke3 Nf5+ 40.Kf3 Nd4+
Section E Mainline after 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5 7.Rxe5+ Be7 8.Bf1 0-0 9.Re1
stockfish_191031
75/34 30:00:15 1,006,869,913k 9,322k 0.00 9...Nf5 10.d4 d5 11.c3 a5 12.Nd2 Nd6 13.Bd3 c6 14.Nf3 Bf5 15.Bf4 Bxd3 16.Qxd3 Re8 17.h3 Ne4 18.Qc2 Bd6 19.Bxd6 Nxd6 20.Rxe8+ Qxe8 21.Re1 Qd8 22.b3 a4 23.bxa4 Qa5 24.Re7 Qd8
Section F Mainline after 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5 7.Rxe5+ Be7 8.Bf1 0-0 9.d4
black has 9...Ne8 or 9...Bf6
0.00/57 9...Ne8 10.d5 Bc5 11.Re1 d6 12.Nc3 Bf5 13.Bd3 Qh4 see 10.c4 below...
+0.13/57 9...Bf6 10.Re1 Re8 11.Rxe8+ Nxe8 12.Bf4 d5 13.c3 Bg5 needs work...
+0.50/57 9...c6 10.d5 Bf6 11.Re1 Nf5 12.Nc3 d6 13.Bf4 h6
F1 9...Ne8
75/114 763:17:12 9,181,570,060k 7,077k +0.13 9.d4 Ne8 10.c4 Bf6 11.Re1 d5 12.cxd5 Qxd5 13.Be3 Be6 14.Nc3 Qd7 15.h3 c6 16.d5 cxd5 17.Bc5 Be7 18.Bxe7 Qxe7 19.Qxd5 Nf6 20.Qd4 Rfe8 21.Rad1 Red8 22.Qe5 Rxd1 23.Rxd1 Rd8 24.Rxd8+ Qxd8 25.b3 h6 26.Nb5 a5 27.Nd4 Bd5 28.Bb5 Be4 29.Nf5 Qd1+ 30.Bf1 Kh7 31.Ne3 Qd2 32.a3 Qa2 33.Qxa5 Qxb3 34.Qb4 Qxb4 35.axb4 Kg6 36.f3 Bf5 37.h4 Ne8 38.g4 Bd7 39.Bd3+ Kf6 40.f4 g6 41.Kf2 Nc7 42.Kf3 Bc6+ 43.Be4 Na6 44.b5 Bxb5 45.Bxb7 Nb4 46.g5+ hxg5 47.hxg5+ Ke7 48.Ke4 Kd6 49.Kd4 Nc6+ 50.Bxc6 Bxc6 51.Nc4+ Ke7
72/104 107:07:56 3,807,076,898k 9,871k +0.13 9...Ne8 10.c4 Bf6 11.Re1 d5 12.cxd5 Qxd5 13.Be3 Be6 14.Nc3 Qa5 15.a3 c6 16.Ne4 Bd5 17.Nc5 Qc7 18.Qg4 b6 19.Nd3 Be6 20.Qf4 Qxf4 21.Nxf4 Nc7 22.g3 Rac8 23.Rac1 Bd7 24.Nh5 Bd8 25.Bg2 Ne6 26.Rc2 g6 27.Nf4 Nxf4 28.Bxf4 Bf6 29.Be3 Rfd8 30.b4 Kg7 31.Rec1 Be6 32.Rxc6 Rxc6 33.Bxc6 Bxd4 34.Rd1 Bf6 35.Rxd8 Bxd8 36.Kg2 f5 37.Bd4+ Kf8 38.f3 Ke7 39.f4 Kd6 40.Bb5 Bd5+ 41.Kf2 Ke6 42.Ke3 g5 43.Be5 gxf4+ 44.gxf4 a5 45.Kd3 Be7 46.Kc3 Bd6 47.Bxd6 Kxd6 48.Kd4 Be6 49.bxa5 bxa5
74/107 177:17:00 3,533,415,932k 5,536k +0.15 10.c4* Bf6 11.Re1 d5 12.cxd5 Qxd5 13.Be3 Be6 14.Nc3 Qa5 15.a3 c6 16.Ne4 Bd5 17.Nc5 Qc7 18.Qg4 b6 19.Nd3 g6 20.Rac1 Ng7 21.Nb4 h5 22.Nxd5 cxd5 23.Rxc7 hxg4 24.Be2 Ne6 25.Rc6 Rac8 26.Rd6 Rfd8 27.Rxd8+ Rxd8 28.Rd1 Rc8 29.Bxg4 Rc2 30.Rd2 Rxd2 31.Bxd2 Nxd4 32.Bd1 Kf8 33.Kf1 Ke7 34.b4 Ke6 35.a4 Be7 36.Bc3 Bf6 37.Bg4+ Ke7 38.Bd2 Nb3 39.Bf4 a6 40.Bd1 Nd4 41.Be3 Ke6 42.Bg4+ Kd6 43.h4 b5 44.axb5 Nxb5 45.h5 gxh5 46.Bxh5 Ke6 47.Bc5 Bc3 48.Ke2 f5 49.Kd3 Bf6 50.g3 Bc3 51.Bd1 Be5 52.g4
*+0.00/67 10.d5 and +0.00/67 10.Re1 are worth a look... but apparently go nowhere.
after 9.d4 Ne8 10.c4 Bf6 11.Re1 d5 12.cxd5 Qxd5 13.Be3
73/107 150:59:33 4,191,583,263k 7,711k +0.13 13...Be6 14.Nc3 Qd7 15.h3 c6 16.d5 cxd5 17.Bc5 Be7 18.Bxe7 Qxe7 19.Qxd5 Rd8 20.Qa5 b6 21.Qa4 Rd2 22.Qf4 Qd6 23.Qxd6 Nxd6 24.Rad1 Rxd1 25.Rxd1 Nb7 26.a3 g6 27.f3 Rb8 28.Nb5 a5 29.Nd4 Bd5 30.Kf2 Kf8 31.g4 h6 32.h4 Rd8 33.Nb5 Ke7 34.Ke3 Bc6 35.Nd4 Bd7 36.Kf4 Kf6 37.g5+ Kg7 38.b4 Ba4 39.Rd2 Rd7 40.Ba6 hxg5+ 41.hxg5 axb4 42.axb4 Nd8 43.b5 Rd5 44.Ke3 Re5+ 45.Kf2 Ne6 46.Nxe6+ fxe6 47.Rd7+ Kf8 48.f4 Rf5 49.Rd6 Rxf4+ 50.Ke3 Rf5 51.Rxe6 Bxb5 52.Bxb5 Rxb5 53.Rxg6 Rf5 54.Rh6 Rxg5 other choices:
71/100 265:30:38 7,345,389,075k 7,685k +0.13 13. ... Qd8 14.Nc3 Nd6 15.Bf4 Be6 16.Bd3 c6 17.Be5 Bxe5 18.dxe5 Nf5 19.Qc2 Nd4 20.Qd2 Kh8 21.Ne4 Qb6 22.b4 a5 23.Rab1 Nf5 24.bxa5 Qxa5 25.Rxb7 Qxd2 26.Nxd2 Rxa2 27.Nf3 c5 28.Ng5 Nd4 29.f3 Rd2 30.Bf1 h6 31.Ne4 Rc2 32.Bd3 Bd5 33.Rc7 Bxe4 34.Bxe4 Rd2 35.Rxc5 g5 36.Rb1 Kg7 37.Rc7 Ne6 38.Rc2 Rxc2 39.Bxc2 Rd8 40.Rd1 Rc8 41.Be4 Re8 42.Rd5 Rb8 43.g3 h5 44.Rd2 Rb5 45.Kf2 Rxe5 46.Bd5 Kg6 47.h3 Kf6 48.Bxe6 fxe6 49.Rd6 Rf5
67/101 130:51:02 3,452,409,954k 7,329k +0.16 13. ... Qa5 14.Nc3 Be6 15.a3 c6 16.Ne4 Qd8 17.Nc5 Bc8 18.Qf3 Nc7 19.Rad1 Nd5 20.Bc4 b6 21.Ne4 Be7 22.Bf4 Be6 23.Be5 Qd7 24.h3 f6 25.Bg3 Bf7 26.Nc3 Rfe8 27.Nxd5 Bxd5 28.Rc1 Rac8 29.Kh2 g6 30.Re3 Kf7 31.Rec3 Bxc4 32.Rxc4 Red8 33.b4 Qd5 34.Qxd5+ Rxd5 35.f3 a5 36.bxa5 bxa5 37.a4 Ke8 38.Rb1 Bb4 39.Kg1 h5 40.Bf2 Kd7 41.Rc2 g5 42.g3 Ke6 43.Kg2 Kd7 44.g4 hxg4 45.fxg4 Re8 46.Rd1 Rd6 47.Kf3
F2 9...Bf6
white now has 10.Re1 or 10.Re2!?. How 10.Re2 works is a mystery - perhaps black is in zugzwang.
F2a 10.Re1 is a logical choice... but which line below do we trust?
79/113 1581 hours +0.13 10...Re8 11.c3 Rxe1 12.Qxe1 Ne8 13.a4 a5 14.Bd3 d5 15.Bf4 g6 16.Nd2 Ng7 17.Nf3 Bf5 18.Bxf5 Nxf5 19.h3 c6 20.g4 Ng7 21.Qe3 Ne6 22.Re1 Qe7 23.Ne5
+0.00/77 10...Re8 11.c3 Rxe1 12.Qxe1 Ne8 13.d5 b6 14.g3 Bb7 15.Bg2 Qe7 16.Qxe7 Bxe7 17.Be3 Bc5 18.Bxc5 bxc5 19.c4 Bc8 20.Nc3 d6 21.Re1 Kf8 22.Bf3 Rb8
F2b 10.Re2!? defies all logic... what a surprise move to play...!
77/95 +0.00 10...b6 11.Re1 Bb7 12.Bf4 Nf5 13.c3 Re8 14.Rxe8+ Qxe8 15.Nd2 d6 16.a4 a5 17.Bd3 Nh4 18.Bg3 h6 19.Qb1 Qe7 20.Be4 d5 21.Bh7+ Kh8
Section G 4.d3
This line does not create an advantage for white (see Section A above), but curious are these older runs
66/86 648:27:04 8,842,848,536k 8,179k +0.13 4.d3 Bc5 5.Bxc6 dxc6 6.0-0 Nd7 7.Nbd2 0-0 8.Nc4 Re8 9.Be3 Bd6 10.d4 exd4 11.Nxd6 cxd6 12.Qxd4 Qe7 13.Rad1 Nf8 14.h3 b6 15.Qxd6 Qxe4 16.Rfe1 Qg6 17.Qxg6 hxg6 18.b4 Bf5 19.c3 Ne6 20.a4 Bc2 21.Ra1 c5 22.a5 f6 23.Re2 Be4 24.Rb2 Bxf3 25.gxf3 Rab8 26.bxc5 Nxc5 27.axb6 axb6 28.Bxc5 bxc5 29.Rxb8 Rxb8 30.Ra5 g5 31.Rxc5 Kf7 32.Rc4 Ke6 33.f4 gxf4 34.Rxf4 Rh8 35.Rf3 Rd8 36.h4 Kf7 37.Rg3 Rc8 38.Kg2 f5 39.h5 f4
and
53/78 24:58:02 802,663,530k 8,930k +0.11 4...Bc5 5.c3 0-0 6.Bg5 Be7 7.0-0 d6 8.h3 a6 9.Ba4 h6 10.Be3 b5 11.Bc2 d5 12.Nbd2 Bd6 13.Re1 Re8 14.Nf1 Be6 15.a4 Qd7 16.Ng3 dxe4 17.Nxe4 Nxe4 18.dxe4 Na5 19.Nh4 Nc4 20.Bc1 Be7 21.Qxd7 Bxd7 22.Nf5 Bf6 23.Ne3 Be6 24.Nd5 Bxd5 25.exd5 Nd6 26.Kh2 Red8 27.f4 Nc4 28.Bd3 exf4 29.axb5 axb5 30.Rxa8 Rxa8 31.Bxc4 bxc4 32.Bxf4
50/63 3:48:52 118,772,644k 8,649k +0.37 4...d6 5.0-0 Be7 6.c3 0-0 7.Ba4 a6 8.h3 Re8 9.Nbd2 Bf8 10.Bc2 Ne7 11.d4 Ng6 12.Re1 Bd7 13.Nf1 h6 14.a4 b5 15.Ng3 c6 16.Be3 a5 17.Qd3 Qc7 18.Qd2 Rad8 19.Rec1 Ra8 20.Rd1 bxa4 21.Rxa4 c5 22.Raa1 cxd4 23.cxd4 Rec8 24.Ba4 Bxa4 25.Rxa4 Rab8 26.d5 Qc2 27.Qxc2 Rxc2 28.b3 Rxb3 29.Rxa5 Rbb2 30.Raa1 Rb8 31.Ra7
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