The Traxler is maybe the most tactically complex of openings, certainly one of the least comprehensible to humans (and, from my analysis with programs, they also struggle to calculate many of the positions correctly). But if a well-prepared black player ventures it OTB, I would fancy his chances every time, since white's position is constantly on a precipice in the 5.Nxf7 lines, and is still very difficult in the 5.Bxf7+ lines.
On the 6.b4 line, christened the Schmidt attack after P Schmidt who first analysed and played the line in high-level competition:
I think Estrin was on the right track with his 6...Bxf2+, it certainly looks the thematic move. 6...Nxb4 doesn't look right to me, while 6...Bxb4 could be playable but seems against the ideas of the opening. So I'll take 6...Bxf2+ as the "main line".
First, as much as I hate "database dumps", some games to whet the appetite:
[Event "W theme corr"]
[Site ""]
[Date "1973.??.??"]
[Round "0"]
[White "Schmidt,P"]
[Black "Estrin,Yakov Borisovich"]
[Result "1/2"]
[Eco "C57"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 5.Bxf7+ Ke7 6.b4 Bxf2+ 7.Kxf2 h6 8.Bc4 hxg5
9.d3 g4 10.c3 d6 11.Be3 Qe8 12.Nd2 Qg6 13.Nf1 g3+ 14.Kg1 Ng4 15.Qf3 gxh2+ 16.Nxh2 Nxe3
17.Qxe3 Bh3 18.Qf2 Raf8 19.Nf3 Rh6 20.Nh4 Qg5 21.Nf5+ Bxf5 22.Rxh6 Bg4 23.Qxf8+ Kxf8 24.Rf1+ Ke8
25.Rh8+ Kd7 26.Rf7+ Ne7 27.Rh7 d5 28.exd5 Bf5 29.Rhxg7 Qe3+ 30.Kh2 Qh6+ 31.Kg1 Qe3+ 1/2
[Event "NED-ch18 corr"]
[Site ""]
[Date "1988.??.??"]
[Round "0"]
[White "Fiorito,Mario V"]
[Black "Lambers,Gerrit Hans"]
[Result "0-1"]
[Eco "C57"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 5.Bxf7+ Ke7 6.b4 Bxf2+ 7.Kxf2 h6 8.c3 hxg5
9.Bd5 d6 10.d4 Ke8 11.Ke1 g4 12.Bg5 Ne7 13.Qd3 Nfxd5 14.exd5 Rh5 15.Qd2 Bf5 16.Kf2 Qd7
17.dxe5 dxe5 18.Bxe7 Kxe7 19.Kg3 Qd6 20.Kf2 g3+ 21.Ke1 Rxh2 22.Rf1 Qg6 23.Na3 Bd3 24.Rg1 Qe4+
25.Kd1 Rf8 0-1
[Event "corr"]
[Site ""]
[Date "1990.??.??"]
[Round "0"]
[White "Mueller"]
[Black "Shoup,Karl"]
[Result "1-0"]
[Eco "C57"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 5.Bxf7+ Ke7 6.b4 Bxf2+ 7.Kxf2 h6 8.Bc4 hxg5
9.d3 g4 10.Nd2 d6 11.c3 Qf8 12.Kg1 Bd7 13.Nf1 Nd8 14.Be3 Nf7 15.Ng3 Re8 16.b5 b6
17.a4 Be6 18.Qb3 Nd8 19.a5 Bxc4 20.Qxc4 Ne6 21.axb6 axb6 22.Ra7 Nd7 23.Nf5+ Kf6 24.Ra1 g6
25.Rf1 Nf4 26.Bxf4 exf4 27.Rxf4 Kg5 28.g3 Ne5 29.Qa2 Nxd3 30.Rf1 Rxe4 31.Qd2+ Kh5 32.h4 Rf4
33.Ng7+ Qxg7 34.gxf4 Nc5 35.Qd5+ Kh6 36.Qg5+ Kh7 37.Re1 Rf8 38.h5 1-0
Okay, so the first point is that in contrast to the 5.Nxf7 Bxf2+ lines, white cannot play 7.Kf1 here since 7...Bh4 8.Nf3 Kxf7 9.Nxh4 d5 (or 9...Rf8) looks like time for white to take an early shower.
After 7.Kxf2 h6 8.Bc4 (The 8.c3 of Fiorito-Lambers looks weaker, it's hard to find too many improvements on white's play (there are some I'm sure) in the opening yet black has a definite edge by 15...Bf5) hxg5 9.d3 g4 (Shredder seems to like the odd 9...Rh5 here, intending to swing the queen to h8 and threatening ...g3+ ideas; perhaps this idea is worth a try, practical tests are certainly needed), I don't know if there's objectively much difference between 10.c3 and 10.Nd2, since the games could easily have transposed within a few moves. The reason for black's loss wasn't his position at this point, but simply that he doesn't understand the plan in the Traxler 5.Bxf7+ lines [which Estrin did, Qe8-g6/h5 is the correct manouevre, whereas 11...Qf8 is tripe; with 11...Qe8 12.Kg1?! g3! black is doing very well, so perhaps 12.Ke1 Qg6 should be preferred, with an unclear position holding chances for both sides (a queenside pawn advance or awkward play with Qa4 is on the cards for white, while black has white's king in the centre, some open lines, and Steinitz would probably like the king position too)].
In the Estrin game, Shredder is adamant that black should play 11...g3+, but I'm not so sure about this, 12.hxg3 Bg4 13.Qg1 and black hasn't enough for the pawn. But Shredder seems to want to play ...g3 in every position.
Also, Estrin may have retained winning chances with 22...Bxe4, when he has an extra pawn, though the complicated nature of the position, and the bishop against knight, offers certain drawing possibilities. Maybe 22...Qxh6 23.exf5 g6 is also playable, again with unclear consequences.
Regards,
Craig