I have been doing some more exploring of the Abrahams Jerome Gambit - 1.e4 e5 2.Bc4 Bc5 3.Bxf7+ - (see "Exploring" for an earlier exploit) and the results have been puzzling, but worth reporting.
One important difference between the Abrahams Jerome and the regular Jerome Gambit is the value of ...Bxf2+ for Black. In the latter, the move serves mostly a "psychological" purpose (You sacrificed a piece to upset my King, so I will sacrifice a piece to upset your King), as discussed in "Trading Down Against the Jerome Gambit" and earlier posts. However, in the former, the return Bishop sacrifice is often the best move available.
ndizvoh - stevebrown
blitz, FICS, 2015
1.e4 e5 2.Bc4 Bc5 3.Bxf7+ Kxf7 4.Qh5+ g6 5.Qxe5
A quick look in The Database shows 4,097 games have reached this position, with White scoring 53%. Only 1,151 games include the "best" response, 5...Bxf2+, which reduces White's scoring to only 52%.
Clearly there are other factors than the "best" move affecting the outcome!
A comparison with the Abrahams Jerome Gambit line 1.e4 e5 2.Bc4 Bc5 3.Bxf7+ Kxf7 4.Qh5+ Kf8 5.Qxe5 is even more puzzling. The Database has 5,026 games reaching this position, with White scoring 41% (suggesting that 4...Kf8 might be a stronger response than 4...g6). Yet, in the 219 games where Black makes his "best" response, 5...Bxf2+, White improves his scoring to 47%.
It's worth repeating: Clearly there are other factors than the "best" move affecting the outcome!
5...Bxf2+
Black sees he will be losing his Bishop, and decides to get a pawn for it.
6.Ke2
Declining the Bishop is rare, according to The Database, and not a good idea. One example: KevinSI - stevebrown, standard, FICS, 2014: 6.Kf1 Qf6 7.Nf3 Qxe5 8.Nxe5+ Ke6 9.Kxf2 Kxe5 10.Re1 Nf6 11.d3 Rf8 12.Kg1 Nc6 13.Nd2 Nd4 14.Nc4+ Ke6 15.Rf1 Kf7 16.Bg5 Kg7 17.c3 Ne6 18.Bxf6+ Rxf6 19.Rxf6 Kxf6 20.Rf1+ Kg7 21.Ne5 d6 22.Rf7+ Kg8 White resigned
6...Qf6
Black protects his Bishop and Rook. He also had the move 6...Nf6, which does the same thing, as 7.Kxf2 would then be met with 7...Ng4+, winning White's Queen.
7. Qd5+
White probably should have settled for 7.Qxf6+ Nxf6 8.Kxf2 Nxe4+ and a roughly equal game.
7...Kg7 8.Nf3 Ne7 9.Qc4 Bb6
Black has retained his extra piece. White has an extra pawn, but given the lack of safety of his King, it is not adequate compensation.
10.Rf1 d6 11.Nc3 Bg4 12.Nd5 Nxd5 13.Qxd5 c6 14.Qc4 Re8 15.d3 d5 16.e5 Rxe5+ White resigned
Putting Black's Queen on f6, with the idea of exchanging Her Majesty, is a common anti-Jerome Gambit strategy. In the following game, Black introduces the plan, then wavers - and the game ends quickly.
Philidor 1792 - guest1862
3 0 blitz, www.bereg.ru, 2015
1.e4 e5 2.Bc4 Bc5 3.Bxf7+
Another example of the Abrahams Jerome Gambit.
As far as I can tell, Alonzo Wheeler Jerome did not play the Bishop sacrifice out of the Bishop's Opening, but Gerald Abrahams attributed the gambit to him nonetheless.
4...Kxf7 4.Qh5+ Ke6 5.Qf5+
Houdini judges the Abrahams Jerome less harshly than it does the Jerome proper, suggesting that here 5.Nf3, instead, equalizes. This bears further examination, as this blog has in the past presented only two losses by White with 5.Nf3 - see "The Abrahams Jerome Gambit (Part II)".
5...Kd6 6.Nf3 Qf6 7.d4 Bxd4
Black overlooks the reason behind his 6th move, that of exchanging Queens, and is subsequently severely punished.
Some contrasting examples: 7...Qxf5 8.dxc5+ Kxc5 9.exf5 (9.Be3+ Kd6 10.exf5 Nf6 11.0-0 [11.Nc3 Re8 12.0-0-0+ Ke7 13.Nd5+ Nxd5 14.Bg5+ Nf6 15.Nxe5 Kf8 16.Bxf6 gxf6 17.Nxd7+ Bxd7 White resigned, Geeeman - ludonix, FICS, 2014] 11...Nd5 12.Rd1 c6 13.Nc3 Rf8 14.Nxd5 cxd5 15.b4 Rxf5 16.Bc5+ Ke6 17.Re1 d6 18.Be3 Nc6 19.b5 Nb4 20.Re2 Bd7 21.Rd1 Bxb5 22.Ree1 Nxc2 23.Rf1 Bxf1 24.Kxf1 d4 25.Bd2 d5 26.Rc1 d3 27.g4 Rxf3 28.Kg2 Rff8 29.f3 Nd4 30.Rf1 e4 31.f4 Rac8 32.Bc3 Rxc3 White resigned, KevinSI - fedand, FICS, 2014) 9...d5 10.Nxe5 Ne7 11.0-0 Nxf5 12.Nd3+ Kd6 13.Bf4+ Kd7 14.Nc5+ Kc6 15.b4 b6 16.Nd3 Nd4 17.Ne5+ Kb7 18.Nc3 Nxc2 19.Rac1 Nxb4 20.a3 N4c6 21.Nxd5 Be6 22.Nxc6 Nxc6 23.Rfd1 Rhd8 24.Nxc7 Rxd1+ 25.Rxd1 Rd8 26.Rxd8 Nxd8 27.h3 Bb3 28.g4 a6 29.Kg2 Nf7 30.h4 h6 31.h5 a5 32.Nb5 Bd5+ 33.Kg3 Kc6 34.Nd4+ Kc5 35.Nf5 Kc4 36.Nxg7 Kb3 37.Nf5 Kxa3 38.Nd4 a4 39.g5 hxg5 40.Be3 Kb4 41.Kg4 Kc4 42.f4 gxf4 43.Kxf4 a3 44.Nc2 a2 45.Bd4 Kb3 46.Ne3 Be6 47.Nd1 b5 48.Ba1 b4 49.Nb2 Kc2 50.Na4 b3 51.Bb2 Bd7 52.Nc5 Kxb2 53.Nxd7 a1Q White resigned, KevinSI - lavaprut, FICS, 2014.
8.Nxd4 exd4 9.Qd5+ Ke7 10.Bg5 Black resigned