I decided to have ChessBase8 give me an Opening Report on the Jerome Gambit, based on The Database. I got a whole lot of information, and I was only dealing with the first few moves...
Opening report
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
9062 games in 'TheDatabase'
b) 4...Kf8
207 games, 2000-2012,
Black scores averagely (44%).
Elo-Ø: 1353, 193 games. Performance = Elo 1304
played by: blackburne, 1778, 2/2; Talwhu, 1722, 1/1; PatOrMat, 1685, 1/1; Rolmx, 1683, 0/1; vilinar, 1666, 1/1
You should play: 5.Nc3
AAlekhine (1586) - blackburne (1795)
thematic ChessWorld.net, 2007
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Nc3 d6 6.d3 Kxf7 7.Ng5+ Kf8 8.Qf3+ Qf6 9.Qxf6+ Nxf6 10.0-0 Nd4 11.Be3 Nxc2 12.Rad1 Bxe3 13.Nf3 Bg4 14.h3 Bxf3 15.gxf3 Bf4 16.a3 Nd4 17.Kg2 Ke7 18.Rg1 g5 19.Kf1 Nxf3 20.Rg2 Rhg8 21.Nd5+ Nxd5 22.exd5 h5 23.h4 Nxh4 24.Rg1 g4 25.d4 Nf3 26.Rg2 h4 27.Ke2 Nxd4+ 28.Kd3 h3 29.Rgg1 h2 30.Rh1 g3 31.fxg3 Rxg3+ 32.Kc4 Rb3 33.Rxd4 exd4 34.Kxb3 d3 35.Kc3 d2 36.Kc2 Kf6 37.Kd1 Re8 38.b4 Re1+ 39.Rxe1 dxe1Q+ 40.Kxe1 h1Q+ 41.Kf2 Qe4 42.a4 Qe3+ 43.Kg2 Ke5 44.b5 Ke4 45.a5 Qf3+ 46.Kg1 Qe2 47.b6 Kxd5 48.bxa7 Be3+ 49.Kh1 Bxa7 50.a6 b6 51.Kg1 Ke4 52.Kh1 Kf3 53.Kg1 Qg2# 0-1
Plejade - erch
ChessWorld.net, 2003
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Nc3 Kxf7 6.Nd5 Nge7 7.Nxe7 Qxe7 8.d3 Rf8 9.Be3 Kg8 10.Bxc5 Qxc5 11.Qd2 Nb4 12.c3 Nc6 13.d4 exd4 14.Nxd4 Nxd4 15.0-0 Nc6 16.Rfd1 Ne5 17.Qd5+ Qxd5 18.exd5 Nc4 19.g3 Nxb2 20.Rd4 b5 21.d6 cxd6 22.Rxd6 Rf6 23.Rxf6 Nd3 24.Rd1 gxf6 25.Rxd3 Kf8 26.Rd6 Kf7 27.f4 a5 28.Rb6 Ba6 29.h4 d5 30.g4 b4 31.cxb4 d4 32.b5 d3 33.bxa6 Rd8 34.Rb1 Ke6 35.f5+ Ke5 36.Kf1 Kd4 37.Ke1 Ke3 38.Kd1 Kd4 39.Kd2 Rc8 40.Rb5 Rc2+ 41.Kd1 Rxa2 42.a7 Ra1+ 43.Kd2 Ra2+ 44.Kd1 Kc3 45.Rc5+ Kd4 46.Rc6 Ke3 47.a8Q Rd2+ 48.Ke1 Rg2 49.Rc3 Rg1# 0-1
Alternative: 5.Bxg8
drewbear (1718) - BrainFreeze (1685)
thematic ChessWorld.net, 2007
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Bxg8 Rxg8 6.d3 d5 7.Ng5 dxe4 8.Nxh7+ Ke8 9.Qh5+ Ke710.Bg5+ Kd6 11.Bxd8 Nxd8 12.Qg6+ Kd5 13.Nf6+ 1-0
SIRMO (1798) - AAlekhine (1625)
thematic ChessWorld.net, 2007
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Bxg8 Rxg8 6.c3 Qf6 7.d3 d6 8.a4 Ke8 9.Bg5 Qg6 10.h4 h6 11.h5 Qe6 12.Bd2 Bd7 13.b4 Bxf2+ 14.Kxf2 Rf8 15.Rh3 Ke7 16.Be3 Rae8 17.b5 Na5 18.Nbd2 Kd8 19.Ke2 Kc8 20.c4 g5 21.Nh2 Qf6 22.Rf3 Qe6 23.Qf1 g4 24.Rxf8 g3 25.Rxe8+ Bxe8 26.Nhf3 Bxh5 27.Qh1 Qf7 28.Qh3+ Kb8 29.Qxg3 b6 30.Bxh6 Nb7 31.Qg7 Qxg7 32.Bxg7 Nc5 33.a5 Ne6 34.Bf6 Nf4+ 35.Kf1 Nxd3 36.axb6 cxb6 37.Be7 Kc8 38.Bxd6 Kd7 39.Nxe5+ Nxe5 40.Bxe5 Ke6 41.Bc7 Kd7 42.Rxa7 Kc8 43.Bxb6 Kb8 44.c5 Bd1 45.Nc4 Bb3 46.Nd6 Bc2 47.Rd7 1-0
Superpippo (1597) - TajniDobrovoljci (1607)
FICS rated blitz game, 2001
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Bxg8 Kxg8 6.0-0 d6 7.c3 Bg4 8.d4 exd4 9.Qb3+ Kf8 10.Nxd4 Bxd4 11.cxd4 b6 12.Be3 Qf6 13.Nd2 Nxd4 14.Bxd4 Qxd4 15.Nf3 Bxf3 16.Qxf3+ Ke7 17.Rad1 Qf6 18.e5 Qxf3 19.exd6+ cxd6 20.Rfe1+ Kf7 21.gxf3 Rhd8 22.Re4 d5 23.Rh4 h6 24.Kg2 Rd7 25.f4 Rad8 26.Kf3 Re7 27.Rh5 d4 28.Re5 d3 29.Ke3 d2 30.Rxd2 Rxd2 31.Kxd2 Rxe5 32.fxe5 g5 33.Ke3 Ke6 34.Ke4 h5 35.f4 gxf4 36.Kxf4 a5 37.a4 Kd5 38.Kf5 Kc4 39.e6 Kb3 40.e7 Kxa4 41.e8Q+ Kb3 42.Qe2 Kb4 43.Qc2 b5 44.Qc3+ Ka4 45.Qa3# 1-0
drewbear (1718) - karmmark (1387)
thematic ChessWorld.net, 11.2007
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Bxg8 1-0
LSS (1875) - KaptKoca (1614)
FICS server game, rated blitz match, 2000
1.e4 e5 2.Bc4 Nc6 3.Nf3 Bc5 4.Bxf7+ Kf8 5.Bxg8 Rxg8 6.0-0 d6 7.d3 h6 8.Nc3 Bg4 9.h3 Bh5 10.Kh1 Ke8 11.g4 Bf7 12.Nh2 Rf8 13.f4 exf4 14.Rxf4 Ne5 15.Nd5 Bxd5 16.Rxf8+ Kxf8 17.exd5 Qh4 18.Qf1+ Kg8 19.Qg2 Rf8 20.b4 Bb6 21.Bb2 Rf2 22.d4 Rxg2 23.Kxg2 Nc4 24.Bc3 Ne3+ 25.Kh1 Qxh3 26.Rg1 Nxc2 27.Bb2 Nxd4 28.Bxd4 Bxd4 29.Rg2 Be5 30.a4 Bxh2 31.Rxh2 Qxg4 32.b5 Qxa4 0-1
Superpippo (1678) - raffa (1406)
FICS rated blitz game, 2002
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kf8 5.Bxg8 Rxg8 6.d4 exd4 7.c3 Qf6 8.cxd4 Nxd4 9.Nxd4 Bxd4 10.0-0 d6 11.Nc3 Bxc3 12.bxc3 Qxc3 13.Bg5 g6 14.Rc1 Qe5 15.f4 Qxe4 16.Re1 Qf5 17.Rxc7 Rg7 18.Qxd6+ 1-0
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c) 4...Ke7
33 games, 1999-2011,
Black scores badly (29%).
Elo-Ø: 1287, 31 games. Performance = Elo 1125
played by: agno, 1607, 0/1; MRKumar, 1602, 0/1; AAlekhine, 1601, 1/2; Brown, 1552, 1/1; Bucephale, 1528, 0/1
You should play: 5.Nxe5
Nesseerd (1111) - nontheist (1291)
FICS server game, rated blitz match, 2009
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Ke7 5.Nxe5 Nxe5 6.Bd5 c6 7.Qh5 Ng6 8.Qe5+ Nxe5 0-1