We have looked at this dilemma a number of times in the past (see, for example, "Jerome Gambit vs Two Knights Defense", parts 1, 2, 3 and 4).
The following game and its notes show that sometimes giving Black a "second chance" can return the game to desired channels. The focus is upon the games of a player who has dealt with this issue many times.
Wall, Bill - Guest165295
PlayChess.com, 2017
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6
4.O-O Bc5
Well, that's more like it. Black's Bishop comes to the party after all.
5.Bxf7+ Kxf7 6.Nxe5+
Bill has also tried 6.d3: 6...Kg8 (6... Rf8 7. Nc3 Kg8 8. Bg5 h6 9. Bxf6 Qxf6 10. Nd5 Qg6 11. c3 d6 12. b4 Bb6 13. b5 Nd8 14. Ne7+ Kf7 15. Nxg6 Black resigned, Wall,B - Munoz,C, Chess.com, 2010) 7. c4 d6 8. Be3 Bxe3 9. fxe3 Be6 10. Qb3 Na5 11. Qa4 Nc6 12. Nc3 a5 13. Ng5 Bd7 14. c5 Nb4 15. Qb3+ d5 16. exd5 Kf8 17. d6 Qe8 18. Nce4 cxd6 19. cxd6 Qg6 20. Rac1 Ke8 21. Rc7 Nfd5 22. Rxd7 Kxd7 23. Qc4 Nxe3 24. Qc7+ Ke8 25. Qe7 checkmate, Wall,B - KRM, Chess.com, 2010.
6...Nxe5
For completeness sake we have to mention 6...Ke7 7.d4 Bb6 8.Be3 Re8 9.Nxc6+ dxc6 10.e5 Nd5 11.Bg5+ Nf6 12.exf6+ gxf6 13.Re1+ Kf8 14.Rxe8+ Kxe8 15.Qh5+ Kf8 16.Qh6+ Kg8 17.Bxf6 Qf8 18.Qg5+ Kf7 19.Nc3 Qg8 20.Qe5 Be6 21.Ne4 h6 22.Re1 Re8 23.Bh4 Qg6 24.Re3 Bd7 25.Rf3+ Kg8 26.Nf6+ Qxf6 27.Rg3+ Kh7 28.Bxf6 Bxd4 29.Rg7+ Kh8 30.Rxd7+ Black resigned, Wall,B - Guest371199, PlayChess.com, 2017
7.d4
The position is beginning to look like a "regular" Jerome Gambit position, if we go ahead and now add 7...Bxd4, transposing, i.e. 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nxe5+ Nxe5 6.d4 Bxd4 7.Qxd4 Nf6 8.0-0
Sometimes Black did play 7...Bxd4, e.g. 8.Qxd4 Re8 (8...Qe7 9.Nc3 c6 10.f4 Ng6 11.e5 Ne8 12.Ne4 b6 13.f5 Nxe5 14.Bg5 c5 15.Qd5+ Black resigned, Wall,B - Guest850136, PlayChess.com, 2017 or 8...d6 9.Nc3 [9.Bf4 Be6 10.Nc3 Re8 11.Rad1 Nc6 12.Qd2 Bg4 13.f3 Bh5 14.Nd5 Nxd5 15.Qxd5+ Kf8 16.Qxh5 Kg8 17.Qd5+ Kh8 18.c4 Nb4 19.Qb5 a5 20.a3 Nc2 21.Rf2 Qf6 22.Bg5 Nd4 23.Qxe8+ Rxe8 24.Bxf6 Nxf3+ 25.Rxf3 gxf6 26.Rxf6 Rxe4 27.c5 Re2 28.Rf7 Rxb2 29.cxd6 Kg8 30.Rxc7 Kf8 31.d7 Black resigned, Wall,B -Guest3687203, PlayChess.com, 2015] 9...Be6 10.f4 Nc6 11.Qd3 Re8 12.f5 Ne5 13.fxe6+ Rxe6 14.Qh3 Ke7 15.Bg5 Qg8 16.Nd5+ Kd8 17.Bxf6+ gxf6 18.Nxf6 Black resigned, Wall,B - Guest547388, PlayChess.com, 2017) 9.Nc3 d6 10.Bf4 Kg8 11.Rad1 Qe7 12.f3 c6 13.Qxd6 Qxd6 14.Rxd6 Nf7 15.Rd2 b6 16.Kf2 g5 17.Bg3 Nh5 18.Bd6 Ba6 19.Rfd1 Rac8 20.a4 Kg7 21.a5 Rcd8 22.axb6 axb6 23.Be5+ Rxe5 24.Rxd8 Nxd8 25.Rxd8 Nf6 26.Rb8 Nd7 27.Ra8 Bc4 28.Rc8 c5 29.Rc7 Re7 30.b3 Be6 31.Rb7 Kf6 32.Na4 c4 33.b4 Re8 34.Ke3 Ra8 35.Nxb6 Nxb6 36.Rxb6 Ra1 37.b5 Re1+ 38.Kd2 Rg1 39.g3 Rg2+ 40.Kc3 Rf2 41.Rb8 Rxf3+ 42.Kd4 Rf1 43.b6 Rb1 44.Kc5 Ke5 45.Re8 Rb2 46.c3 Rb3 47.g4 Kf6 48.h3 Ke5 49.Kc6 Rxc3 50.b7 Rb3 51.b8=Q+ Rxb8 52.Rxb8 c3 53.Rb1 Bxg4 54.hxg4 Kxe4 55.Kd6 c2 56.Rc1 Kd3 57.Ke7 Drawn, Wall,B - Guest128013, PlayChess.com, 2017.
7...Nxe4
Playable, as are several lines that Bill has faced (and one that is not):
7...d6 8.dxc5 dxc5 9.Qe2 Rf8 10.Bf4 Ng6 11.Bg3 Be6 12.Nc3 Kg8 13.h3 a6 14.a4 c6 15.a5 Qd4 16.Rfd1 Qb4 17.Qe3 c4 18.Bd6 Qxb2 19.Rab1 Qxc2 20.Bxf8 Rxf8 21.Rd2 Nd5 22.exd5 Black resigned, Wall,B - Guest1193385, Play.Chess.com 2017;
7...Bd6 8.dxe5 Bxe5 9.f4 Bd4+ (9...Nxe4 10.fxe5+ Nf6 11.exf6 g6 12.Qd5+ Kf8 13.Bh6+ Ke8 14.f7+ Ke7 15.Qe5 checkmate, Wall,B - Marz, PlayChess.com 2014) 10.Qxd4 Re8 11.e5 Ng4 12.h3 Nh6 13.f5 Ng8 14.Nc3 c6 15.Ne4 Qb6 16.Ng5+ Kf8 17.Nxh7+ Ke7 18.f6+ gxf6 19.exf6+ Nxf6 20.Qxb6 axb6 21.Nxf6 Black resigned, Wall,B - Guest293396, PlayChess.com, 2015;
7...Re8 8.dxc5 Kg8 (8...Nxe4 9.Qd5+ Kf8 10.Qxe4 d6 11.Qxh7 Be6 12.cxd6 Qxd6 13.Nc3 Bg8 14.Qf5+ Qf6 15.Qh5 Bf7 16.Qh8+ Ke7 17.Qh7 Kf8 18.Ne4 Qg6 19.Qh8+ Bg8 20.f3 Qb6+ 21.Kh1 Ng6 22.Qh5 Re5 23.Qg4 Bf7 24.b3 Kg8 25.Bb2 Re7 26.Ng5 Qc5 27.Nxf7 Kxf7 28.Bd4 Qc6 29.Qf5+ Kg8 30.Rad1 Rae8 31.c4 Re2 32.Bc3 b5 33.Rd7 R2e7 34.Rxe7 Rxe7 35.Qxb5 Qd6 36.Qb8+ Kh7 37.Qxa7 c5 38.Qa3 Re2 39.Qc1 Qd3 40.Qd1 Qxd1 41.Rxd1 Rc2 42.Bd2 Rxa2 43.Be3 Nh4 44.Bxc5 Nxg2 45.Bd4 Nh4 46.Rd3 Ng2 47.c5 Nf4 48.Rd1 Rc2 49.Be3 Ne6 50.Rd6 Nc7 51.b4 Nb5 52.Rd7 Rc3 53.Bg1 Rc1 54.Rb7 Nd4 55.Kg2 Ne6 56.b5 Nf4+ 57.Kg3 Ne2+ 58.Kf2 Nxg1 59.c6 Nh3+ 60.Kg3 Ng5 61.c7 Ne6 62.b6 Black resigned, Wall,B - Guest6864060, PlayChess.com, 2016) 9.f4 Ng6 10.e5 Ne4 11.Qd5+ Kh8 12.Qxe4 Qh4 13.g3 Qh3 14.Nc3 Rb8 15.Nb5 b6 16.Nxc7 Bb7 17.Qe2 Rf8 18.Be3 Rbc8 19. Nb5 bxc5 20.Nd6 Rb8 21.Nxb7 Rxb7 22.Bxc5 Re8 23.b4 d6 24.Bxd6 Black resigned, Wall,B - Guest7492034, PlayChess.com, 2014; and
7...Rf8 (too generous) 8.dxe5 Ne8 9.Qd5+ Kg6 10.Qxc5 Black resigned, Wall,B - Guest848078, PlayChess.com, 2012
8.Qh5+ Ng6 9.Qd5+ Kf8 10.dxc5 Nf6 11.Qd4 Qe7
Black could also have tried 11...d5 12.Nc3 c6 13.Bg5 Kf7 14.Rae1 Rf8 15.Re2 Kg8 16.Rfe1 Bf5 17.f3 Qd7 18.g4 Nxg4 19.fxg4 Bxg4 20.Re7 Nxe7 21.Rxe7 Qf5 22.Qxg7 checkmate, Wall,B - Mydrik,M, PlayChess.com, 2015.
12.Nc3 c6 13.Be3
White develops and hopes to take advantage of Black's King's position. "Objectively" Black is still better, with a piece for a pawn; but the d-pawn blocking the Bishop which hems in the Rooks is always an ominous sign...
13...Ne5
Instead, 13...Qe5, looking to exchange Queens and reduce the danger of an attack on his King, might have been more prudent.
14.Rae1 Neg4
Black is spending too much time moving the Knight. Perhaps he can not find a plan of play. Stockfish 8 gives a subtle line that leads to an advantage (a pawn) for White, but which has plenty of play (Black has Bishop vs Knight and more central pawns): 14...b6 15.Bf4 Qxc5 16.Qxc5+ bxc5 17.Rxe5 Kf7 18.Rxc5 Re8 19.Be5 Bb7 20.Bxf6 Kxf6 21.f3 d6 22.Ne4+ Ke7 23.Rh5 h6 24.Rd1 Rad8 25.Ra5 a6 26.Kf2 c5 27.c3 g6 28.h3 Rf8 29.Nd2 Rf6 30.Nc4
15.Bf4
The benefit of pursuing development while the opponent dithers. White's Bishop not only exposes a Rook attack on the enemy Queen, it eyes the fantastic d6 square.
15...Nd5
The simplest response - 15...Qf7, withdrawing the Queen to a safe square - is the best, although then White would have the powerful 16.Bd6+ as a reply. In the excitement, Black seems to have forgotten about Her Majesty.
16.Nxd5 cxd5 17.Rxe7 Black resigned
Checkmate is coming.
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