Chances

What "chances" White has in the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) come from a myriad of sources, not the least of which is opponent loss of focus or intensity. Too many games have ended up "1-0" because the defender did not see the necessity of putting all of his skill to use against a foolish, refuted opening.

perrypawnpusher  - spydersweb
blitz, FICS, 2012

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+

4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ke6 7.Qf5+ Kd6 8.f4 Ng6 

Since one of the time-proven strategies to defuse the Jerome Gambit has been returning a piece, this defense can not technically be considered "bad". 

Yet, after 11 moves (see diagram below) the players reach a position in which White has an extra move (f2-f4) in comparison to the line 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ng6 7.Qd5+ Ke7 8.Qxc5+ d6 9.Qe3. So, if Black wants to give up his King's Bishop and post his Knight at g6, the alternative might be a better choice.

9.Qd5+ Ke7 10.Qxc5+ d6 

10...Ke8 is an alternative, as in perrypawnpusher - parlance, blitz, FICS, 2011 (0-1, 22). 

11.Qe3 

Notable is 11.Qf2 Nf6 12.d3 Rf8 13.0-0 Kf7 14.Nc3 Kg8 15.f5 Ne5 16.Bg5 Nf7 17.Bh4 c6 18.Ne2 Ne5 19.h3 Bd7 20.g4 h6 21.Nf4 a6 22.Rae1 Qe7 23.d4 Nf7 24.Ng6 Qd8 25.Nxf8 Qxf8 26.Bxf6 gxf6 27.h4 Kg7 28.Kh2 Qe7 29.Qf4 Re8 30.Rg1 Kh7 31.c3 Rg8 32.Re3 Rg7 33.Reg3 Bc8 34.g5 fxg5 35.hxg5 Nxg5 36.f6 Qf7 37.Qh4 Qxf6 38.Qh5 Qf4 39.e5 dxe5 40.dxe5 Qxe5 41.Kh1 Be6 42.Qd1 Bd5+ 43.Kh2 Nf3+ 44.Kh3 Nxg1+ 45.Rxg1 Qe3+ 46.Kh2 Qf2+ 47.Kh3 Rxg1 White reigned, guest725 - guest114, Internet Chess Club, 2002.

11...Nf6

Alternatives:
11...Kf8, perrypawnpusher - Valseg, blitz, FICS, 2011 (1-0, 39); 
11...Be6 12.f5 Black resigned, perrypawnpusher - MrNatewood, blitz, FICS, 2010; 
11...Bd7 perrypawnpusher - GabrielChime, blitz, FICS,2009 (1-0, 29).

12.0-0

It is probably better to tuck away the King first than create a broad center with 12.d4, as in perrypawnpusher - thinan, blitz, FICS, 2010 (1-0, 31).

Also seen was 12.Nc3 as in mrjoker - PhlebasP, Internet Chess Club, 2008 (0-1, 34).

12...Re8 13.f5 Ne5 14.d4 Neg4 

It's always fun to harass the Queen, but 14...Nc6 was the right idea, as White then does not get much with 15.e5 Kf8 16.e6. Instead, I had planned on 15.Qd3 Kf8 16.Bg5. 

15.Qd3 Kf8 16.Bg5

A bit better might have been the thematic 16.h3 Nh6 17.Bxh6 gxh6 18.Nd2

16...h6 17.Bxf6 

This capture is not actually necessary as 17.Bh4 g5 18.fxg6 leads to an advantage for White. Best for Black after 17.Bh4 would be 17...h5, giving Black's advanced Knight a retreat square. Still, the second player's Kingside looks weakened, and White would probably not be worse.

17...Qxf6 

The Queen is poorly placed only because the Knight is poorly placed. Better was 17...Nxf6 18.Nc3 with an edge to Black. 

18.h3 Ne5

Played perhaps a bit too automatically. Play looks relatively equal after 18...d5 19.hxg4 Rxe4 20.c3 Rxg4 21.Nd2 c6 22.Rae1 Bd7. 

19.dxe5 Qxe5 20.Nc3 

How many times has White's advantage in the Jerome come down to better development, while Black's Queen Bishop sits at home, cutting off his Queen's Bishop?

20...c6 21.Rad1 d5 

A miscalculation. 

22.exd5 c5 

Better, but not saving, was 22...Qe3+ 23.Qxe3 Rxe3 24.dxc6 bxc6. 

23.f6 g5 24.Qg6 Black resigned