Playing the Jerome Gambit and its relatives regularly is like participating a seminar on "The Psychology of Error in Chess." White can only win after giving "Jerome Odds" if his opponent errs, but there are so many ways that Black can suddenly become cooperative...
iplayforsean - Leftang
blitz, FICS, 2008
1.e4 e5 2.Nf3 Nc6 3.Bc4 Na5
Not a good idea, for a number of reasons. See "A Line of Play Everyone Should Know About" for a few of them.
Not the best reason (4.Nxe5 is top of the picks), but reason enough to avoid 3...Na5.
4...Kxf7 5.Nxe5+ Ke6 6.d4
One of several moves that White has at his disposal, to keep the game interesting and going forward. The most precipitate is 6.Qg4+ when Black probably does best to take the offered piece with 6...Kxe5, as White has an edge after 6...Ke7 7.Qg5+ (likely better than 7.Qh5+ Nf6 8.Ng6+ hxg6 9.Qxh8) Nf6 8.Ng4 Nc6 9.e5 Kf7 10.exf6 d5 although things remain complicated. After 6.Qg4+ Kxe5 7.Qf5+ Kd6 8.Qxa5 Qf6 Black may have a edge, but his King's position and lag in development keeps it small.
White might do better with the maneuver mentioned above: 7.Qg4+ Ke7 8.Qh4+ Nf6 9.Ng6+ hxg6 10.Qxh8
Sometimes it is nice to be two pieces ahead, like in the line mentionied in the note after White's 6.d4, above. But not this time.
Black could survive with 7...Ke7, although after 8.Nf3 Nf6 9.0-0 his King would remain a major headache.
Only temporary relief comes from 8...g5, e.g. 9.Bxg5 Nf6 10.f4+ Kd4 11.Qf3 and the Black King will come to grief.
9.Bg5+ Ke5 10.Bxd8+ Black resigned
Losing his Queen was enough punishment for Black.
Attackers might figure out that the alternative 10.c3 led to checkmate, for example 10...Nf6 11.Bf4+ Kxf4 12.g3+ Kxe4 13.Nd2+ Kd3 14.Qe2+ Kc2 15.Nf1. (After the text, if it were needed, White could still mate in about 10 moves, but this proved unnecessary.)