Recently I took another, brief, look at what I have called the Overlook Gambit, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Nxe5 (see "Jerome Gambit: Wandering [Part 1]) - because it looks like White overlooked the fact that Black's e5 pawn was protected.
In that, the Overlook is similar to the Chicago or Irish Gambit, 1.e4 e5 2.Nf3 Nc6 3.Nxe5 and the Halloween Gambit, 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5 although the presence of the Bishops makes a difference.
I might as well have called the opening the Ooops Variation of the Jerome Gambit - if playing the Jerome Gambit is what White was intending - only he accidentally played his 5th move before his 4th move (Ooops), in the sequence 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nxe5+.
The Overlook is not very strong. A check with the lichess.org database shows 247,034 games, with White scoring 39.5%.
Still, it can be played for fun, and even as a surprise weapon (preferrably in games with a fast time control).
I checked The Database and found that Bill Wall has both played and faced the Overlook.
Guest4931371 - Wall, Bill
internet, 2017
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Nxe5
4...Nxe5
Or
4...Nh6 5.Qh5 O-O 6.Nxc6 Bxf2+ 7.Kxf2 dxc6 8.d3 Bg4 9.Qc5 Qh4+ 10.Kf1 Kh8 11.Bg5 Qh5 12.Be7 Rfe8 13.Qxh5 Bxh5 14.Bg5 Ng8 15.Nd2 b5 16.Bb3 h6 17.Bf4 Re7 18.h3 g5 19.Be3 a5 20.g4 Bg6 21.a4 Kh7 22.h4 Black resigned, Wall,B - Guest2075193, playchess.com, 2012; or
4...Bxf2+ 5.Kxf2 Nxe5 6.Be2 Qf6+ 7.Kg1 Ne7 8.d4 N5g6 9.Nc3 c6 10.e5 Qh4 11.g3 Qh3 12.Bg4 Black resigned, Wall,B - Guest2095477, playchess.com, 2012
5.d4
Or 5.Bd5 Qg5 6.O-O Qg6 7.d4 Bxd4 8.Qxd4 Nf3+ 9.Kh1 Nxd4 White resigned, Ortiz - Wall,B, internet, 2011
5...Bb4+ 6.c3 Nxc4 7.cxb4 d5
8.b3 Nb6 9.Qe2 dxe4 10.Qxe4+ Qe7 11.Qxe7+ Nxe7
12.O-O Nc6 13.Re1+ Be6 14.b5 Nxd4 15.Nc3 Nc2 White resigned
White has had enough.
(By the way, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+, the Jerome Gambit itself, scores 49.5% on 63,4802 games at lichess.org)