I spent a little time with The Database today, and came up with the following numbers.
All statistics need to be approached cautiously. In this case it is useful to remember that the vast majority of games in The Database are drawn from over a decade of games played online at FICS, regardless of outcome; so they should be somewhat representative of Jerome Gambit play among club players who contest online.
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5
The Database has 5,307 games where the game continues 3...Nd4 4.Bxf7+ instead. White scores 56%.
4.Bxf7+
The Database has 12,662 games reaching this position. White scores 45%.
The Database has 4,589 games where Black plays 4...h6 instead. White scores 55%. This includes 187 games which continue 5.0-0 Bc5 6.Bxf7+, where White scores 65%; and 141 games which continue 5.Nc3 Bc5 6.Bxf7+, where White scores 54%.
4...Kxf7
The Database has 12,763 games reaching this position. I am not sure why this number is larger than the earlier one! White scores 45%
The Database has 272 games where Black declines the Bishop with 4...Kf8. White scores 55%. The Database has 41 games where Black declines the game with 4...Ke7. White scores 72%.
5.Nxe5+
The Database has 5,613 games reaching this position. White scores 54%.
The Database has 2,510 games where the game continues 5.Nc3 Nf6, or the game reaches the Four Knights variation by transposition. White scores 38%
5...Nxe5
The Database has 5,348 games reaching this position. White scores 54%.
The Database has 202 games where Black replies, instead, 5...Kf8. White scores 52%. The Database has 103 games where Black replies 5...Ke8; White scores 59%. The Database has 24 games where Black plays 5...Ke6; White scores 65%. The Database has 12 games where Black replies 5...Ke7; White scores 67%.
6.Qh5+
The Database has 3,804 games with this position. White scores 55%.
The Database has 1,528 games where White plays 6.d4 instead. White scores 52%.
6...g6
The Database has 471 games with this position. White scores 71%.
The Database has 570 games where Black plays 6...Kf8 instead. White scores 50%.
The Database has 960 games where Black plays 6...Ke6. White scores 54%.
The Database has 1 game where Black plays 6...Ke7. White scores 100%
Of course, were I to subject each of these positions to the scrutiny of, say, Stockfish 8, the computer's evaluation would likely, in some cases, vary significant from the game outcomes in The Database!
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