What can we make of the last two posts (see "Jerome Gambit: What Are the Odds?" and "Jerome Gambit: Stockfish 8 Checks In"), each of which provides useful information about the Jerome Gambit?
First, we need to recall Geoff Chandler's very useful and very practical chart.
Here is a one-move blunder table showing how severe the blunder needs to be in a game between two players of the same grade.
All players should be able to spot their opponent leaving a mate in one on.This chart immediately addresses a couple of questions:
A 1200 player should win if an opponent blunders a Queen or a Rook. But not necessarily if they pick up a Bishop or Knight.
1500 players often convert piece-up games into a win, but this is not the case if a pawn or two up.
An 1800 player usually wins if they are two pawns up.
In a game between two 2000+ players a blundered pawn is usually enough to win.
Q: Why do masters not play the Jerome Gambit?
A: According to Chandler, a pawn advantage is enough for a master to win the game. In the Jerome, White sacrifices one or two pieces, and Stockfish 8 evaluates the position with 4.Bxf7+ as giving Black a 1.85 pawn advantage. That would be self-injurious in a master vs master game.
Q: So why is it that, according to The Database, White scores 45% after 4.Bxf7+ ?
A: Recall that The Database contains primarily club-level games played on the internet. We can see from Chandler's chart that players rated 1200 and 1500 often need more than "almost two pawns" to win. Even an 1800 rated player only "usually" wins when two pawns up - and the Jerome Gambit sacrifices 1.85. The errors of the Jerome Gambit fit right in with the errors of club play.
Both practice and computer analysis (as well as common sense) strongly suggest that Black should accept the Bishop after 4.Bxf7+. To refuse it is to give White a better (but not necessarily winning) game.
Black should also accept the Knight after 5.Nxe5+ (Stockfish 8's top choice for White here, at 30 ply search; although it rates almost as good 5.0-0, 5.c3, 5.d3, 5.Qe2 and 5.Nc3.) Best play is for the defender to be brave, but that does not always come easy for club players.
Practical play and computer analysis suggest that White garners further risk in playing the Italian Four Knights Jerome Gambit, as opposed to the main line classical variation.
The Database and Stockfish 8 slightly prefer 6.Qh5+ over 6.d4, but only slightly. It is worth being comfortable with both.
Both the Semi-Italian Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 h6 4.0-0 Bc5 5.Bxf7+) and the Blackburne Shilling Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4 4.Bxf7+) improve White's chances over the main line Jerome Gambit, according to both The Database and Stockfish 8.
Based on practice, Black defends best against 6.Qh5+ with 6...Kf8. Stockfish 8, instead, prefers 6...Ke6. The move 6...g6 - from Blackburne's wonderful crush of the Jerome - scores poorly according to The Database, while Stockfish 8 says it leads Black to an advantage of 1.55 pawns.
The computer's choice of 6...Ke6, which it rates as -2.42, fits in well with computers in general preferring the "annoying defense" (continuing 7.f4 d6) and pushes the defender's advantage to almost 2 1/2 pawns. It may be the complexity of the line, or it may be that it is played by weaker club players, that accounts for being less successful (per The Database) than 6...Kf8 in play.
Finally: the Jerome Gambit is a light-hearted opening for practicing attack (or defense) and performs best in casual or blitz play, or when White is giving a lesser-rated player "Jerome Gambit" odds. You are not likely to see Magnus Carlsen playing any time soon.