Opening Discussion, Not Quite Closed

I have been looking at a Jerome Gambit-related opening line that does not appear to have a name. Although I have covered it a number of times on this blog -  "Offside!" "The Other Side" "Bishop in A Hurry", "Watch that last step...", "It Worked -- This Time", "A Line of Play Everyone Should Know About", "The Psychology of Error in Chess", "It Takes More Than Just One Move",  "Checking Back", "Huh?", "A Snack", "Betcha Can't Eat Just One", "Entertaining and Educational", "Barely Got His Coffee Sipped", "Crime and Punishment", "Hard to Believe", "Poison", "Puzzling", "A New Mate", "On the Other Hand", "Chess Marches On", "Chess Marches On (Again)", "Always Good To Remember", "Cure Worse Than the Disease", and "Repetition Helps Those Who Pay Attention" - I have only played it twice, and only faced Black's best response once.

I am talking about 1.e4 e5 2.Nf3 Nc6 3.Bc4 Na5,

which certainly can be met with 4.Nxe5 with an edge for the first player, but which I like to meet with 4.Bxf7+.

After 4...Kxf7 5.Nxe5+ (there are 1933 games with this position in The Database, and White scores 72%) the strongest reply appears to be 5...Ke7  (although this move is seen only 371 times in The Database, that is less than 1/5 of the time, and White scores 70%).

How should White proceed?

As in "A Discussion Continued" I invited Stockfish 6, Houdini 3, Rybka 3 and The Database to consult with me. There were ideas and disagreements galore.

In my original notes to perrypawnpusher - wred, blitz, FICS, 2011, I pointed out that Rybka 3 preferred 6.Nc3. The move appeared 11 times in The Database. White scored 73%. The most recent game with the line continued 6...d6 7.Nd5+ Ke8 8.Qh5+ Black resigned, Alnischu - Kaliz, blitz, FICS, 2013.

On the other hand, 6.d4 was preferred by Stockfish 6. The move appeared 171 times in The Database. White scored 64%. The most recent game with the line continued 6...Nf6 7.Bg5 d6 8.Bxf6+ Kxf6 9.Ng4+ Kf7 10.Qf3+ Bf5 Black forfeited by disconnection, seinfeldaddict - JDZAAA, standard, FICS, 2014.

However, Houdini 3 preferred 6.Qf3. The move appeared in 27 games in The Database. White scored 70%. The most recent game with the line continued 6...Nh6 7.d3 Qe8 8.Bxh6 gxh6 9.0-0 Bg7 10.d4 d6 11.Nd3 Bxd4 12.c3 Bf6 13.Nd2 Rf8 14.Qe2 h5 15.Nf4 Bg4 16.Nd5+ Kd7 17.Nxf6+ Rxf6 18.f3 Be6 19.Rfe1 Rd8 20.c4 Kc8 21.b3 Qg8 22.Qf2 Nc6 23.Nf1 b6 24.Ng3 Ne5 25.Rad1 Ng4 26.Qd2 Ne5 27.Qd4 h4 28.Qf2 hxg3 29.Qxg3 Rg6 30.Qf2 Bh3 31.g3 Nxf3+ 32.Qxf3 Bg4 33.Qg2 Bxd1 34.Rxd1 Rf8 35.Qh3+ Kb8 36.Qd7 Rgf6 37.e5 Rf2 38.exd6 Rc8 39.dxc7+ Rxc7 40.Qd6 Rxa2 41.Rf1 Qe8 42.Rf8 Qxf8 43.Qxf8+ Rc8 44.Qf4+ Rc7 45.Qe5 Kb7 46.Qd5+ Kb8 47.b4 Re7 48.Qd8+ Black resigned, sadhamlet - whickmeister, blitz, FICS, 2014.

What did I actually play in my game against wred? Why, 6.Qh5. The move appeared in 107 games in The Database. White scored 73%. The most recent game with the line continued 6...Nh6 7.d4 Qe8 8.Bg5+ Kd6 9.Qxe8, Black resigned ffdallagnol - praiseanosyk, FICS, 2014.

The answer to the question of the best continuation for White in this line remains unsettled, although all four moves given have been successful in practice.