Jerome Gambit: The "Debate" Again

The Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) is a collection of "debates", starting with Is a "refuted" opening playable?

The following game gives an example of another ongoing "debate", dating back 20 years.

Wall, Bill - Gilex

internet, 2022

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ 

4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ng6 

7.Qxc5 d6 8.Qd5+ Be6 9.Qxb7 

This position illustrates a Jerome Gambit "debate". 

Is capturing the b-pawn worth the spent tempo for White? Does Black get compensation in developing his Bishop? Will Black have to give back the tempo after White plays f4? 

The Database has 234 game examples. White scores 49%.

The earliest example in The Database is Toromic - Shred, blitz, FICS, 2000 (0-1, 25).

9...N8e7 

Better was 9...Nh4, e.g. 10.O-O Qg5 11.Qxc7+ Ne7 12.g3 Nf3+ 13.Kh1 Qh6 14.h4 Bh3 15.Rd1 Qe6 16.Qa5 Bf1 17.Qh5+ Ng6 18.Qxf3+ Kg8 19.Rxf1 Qh3+ 20.Kg1 Ne5 21.Qb3+ d5 22.Qxd5+ Nf7 23.Qxa8+ Black resigned, Wall,B - CheckMe, Chess.com, 2010 

Slightly better was 9...Ne5, e.g. 10.f4 Nd7 11.O-O Nc5 12.Qb4 a5 13.Qd4 Nf6 14.f5 Bd7 15.e5 Nfe4 16.e6+ Ke8 17.exd7+ Qxd7 18.d3 Nf6 19.Nc3 Kd8 20.Bg5 Kc8 21.Rae1 Re8 22.Bxf6 gxf6 23.Rxe8+ Qxe8 24.Qxf6 Qe3+ 25.Kh1 Kb7 26.Nd5 Qe2 27.Kg1 Qxc2 28.Qe7 Nxd3 29.Qe4 Qc5+ 30.Ne3+ Black resigned, Wall,B - Guest249301, PlayChess.com 2013 

10.f4

Also 10.O-O Re8 11.f4 Bd7 12.Qb3+ Kf8 13.f5 Ne5 14.d4 Nf7 15.f6 gxf6 16.Rxf6 d5 17.Bh6+ Kg8 18.Qg3+ Ng6 19.Rxg6+ Kh8 20.Bg7+ Kg8 21.Bf6+ Black resigned, Wall,B - Guest1352598, PlayChess.com, 2021 

10...Nxf4 

Black has three minor pieces developed, as opposed to White's Queen (which is somewhat offside), so he decides that he can grab a pawn, as well.

11.O-O Neg6 12.d3 

12...Rf8 

Bill prefers 12...Qg5. 

13.Bxf4 Nxf4 

Black had prepared 13...Kg8, which was a stronger choice. 

14.Rxf4+ Kg8 15. Rxf8+ Qxf8 

Black does not have enough compensation for his two missing pawns.

16.Nc3 Rb8 17.Qxc7 Rxb2 18.Ne2 Kh8 

Black would have done better to challenge the enemy Queen immediately with 18...Qb8.

19.Nd4 Bg8 20.Rf1 Qa8 21.Nf5 Black resigned

The checkmate threat will allow White to grab the d-pawn, leaving him with three connected passed pawns.