If chess players were guided by "objectively best" assessments of the positions they were playing, there would be no Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) or its related openings: after White's Bishop sacrifice, he could just resign.
In whatever way the positions are evaluated, however, play continues - that is what the rest of the game is for.
The following game is a good example. White persists, despite facing prevailing wins, because he is well aware that in club level blitz play, anything can happen.
Robepersky - JohnInWales
10 0 blitz, FICS, 2023
1.e4 e5 2.Nf3 Nc6 3.Bc4 h6
The Semi-Italian Opening.
4.O-O Bc5 5.Bxf7+
The Semi-Italian Jerome Gambit.
Black's hope to protect his himself from the Fried Liver Attack - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Nxd5 6.Nxf7 - by making the g5 square "off limits" for enemy pieces is foiled by White's Jerome Gambit treatment.
For some background see "A Jerome Look At The Semi-Italian Opening (Parts 1 & 2)" and "Semi-Italian Jerome Gambit"
According to The Database, Robepersky is 17 - 8 with this sacrifice.
5...Kxf7 6.Nxe5+ Nxe5 7.Qh5+
By adding O-O and ...h6 to the normal Jerome Gambit line, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Qh5+, White has improved his position by about a pawn's worth, according to Stockfish 15.1.
7...Ke6 8.c3
This preparatory move is Robepersky's choice, and The Database shows that it has scored 5 - 5, but more dynamic for White would be 8.Qf5+ Kd6 9.b4!?
8...Qg5
Black calmly offers to exchange Queens, to dampen White's attacking chances.
Robepersky has also faced
8...Qf6 9.d4 Bxd4 10.cxd4 Nf7 11.Qd5+ Ke7 12.e5 Qe6 13.Qc5+ d6 14.Qxc7+ Qd7 15.exd6+ Nxd6 16.Re1+ Kf8 17.Qc5 b6 18.Qb4 Bb7 19.Bf4 Re8 20.Bxd6+ Kf7 21.Qc4+ Kf6 22.Be5+ Ke7 23.Bxg7+ Kd8 24.Rxe8+ Qxe8 25.Bxh8 Bc6 26.Nd2 Kc7 27.Be5+ Kb7 28.a4 Ne7 29.a5 Nd5 30.a6+ Kc8 31.Rc1 Ne7 32.d5 Kd7 33.dxc6+ Nxc6 34.Qxc6+ Ke7 35.Bd6+ Kf7 36.Qf3+ Ke6 37.Re1+ Kxd6 38.Rxe8 Black resigned, Robepersky - EddyTorrance, 5 0 blitz, FICS, 2021;
8...Be7 9.Qf5+ Kd6 10.d4 Bf6 11.dxe5+ Bxe5 12.Rd1+ Ke7 13.Qxe5+ Kf8 14.Nd2 d6 15.Qf4+ Nf6 16.e5 dxe5 17.Qxe5 Nd7 18.Qf4+ Kg8 19.Qc4+ Kf8 20.Nf3 Qf6 21.b3 Ne5 22.Ba3+ Ke8 23.Nxe5 Rh7 24.Nf3 Be6 25.Re1 Kd8 26.Rad1+ Ke8 27.Rxe6+ Qxe6 28.Qxe6 checkmate, Robepersky - Tenet, 10 0 blitz, FICS, 2022; and
8...Nf6!? 9.Qh3+ Kf7 10.d4 d5!? 11.dxc5?! (11.Qg3 Re8) 11...Bxh3, White resigned, Robepersky - tutekk, blitz, 5 2 blitz, FICS, 2023
9.Qxg5 hxg5 10.d4
White achieves his pawn fork, but, to be fair, it is not enough to alter the fact that Black is better.That is what the rest of the game is for.
10...Nf3+
A spririted idea: if Black needs to return a piece, why not do so to break up White's castled position?
11.gxf3 Be7 12.Nd2 Bd6
Yes, the Bishop is safer on e7, but more aggressive on d6.
13.d5+
I would have sent the Bishop scurrying back to e7 with 13.e5.
13...Ke7 14.f4
Clearance sacrifice.
14...gxf4 15.Nf3
The Knight takes up guard duty on the Kingside, keeping a special eye on h2, which is threatened by the enemy Rook.15...Nf6
Business as usual. In a blitz game, this kind of thing happens. More in line with the demands of the position was 15...Kf8.
16.e5 Bxe5 17.Nxe5 Ng4
Clock? Nerves? Caffeine deficiency disorder?Instead, after the routine 17...Re8 18.c4 d6 19.Ng6+ Kf7 20.Nxf4 the game would be even, according to Stockfish 15.1 (34 ply) despite White's extra pawn.
Black resigned