I recently played two endgames that had the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) style imbalance of a piece vs two pawns. Both taught me something about what chances I would have, should my games last until there were only a few pieces on the board. Advantage: piece.
This position is from perrypawnpusher - zulugodetia, blitz, FICS, 2011. Although I had the White pieces, it was not a Jerome Gambit (notice Black's f-pawn). I had just exchanged Queens, being pleased to have the extra piece, not the extra pawns.
34.Nf2 f5
Black would do better to start his h-pawn running. White's plan would be to use his King to stop the Kingside pawns while using his Knight to nab a couple of Queenside pawns. Once White's Queenside pawns can take care of themselves, then the Knight will travel to the Kingside to capture those pawns. Then: back to the Queenside to promote a pawn...
35.Nd3 h5 36.Ke2 Kf7 37.Nxc5 Kf6 38.Nd7+
A change of plans. Simpler would have been 38.Nb7, planning to grab Black's a-pawn; as the Knight can still get back in time to help his King.
38...Ke6 39.Ne5 g5 40.fxg5
Yes, the Knight is expendable. That is why it came back instead of grabbing another Queenside pawn.
40...Kxe5 41.Kf3 h4 42.g6 Kf6 43.c5
43...h3 44.Kg3 f4+
A great try at a swindle: now 45.Kxf4?? loses to 45...h2 and Black Queens a pawn.
45.Kxh3 f3 46.Kg3 f2 47.Kxf2 Black resigned
This position is from perrypawnpusher - Cibola, blitz, FICS, 2011, a Semi-Italian Jerome Gambit.
In some time trouble, I decided on the simple (if not best) plan of exchanging my Bishop and weak Queenside pawns for Black's Knight and Kingside pawn, leaving me with two connected passed pawns in a Rook endgame...
34...Nxc3 35.Ra6+ d5 36.Rxh6??
Simply reversing my planned moves. After 36.Bxc3 Rxc3 37.Rxh6 Black can clean up the Queenside with 37...Rxc2+ 38.Kf3 Rxa2 but my two passed pawns on the Kingside will eventually decide the game in my favor.
36...Kxd4
Ooops...
In contrast to my game against zulugodetia, above, White has the extra pawns against Black's extra piece.
Perhaps a master could convert the win for either side, but I could only see a draw. My opponent eventually agreed.
37.Rh4+ Kd5 38.Rh5+ Kc4 39.Rh4+ Kb5 40.Ke3 Nxa2 41.Kd2 Nb4 42.c3 Nc6 43.Re4 Rd8+ 44.Kc2 Rg8 45.Re2 Kb6 46.Kb3 Na5+ 47.Kb4 Rg4+ 48.Ka3 Rc4 49.Re6+ Nc6 50.Kb3 Rg4 51.Re2 Na5+ 52.Kb2Nc4+ 53.Kb3 Na5+ 54.Kb2 Nc4+ 55.Kb3 Na5+ 56.Kb2 Nc4+ 57.Kb3 Na5+ Game drawn by repetition