Although the King's Gambit does not provide a theoretical advantage, it often leads to a dynamic equality with best play, and many of these lines with Nf3 and ...g5 lead to wild complications, with White sacrificing further material in order to accelerate the attack. But Black's idea of playing an early ...g5 is not just to hold onto the f4-pawn, defend and win the endgame- quite often Black gets counterattacking chances thanks to the advanced f and g-pawns, and opportunities to force White's king (which is relatively exposed thanks to White's early f2-f4) to go for a walk.
3.Nf3 and ...g5- A round-up from White's point of view
1) After 1.e4 e5 2.f4 exf4 3.Nf3 g5, 4.h4 g4 5.Ne5 is the sound and respectable Kieseritzky Gambit, which leads to interesting and equal play after 5...Nf6, 5...d6 or 5...Nc6, but I think generating good winning chances is tricky against 5...Qe7.
2) The Hanstein Gambit with 4.Bc4 is not as bad, or harmless, as its reputation. There are various lines where Black castles queenside and White attempts to storm Black's queenside with the a and b-pawns, while the line with 4...Bg7 5.0-0 Nc6 6.d4 d6 7.c3 h6 8.Qa4!?, encouraging 8...Bd7 9.Qb3, wins the pawn back and probably suffices for dynamic equality. Note that if Black plays 4...g4 then 5.0-0 gxf3 6.Qxf3, the Polerio or Muzio Gambit, is very dangerous.
3) A good alternative for White is to play d2-d4 and Nb1-c3, followed by g2-g3, challenging Black's f4-pawn. The Rosentreter Gambit (4.d4) offers a piece sacrifice with 4...g4 5.Bxf4 gxf3 6.Qxf3, while the Quaade Gambit (4.Nc3) intends 4...g4 5.Ne5 and if 5...Qh4+ then 6.g3 fxg3 7.Qxg4.
4) The Allgaier Gambit with 4.h4 g4 5.Ng5, intending to sacrifice on f7, is somewhat dubious, but offers White dangerous attacking chances in over-the-board play. The Hamppe-Allgaier Gambit, with 4.Nc3 Nc6 and then 5.h4 g4 6.Ng5, offers White better chances than the "pure" Allgaier, although objectively White probably falls a little short of full compensation for the sacrificed knight.
5) After 4.Nc3 Nc6, White's other main options are 5.d4, the Pierce Gambit (which strikes me as an inferior relative of the Rosentreter, for Black's c6-knight gives Black automatic counterplay against d4) and 5.g3!?, which appears reliable.
3.Nf3 and ...g5- A round-up from Black's point of view
1) I used to favour 3...Nc6 followed by ...g5, but against this, 4.d4 g5 5.d5 is rather irritating for Black, and often leads to queenless middlegames with a slight pull for White (though I'd point ambitious White players towards 5.h4 g4 6.Ne5 or 6.Ng5 in that line). Those who prefer the early ...Nc6 lines should prefer 3...g5 followed by a quick ...Nc6 in most cases, and after 3...g5 4.d4 should settle for an alternative reply (4...g4, 4...Bg7 and 4...d6 are all reliable).
2) I don't think the Becker Defence with 3...h6 is particularly reliable because of 4.Nc3 g5 5.d4 (or 4.d4 g5 5.Nc3) with 6.g3 to follow, where ...h7-h6 is not particularly useful.
3) The Fischer Defence with 3...d6 is a good way to avoid the Kieseritzky and Allgaier Gambits, but commits Black to meeting 3.Nf3 g5 4.Nc3 and 4.d4 with 4...d6. This is one of Black's better responses to those lines, but it means that Black's options there are more limited.
4) 3...g5 appears to be the most flexible of these continuations for Black, though it allows the Kieseritzky and Allgaier Gambits. I don't think this should be much of a concern though, because Black has four good responses to the Kieseritzky, and the Allgaier leads to unbalanced play in which Black is theoretically better, though has to take care due to the exposed black king.
