What to play if someone ignores your King's Gambit? So I'm an (unranked, but ~1500 on lichess) amateur who's been working on developing my opening strategy for some time, and I've basically been using the King's Gambit for a variety of reasons:


It is easy to play and fairly straightforward
Castling opens my kingside rook, which I tend to use a lot
Most casual players are unfamiliar with the technicalities of the gambit


While I may not be using the King's Gambit for the most optimal reasons, I am fairly comfortable with it and usually play the following:


e4 e5
f4 exf4
Nf3


After this I pretty much know all the major strategy, and can also play against some of the more common defenses (classical defence, Falkbeer Counter Gambit, etc).

What really gets me, however, is when players just ignore the gambit altogether and do something like


Nf3 Nc6


Now what am I supposed to do? I know that these are not good moves and will be appropriately penalized, but I often find it frustrating because all of a sudden I am placed in an unsure position. This particular case has happened to me several times in the past, but players often also play other strange moves like 


Nf3 d6


What would I attempt when players simply ignore the Gambit (i.e. neither accept nor defend?)
Well, it is funny that 4.Nc3 is then the most popular move, with 4.d4 a distant second. In practice though, 4.d4 scores a very high 73.3% for white, compared to only a typical 56.7% for 4.Nc3. In addition, Stockfish much prefers 4.d4, and it is not even close (-.54 to +.92).

I will take that big center, and get my pawn back with an open f-file any day. The reality is that you do not have to do much there other than to develop your pieces as black has no space. I will give a suggested setup below. Black really should fight back earlier, try to hold the pawn, or maybe not take on f4 to begin with.

For the record, as soon as they play exf4, they have accepted the gambit, but they may not try to hold it with g5.

 [FEN ""]

 1. e4 e5 2. f4 exf4 3. Nf3 Nc6 4. d4 d6 5. Bxf4 Bg4 6. Nc3 Nf6 7. Be2 Be7 8. O-O O-O 9. Qd2 {With a fantastic position.}


Here is a suggestion based on your supplemental question. Keep in mind that there are a virtually infinite number of ways that black can deviate from the path, but just develop your pieces, and you will get a decent game.

 [FEN ""]

 1. e4 e5 2. f4 Nc6 3. Nf3 d6 (3... f5 {The most popular move here.} 4. d3 {This is the main line, but does not really try to punish black.} (4. exf5 {Might be a better try, but there are many lines here.}) 4... d6 5. Nc3 Nf6 6. g3 g6 7. Bg2 Bg7 8. O-O) 4. Nc3 Nd4 {And this strange moving of a piece twice is the computer's first choice, and the most commonly played in practice.} 5. d3 {And just finish developing with Be3, Be2 and Qd2.} Bg4 6. Be2 Bxf3 7. Bxf3 Nf6 8. O-O Be7 9. Be3 $16 {With a very comfortable game.}