I should point out that by "offensive," I mean an opening which gives me many winning chances, tactical, and/or gives me a position where I am attacking White.
Alternatives to the Budapest Gambit
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Anyone?
i usually play g6 there (also playing the budapest)
c5!
BTW 8...QA3
in the 1930s whites played nf3 just to avoid the budapest!
I'm thinking King's Indian because I would've already avoided the Samisch and Four Pawns Attack.
if you know the king's indian or want to learn it then go for it. i personally play c5 and go into benoni type positions but really, people at my level never seem to play d4 as white so i don't spend too much time thinking about it!
2...d5 is probably the simplest response although it sounds like that isn't your style. However, the fact that White avoided the Budapest gives me the hunch that they will play some dud opening instead or maybe something like the Trompowsky Attack. if they were too cowardly to face the highly suspicious and positionally unstable Budapest. This is just a guess on my part however...
BTW I've played the Budapest on and off sporadically for decades so I'm not "prejudiced" against it, if it works for you keep on playing it when possible.
How about the Blumenfeld Gambit!
Since the Budapest Gambit needs the moves 1. d4 Nf6 2. c4 to be an option, one can't play the Budapest if White plays, say, Nf3. I was wondering if anyone had any suggestions for what to play after this. I'm looking for something that isn't the most common, but if your suggestion is purely offensive please share!