Wow. Pretty interesting Gambit. After playing the Keoni Hiva and Franco Hiva Gambits, I'm fond of the move d3 after dxe4. I ran the position briefly though Rybka on Fritz and its first choice was in fact like your games Nc3 but the d3 idea was second and not far off point wise. Of course I only ran it through for a couple of mins. Here is a quick line Rybka suggested after d3.
The Williams Gambit
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Interesting. I like how f4 usually leads to closed games (unless the From is played), but this is clearly a wide-open center. It's a good for white to force an open game.
Another example of this gambit being playable.
I am a scandinavian player. And when i face the scandinavian, i want to surprise my opponents. So i can transpose into this gambit from the scandinavian. 1e4 d5 2f4.
So my prefered opening as white is the Bird. And of course, my favorite gambit is the From, my normal response as black to 1. f4. However, when learning the Bird, I was shown a rather cute but unfortunately unsound gambit against 1. f4, d5. It's called the Williams Gambit (concieved by a mid-ranking chess enthusiast named William L. Williams).
If declined, the gambit can transpose easily into a French, Caro-Kann, Sicillian, or Nimzovitch game. If accepted, black will surely be dumbfounded and weaker players (in blitz) may make easy to miss mistakes. Here is the so-called main-line followed by a couple of miniatures that show how Black can easily mistep.
Once again, do not expect to play this gambit and win with any sort of consistency against stronger players! It's unsound, but still an entertaining thought. I hope you enjoy these real games, as played by Williams: