It's called the Smith-Morra gambit, you'll see quite a lot writen about it here, e.g. this thread http://www.chess.com/forum/view/chess-openings/smith-morra-gambit9?lc=1#last_comment
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Playing black, I recently lost to the following opening, which leaves black a pawn up but with white having the development advantage:
1.e4 c5
2.d4 cxd4
3.c3 dxc3
4.Nxc3 ...
(You can see my game vs. nor1nor in the current Chess in the City Tournament, if you're interested).
What is the winning line for black to play, to exploit his material advantage?
Thank you for any insights.