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Also known as the Greco Counter-Gambit, this rather shocking move is an attempt by Black to grab the initiative and lead the game quickly into unknown territory, much like its cousin the Elephant Gambit. It can be quite effective, especially against an unprepared player, and over the years has accumulated quite a body of theory as it undergoes sporadic revivals. It takes the form of a King's Gambit with colours reversed, and therefore with White enjoying an extra move when compared to normal King's Gambit lines. This makes it very dangerous for Black, with one slip often costing the game.
White's main options are whether to capture one of the offered pawns, or stick to development.
This is regarded as the main line. White accepts Black's challenge, capturing the gambit pawn on f5. A typical continuation is:
A complex tactical position arises, in which Black has lost the right to castle, but in return has obtained a strange and complex position in which a White player who does not know his theory can easily go astray.
An interesting and not well-known way to decline the gambit is give on Garry Kasparov's chess home page:
3.Nc3!? Usually the gambit is declined by 3.Bc4!?
6.Nd5! White seems to be doing well here, with threats of Nxc7+ which are difficult to deal with.
The Latvian Gambit is not currently regarded as sound enough for a grandmaster to play in a serious match, but it makes frequent appearances at lower-ranked tournaments.
An excellent resource on the Latvian Gambit can be found at the home page of an enthusiastic amateur called Marek Trokenheim: http://www.algonet.se/~marek/lg-toc.htm