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After the first two moves of the Greco Defense
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1. e4 e5 2. Nf3 Qf6
what should White's agenda be? I see that the wikibook Chess Opening Theory suggests 3. Bc4, but it doesn't go into detail. I'm not used to this opening as White, and never play it as Black, so I'm not sure 1) what to aim for in order to undermine Black's early Queen advance, and 2) how to guard against a possible kingside attack. For instance, should I castle Queenside, or isn't that necessary?
2... Qf6, while not strictly unsound, is definitely an inferior move, not only because it develops the queen prematurely, but also (and more importantly) because it deprives the black king's knight of a very natural square on f6. Don't panic about a possible king-side attack -- black cannot mate with no minor pieces developed. There are a number of reasonable continuations for white:
3. Nc3, a natural and flexible developing move that eyes the d5 square, threatens to chase the queen with gain of time, and doesn't commit to any particular pawn structure.3. d3, a perfectly valid move, but somewhat passive and has the distinct flaw of locking in the light-square bishop. Unless you strongly prefer to play slow, positional chess, I would develop with 3. Bc4 prior to playing d3 (if at all). If you play d3, the logical plans are either to prepare a central break with c3 and a subsequent d4, or to castle kingside and prepare f4 after re-maneuvering the f3 knight. Which of those plans is preferable depends on your opponent's development, of course.3. Bc4, versatile and potentially very aggressive, threatening an eventual Ng5 and pressure on f7 after white's d-pawn moves. This is definitely the move I'd favor in a rapid game, and I don't think it's objectively worse than 3. Nc3.Other moves, such as 3. d4 and 3. c3, are probably sub-optimal. An immediate 3. d4 push is likely to lead to exchanges and a relatively drawish position (and might end up transposing to lines of the Scotch that are not particularly good for white), while 3. c3 is slow and somewhat crude and might allow black to equalize with dynamic piece play.
As White, I'd concentrate on chasing Black's queen. 3. Nc3 is a normal developing move, and threatens 4.Nd5.
Another move is 3. d3, which threatens 4. Bg5. Black's most threatening countermove is 3.... Bc5, which can be met by 4. Be3. If Black exchanges bishops, it opens the f file for the (castled) rook to chase the queen.
No need to sweat this one because the Greco Defense is an inferior opening. Just make good developing moves and Black will fall behind in development.
What about a gambit try?
[fen ""]
1. e4 e5 2. Nf3 Qf6 3.d4 exd4 4. c3 dxc3 5. Nxc3
and I like white's position, though maybe black has better 3rd and 4th moves.
I understand that one might not be willing to take on the risk in a situation where stable advantage is fairly easily obtained as shown by the other posts, but this an option that white has.
1.e4 e5 2.d4 exd4 3.c3 dxc3 4.Bc4 cxb2 5.Bxb2, but it doesn't look as poignant.
[fen ""]
1. e4 e5 2. Nf3 Qf6 3. d4 d6 4. dxe5 dxe5 5. Bg5 Qe6 6. Qd8#
The Greco Defence is easily broken in my opinion
