From the Wikipedia article on the Fried Liver,
Italian way of cooking liver ("Fegatello" means to put the liver in a
net and cook it over a fire, or, in modern times, in a pan. Here we
can see a metaphor for what happens to Black’s king in this line: it
is cooked like a "fegatello". Usually Black’s king is caught in the
mating net and White ...
I mean, this is the main line and for a reason.
But I would be very surprised if most people's repertoire ended here, this is where it begins. The line goes
6.Bb5+ c6 7.dxc6 bxc6
And now White has a number of options. In all of them White stays up a pawn however Black gets some counter play. (and there isn't a great line to give back that pawn for initiative,...
4.Ng5 is a provocative move, threatening to take on f7.
The main line is 4...d5, and after 5.exd5 the best move might be 5...Na5. After 6. Bb5+ c6 7. dxc6 bxc6 Black has sacrificed a pawn but has gained a slight lead in development. If instead you play 5...Nxd5, White will often play 6. Nxf7 Kxf7 7. Qf3+ Ke6, known as the Fried Liver. White has a very good ...
I believe you should go for 9.h4 in the main line:
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Na5 6.Bb5+ c6 7.dxc6 bxc6 8.Bd3 Nd5 9.h4
White is trying to keep his pieces on active squares at all costs.
There is a lot of complexity here, e.g. in the line 9...h6 10.Qh5 Qf6 11.Nh7!? Rxh7 12.Bxh7 g6 (don't play 11.Nxf7 hoping for 11...Qxf7 ...
In response to:
4.c3. This outright loses a pawn to 4...Nxe4. I have a hard time believing White will play this often.
4.Nc3. This move is tame, effectively accepting a symmetrical position with minimal advantage if Black plays 4...Bc5. Black does not have to acquiesce and could play 4...Nxe4 5. Nxe4 d5 giving Black easy development and a comfortable game. ...
The Traxler counter-attack starts if White plays Ng5 in this position.
[FEN "r1bqkb1r/pppp1ppp/2n2n2/4p3/2B1P3/5N2/PPPP1PPP/RNBQK2R w KQkq - 4 4"]
Without Ng5, there is no Traxler counter-attack.
I think that 1.e4 e5 is not the best way of preparing an attacking and aggressive battle with Black. That is why I play 1.e4 c5 and go for the ...
I recently showed an interesting variation for black to a few friends at a tournament. There were the good old times when me and my chess club buddies spent hours on end analyzing these sorts of positions. Well, it goes like this:
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Nd4 6.c3 b5
Yes, it looks totally crazy! And it is, too! As far as I ...
It's better to castle on move 7 and sacrifice the knight next move. Black will have a hard time defending against this.
The variation with 5.Ng5 is called the Perreux Variation and is extensively analysed at the following site:
The Perreux Variation of the Two Knights Defense
A critical line begins with 6...Qe7+!
1.e4 e5 2.Nf3 Nc6 3.Bc4 ...
There is a very interesting counter to the fried liver attack that i came across.
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 Bc5 5. Nxf7 Bxf2
There are lots of variations covered by matoJelic, please have a look.
This does not actually answer your question, but if you are asking about this from the perspective of the white player, you are probably better off playing the modern move 6.d4 and studying the lines that follow from that. The reason for this is that most black players don't play 5...Nxd5, so it would not be very good use of your time to look into a line ...
Recently, GM L'Ami made a DVD covering the Two Knights and the Fried Liver attack. According to the article, he suggests ideas for both white and black, so maybe he discusses 9.Bb3 (instead of 9.a3) and 11....Qh4 (instead of 11....Kd6).
Furthermore I'd like to add that, although it has been played by a couple of grandmasters, 5....Nxd5 is considered to be ...
Most people agree that the Fried Liver attack is better for white. So black's 5...Nxd5 is inferior to the less scary 5... Na5. Assuming that black goes in for the Fried liver though, white can play either 6. Nxf7 or 6. d4. Both lead to similar attacks.
In the Nxd5 Nxf7 line, however, black's moves are forced until move 8, where black has the choice to ...
As others have correctly said, once you have played 3..Nf6 there is no going back. A very reasonable alternative is the Hungarian Defence 3..Be7, against which White cannot launch a wild attack. If he plays too quietly (c3, h3..), you can often take the initiative by playing ..d5.
Books will you that ..Be7 is a bit passive, but at your present level your ...
Responding 3...Nf6 to the Italian Game initiates the Two Knights Defense. This isn't an opening to play if you're looking for a calm positional game with material equality; in fact, it's been suggested that the name "defense" is inappropriate and the opening should've been called a "counterattack" or even "gambit" instead. White playing 4.Ng5 practically ...
The Danish Gambit.
A variation of the four knights with 4. Bc4 will lead to an opening of the game for black by the means of 4...Nxe4 5. Nxe4 d5.
Alternatively, 5. Bxf7+ Kxf7 6. Nxe4 may also occur with sharp play (although you do give up the bishop pair, Black also gave up his right to castle).
Related: Very Aggressive Openings
I wanted to have this as a surprise weapon with black, but was very disappointed even with immediate d4. Plus after Nxf7 black is on the edge of losing in the Kf1 line as was played in some correspondence games. And it is by far not clear what problems white has in Bxf7+. So for me this looks more like a rapid/blitz attempt. But for players who like mess and ...