Two Knights Defence 5...Nxd5!

You are all victims of a massive fraud. In the Two Knights Defence, a recapture on d5 does not lose. It only results in the doubling of your pawns. Other defences for black lose a pawn for insufficient compensation. Nxd5 is therefore the BEST move. The Fried Liver is unsound

Someone played Be6 against me when he didn't know the Lolli Attack

Hmm, not sure if you are ignorant or trolling.  As someone who plays the Italian game, I encounter this line a lot, and I dislike the Na5 variations.  Black has a lot more initiative and compensation than you claim, with h6 and e5 coming.  And your "refutation" of the Fried Liver is ridiculous, with 9. a6! giving black a lot of problems, and a difficult defence.  Put simply, I feel I have better chances with the Fried Liver, than I do against the Na5 lines.

a6 is impossible, and a3 allows Nxc2. Surprising that a 1773 thinks that pawns can move 4 squares at a time

Sorry, I meant a3 (though a6 would give problems!).  Nxc2+ isn't a problem.  10. Kd1 Nxa1 and despite being well down in material, white has excellent chances.

After which black is losing.

9. a3 is a good move. After 9... Nxc2 10. Kd1 Black can either play 10... Nd4 where the position is pretty equal or 10... Nxa1?! where Black will have to defend against a strong attack.

If you doubt me, look at Game Explorer in this line (and incidentally 5...Na5 is a move much prefered by masters).  I know this doesn't always mean much, but trust me, in this case it does.

Can't look that far, I'm not premium

Kd1 Nd4!

9.a3 is a lemon. Black is winning after 9...Nxc2+ 10.Kd1 Nxa1 11.Nxd5 Qh4!

White has as many as three better moves (9.Qe4, 9.0-0 and 9.Bb3) with compensation for the sacrificed piece (but most probably no advantage at all).

Black is just suffering after 6.d4! Be6 7.Nxe6 fe6 8.0-0 (8.de5 Bb4+!? gives Black some chances) so he has to give up a piece by 6...Nxd4! 7.c3 b5 8.Bxd5 Qxd5 9.f3. He certainly has compensation, but it seems it's not quite enough.

5...Na5! is of course best, when by correct play Black has full compensation for his pawn.

I dont know about 9.a6 but 9.a3?? loses (9.Qe4 is best) after nxc2+ and nxa1 (White wins the rook on a8 but his knight gets trapped on a8, while the a1-knight escapes, as in an old game Roeczak-pfren where I resigned after 23 moves after 9.a3?? . It is even recommended by Alterman and most players don't know that it is losing (I didn't until I asked IM pfren)

However after 9.Qe4(!) white is definitely equal and black has to make a lot of good moves.

Pfren- I know that I have asked you a billion times but can you post the game?

Bxd5 maybe?

LOL- I started my post before pfren's post I did not know that he posted

pfren, seems like you're here when we wnt you to be

Kd1 nxa1!

Sorry, forgot about that knight on d5, so 10...Nxa1 leaves black a rook up

9.a3?? isthe problem

it is hilarious that 3 intermediate (like me) players (Scottrf, RigasUT, 06-jwagg) dont know that 9.a3?? is a blunder. I feel like a GM now :D

Roeczak refers to that game (not really a game, since all Black moves were cooked long before...)

White has no real improvements- he must enter that ending which is just lost with correct play.

and thats why 9.a3 is bad