Fork trick in four Knights

In the four knights game after white plays his bishop to C4 the following fork has been recommended to me, by a video on youtube and multiple players.

However it seems to me like the entire knight sacrifice can be refuted after Bxf7, thoughts?

Whoops I meant to write in the first diagram that black supposedly has an edge.

Black has the two bishops and more center pawns.

In my database, White only scores 23.4% from the position in your second diagram (probably black was the better player most of the time as well, but still).

Take it a few moves further, and black looks clearly better:

I was just told in this line by FM Eric_Schiller that the Kg8 is considered a very strong move and that black does end up better.

But what about this move instead...

Right you are, that does look good keyif.

Scarblac you are also right, as I realised when I set up my board and played some lines from that position, black only looks worse but he can easily castle manually and be fine with two bishops.

All the moves in this are uncommon. I doubt that you'll ever see this too much.

I see these lines fairly often, they are a must know if you plan to play the two knights defense.

I see B c4 in the four knights game as black almost every time it is played.

I believe Black is still a tiny bit better after the Bishop is preserved. Black has a It's exposed in the middle of the board. After Bd6 Black will hit it with f5. The Bishop must retreat again or be traded for a knight when the Bishop pair is lost anyway and Black's queenside pawns aren't so bad. Black has more control in the center with pawns on e5 and f5. It's as if Black is playing White with a center like that. Maybe Black is not technically any better at all, but s/he's certainly not any worse anymore. Nxe4 has equalized. I believe this variation is exactly why these moves are uncommon and you won't see Bc4 as often as d4 or Bb5 if your opponent has studied the 4 knights and isn't making it up as s/he goes along. Though there is a dangerous gambit here somewhere. I think it's if if White just castles on move 5. You might see booked up players try to catch you off gaurd in that line.

Well Nxe4 should lead to a small advantage for black but things are not as easy as they seem and black needs to make a few accurate moved to avoid getting a worse position.

An interesting read is: http://www.chesscafe.com/text/abby37.pdf

A nice lesson on a failed fork trick: Fork Trick or Treat

The engine hates this line, by move 8 the score is under -1, IMO white loses too much time and the King on f7 is not in any danger, I might post the suggested line tomorrow after it analyses overnight.

It's an old trick and one that makes Bc4 in the 4 Knights a non-starter.

Did you guys ever consider this is why 4 knights books cover 4.Bb5, 4.d4, and 4.g3, but not 4.Bc4?  It is because the first 3 are superior moves for white.

I play this myself all the time and encounter the second line you showed fairly often.
With correct play black is supposed to be quite a bit better according to the computer.
In practice i find that correct play isn't always easy to find for black and the cost of an inaccuracy is higher for black than for white. 
The idea is to put the king on g8 and play with h6 g5 or sometimes h5, but timing is important and it can get pretty double edged unless you've done your homework, which i never do.

First of all, I recommend the main article on Four Knights Game with 4.Bc4! Nxe4 5.Nxe4! d5 6.Bd3! dxe4 7.Bxe4! Bd6 8.Bxc6+! etc. by Yury V. Bukayev ( https://chessproblem.my-free-games.com/chess/games/ChessArticle.php?art=C55 )! Thus, White gets the advantage after 7...Bd6 8.Bxc6+!, and 7...Ne7 8.c3!, and 7...Nb4 8.a3!, and after other responses (you can find them in this article too). ChessCafe linked it in 2012 (see Abby Marshall's article "The Two Knights Defense, Center Fork Trick": "Pertinent responses").

@pfren everyone knows that, I suggest not to waste your time here in these forums

The only people who ever played this against me were noobs who got clobbered pretty quickly. Often they don't retreat the B to d3 and recapture, they "save" the knight and make me take the B. Their position usually falls apart pretty quickly. I played this at the chess club last night in fact.

Mr. Frendzas, you are a boor. I'll not discuss with boors. Here are my words for polite users: the move 9...e4 can't make Black's pawn structure normal, and the pair of Bishops isn't enough compensation for such pawn structure, you may try to refute these words, but with your enough long variations, please.