Take with pawn towards the center, or away?

Hey, there are many times in opening positions where your opponent will take your knight with his bishop or knight etc, and when all is said and done you are left with the decision of taking with the pawn toward the center, or away. (e.g. Roy Lopez where the bishop takes the knight, or the position I have shown.) I've heard the general rule is take towards the center but we all know that this is not always best, as is the case with the positions I have mentioned. What are the strategies that go into this?

That guideline of capturing toward the center usually holds, though there exist a few general exceptions of which I'm aware:

(1) In double e-pawn openings (like the one you showed, especially in the Ruy Lopez, Petrov's Defense, and Four Knights Game), the d-file needs to be left open for either player recapturing at QB3, since that gives the queen mobility along that file, which is critical for regaining the e-pawn by tactical means in some variations. In such cases, Black would prefer to play ...dxc6 instead of ...bxc6. A look at a database for such positions will confirm this.

(2) Sometimes in double e-pawn openings (especially in the Four Knights Game), a player wants the b-file open for aiming a rook down that file, especially if all the other files are closed or half-closed. In such games White would prefer to play bxc3 instead of dxc3.

(3) Occasionally (though I can't think of any specific openings or examples offhand), immediately after castling kingside a player wants immediate use of his rook on the f-file for attacking or tactical purposes, whereupon White prefers fxg3 over hxg3.

How did I learn those important exceptions? Sadly, they're rarely mentioned in books, except as a side comment instead of a general principle to know, so I had to figure those out from such book asides and extensive database game perusal.

Take towards the center unless you can open one of your bishops by capturing away from the center.

In your example, you shouldn't take with dxc6 immediately - you should play Qf6 THEN take with dxc6. The idea is that White has to prevent checkmate via Qe2 or Qd2, but then his bishops are blocked in with either move, while Black's development of the bishops has actually accelerated. However, this comes at the expense of White inflicting doubled c-pawns.

      Good question OP from my experience you need an extremely good reason to violate that solid chess principle. like if the capture opens a critical  file against the enemy during your attack  which happens more often than you may think. But generally most of the time it would not be wise to violate this rule !

White is threatening to attack with Queen at h6.
The defence is to shift the e-pawn forward so the queen covers the 7th rank.
In the game h7xg6 was played when it should have been f7xg6.

It really depend from the situation and the opening variation too.

( in this last example somtimes fxg6 is better if a defence form the seventh rank is possible.

For example a rook or Queen can defend h7 from the side. )

In the exchange variation from the Spanish   1.e4 e5 2,Nf3 Nc6 3.Bb5 a6 4.Nxc6 dxc6! is clearly the strongest move. and 5.Nxe5 is not dangerous because of 5...Qd4! and black wins back the pawn.

In the Scotch four knights game after  1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.d4 exd4 5.Nxd4 Bb4 6.Nxc6 bxc6!  is the best because black want to play d5 and occupy the center with his d-pawn. After 7.Bd3 d5 8.exd5 cxd5 9.0-0 0-0 10.Bg5 c6 black is Ok.

After a variation in the Petrov 1.e4 e5 2.Nf3 Nf6 3.Nxe5 d6 4.Nf3 Nxe4 5.Nc3 ( 5.d4 is the mean line ) 5...Nxc3 6.dxc3! is the best. White opens the diagonal for his Queenside bishop and gets an half open d file and will castle long.   In a variation of the reversed Dragon  after 1.c4 e5 2.Nc3 Nf6 3.Nf3 Nc6 4.e3 ( or also 4.g3 )  4...d5 5.cxd5 Nxd5 6.Bb5 Nxc3 7.bxc3! Bd6 8.d4   Of course is also taken towards the center to play d4 and so you can go on.

Sometimes it is even possible both for example in the variation of the Caro Kann  1.e4 c6 2.d4 d5 3.Nd2 dxe4 4.Nxd4 Nf6 5.Nxf6+  and here black can choose between 5...exf6 with is sollid but white has an easy game and the marority of pawns on the queenside so an very nice endgame. Or black can also play 5....gxf6!? with is sharper and black will play for e5 and have Rg8 an open file to play on. More risky and sharper play.

Thanks, Rat1960, for finding a good example where fxg6 is better.