Engine likes gxf6 better by over a half-pawn. Click on the little analysis button on the lower left of the diagram and you can see the numbers yourself.
Take back with the pawn?!

Hey there @sholom90, I've seen some lines in Caro Kann where in fact ...gxf6 is the preferred line. Open file for Rook, etc. Of course the King is a bit drafty, but there are variations like that...

I suspect it's because you're getting anemic on the d7-c6-b5 squares and you don't want to leave them alone, plus the pawn on f6 keeps out a knight on e5 (which again hits those squares).
To test this I had the engine look at the same position except the black pawn is on a6 instead of a7. In that case Qxf6 and gxf are both 0.00
Another test, put the black bishop on c7 instead of f8 (this means the king can quickly castle away from the e8-a4 diagonal), and now Qxf6 is evaluated as slightly better than gxf.

So probably earlier in the game you shouldn't have fallen so far behind in development. It looks like you captured on e4, brining your opponent's bishop there and getting rid of your central pawn. That was probably a mistake.
Actually... it's weird. Looks like black has only made ~5 moves and white has made ~7. Definitely some capturing black shouldn't have been doing... and I have no idea how both queenside knights are gone in that position.
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So... it's not an engine move and it's not a "every Russian schoolboy knows"
It's also probably not a move I'd play in a speed game... because Qxf6 is normally the good move... because normally black hasn't misplayed the opening. In this case it seems black has misplayed things though, so I'd say gxf is damage control. You accept the weakened structure for defensive reasons.

If you take back with the pawn, you can kick the B on f4 on the move, then B from f1 to g6, placing him on the long diagonal.

I think my first instinct would be to take back with the queen, as it would preserve the pawn structure. However, the potential to drive back the from e4 and have it block W Q's defense of the d-pawn seems to outweigh the liabilities.

Thank you for all the constructive comments.
@llama51 -- in case you're wondering how I'm behind in development, here are the first 9 moves of the game (French, Rubinstein, Blackburne)
And, btw, this is awesome:
To test this I had the engine look at the same position except the black pawn is on a6 instead of a7. In that case Qxf6 and gxf are both 0.00
Another test, put the black bishop on c7 instead of f8 (this means the king can quickly castle away from the e8-a4 diagonal), and now Qxf6 is evaluated as slightly better than gxf.
I really appreciate you doing this, and for exposing me a whole new way to evaluate positions, I'd never thought of that before.
@NervesofButter -- also great stuff. Thanks. I appreciate the diagrams.
To both of you -- that's very kind of you to put so much effort into this in order to teach.
Let me also add -- I posted the above Q on twitter and a chess coach wrote back with the following
I prefer ...gxf6 personally. Here's why:
1. Queen feels misplaced on f6. I want her on c7/b6/a5
2. Taking with queen allows him to potentially retain use of the e5 square.
3. ...gxf6 takes control of extra dark squares in the center (esp e5).
4. ...gxf6 opens g-file for rooks.|
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PS: my 1700 daily rating is a total fluke. I have won over 28% of my daily games on time (!!). I still don't understand strategy like this. I'm just pretty decent at tactics when I have 3 days to make a move. My rapid rating is in the mid-1200's, which is probably my "real" strength at this point.

yes, that makes sense. A 5 forces a move, b6 attacks the B-pawn also forcing a move, and on c7 it prepares a battery with the bishop on f3, along with the open g file that puts a lot of pressure on the K-side.

Thank you for all the constructive comments.
@llama51 -- in case you're wondering how I'm behind in development, here are the first 9 moves of the game (French, Rubinstein, Blackburne)
And, btw, this is awesome:
To test this I had the engine look at the same position except the black pawn is on a6 instead of a7. In that case Qxf6 and gxf are both 0.00
Another test, put the black bishop on c7 instead of f8 (this means the king can quickly castle away from the e8-a4 diagonal), and now Qxf6 is evaluated as slightly better than gxf.
I really appreciate you doing this, and for exposing me a whole new way to evaluate positions, I'd never thought of that before.
@NervesofButter -- also great stuff. Thanks. I appreciate the diagrams.
To both of you -- that's very kind of you to put so much effort into this in order to teach.
Let me also add -- I posted the above Q on twitter and a chess coach wrote back with the following
I prefer ...gxf6 personally. Here's why:
1. Queen feels misplaced on f6. I want her on c7/b6/a5
2. Taking with queen allows him to potentially retain use of the e5 square.
3. ...gxf6 takes control of extra dark squares in the center (esp e5).
4. ...gxf6 opens g-file for rooks.|
============
PS: my 1700 daily rating is a total fluke. I have won over 28% of my daily games on time (!!). I still don't understand strategy like this. I'm just pretty decent at tactics when I have 3 days to make a move. My rapid rating is in the mid-1200's, which is probably my "real" strength at this point.
Ah I see. You moved both knights twice. I assume Nxe4 and especially Ndf6 are not book.

Gross, those moves are book.
This is why lesser players shouldn't play these defenses. They let you get far behind in development just because some precise moves afterwards save you from complete collapse. By playing these openings I imagine the players don't develop the proper feeling for how much things like the center and development are worth.
I know this must sound silly coming from me, the person who misjudged the position... but really... gross moves. This is not how to play chess.
Looking with my database + engine... SF says after 8.Bg5 it's essentially an equal position... and the database stats say white scores a disproportionate amount (65-70% depending on the variation)... I'm not surprised.

Gross, those moves are book.
This is why lesser players shouldn't play these defenses. They let you get far behind in development just because some precise moves afterwards save you from complete collapse. By playing these openings I imagine the players don't develop the proper feeling for how much things like the center and development are worth.
I know this must sound silly coming from me, the person who misjudged the position... but really... gross moves. This is not how to play chess.
Looking with my database + engine... SF says after 8.Bg5 it's essentially an equal position... and the database stats say white scores a disproportionate amount (65-70% depending on the variation)... I'm not surprised.
By "these defenses", I presume you don't mean French, but rather just this particular line?
Indeed, it might be time for me to ditch the Rubinstein Variation. I first picked it up because I was just learning the French, and it was a way to simplify my learning -- as you can play it against 3 Nf3 and 2 Ne3. But perhaps now I should graduate into something stronger for black.
Quite fascinating regarding the huge discrepancy between engine eval and actual results (particularly given that the "conventional wisdom" is that engines generally undervalue the French for black).

Yeah, I don't mean every French variation... although there's certainly a lot for someone like me (not even titled) to whine about... but in my defense, even Fischer disrespected the winawer for example, thinking it was fundamentally unsound.
IMO ideally an opening places (and maintains) a pawn in the center or, if not that, has fast and easy development where you can put a pawn in the center during the early middlegame... if you have neither of these... it's just gross to me. The open Sicilian has a lot of these types... where black is just way behind, but the position is compact and solid enough that white can't immediately kill it, so eventually black catches up, and can even have a slightly better position... and that can be exciting chess, anyway I'm rambling. Play whatever you want.

I am really enjoying the study of openings, trying to figure out what something was played, i.e., what it does, and why I can't make the move I want. I have learned a lot about the game. This type of study takes and does not immediately to games.
I have observed, however, that my score is higher for the openings where I spend sufficient study time, ranging from the 30 to 56 in my best prepared opening, for white and 47 for black

The chess.com engine is so weak that 0.5 difference means nothing. And even strong engines are not that reliable in "boring" positions like this.
I think there are some concrete problems with 1...Qxf6. 2.Qd3! now comes with much more sting as Bxb7 becomes a threat. ...a6 is essentially forced but Black loses even more time.
1...gxf6, as ugly as it looks, allows the black queen to remain closer to the black king and defend the king better. Although detrimental to the pawn structure, in fact it is actually safe to castle kingside in many of these French positions where you snap on e4 (with the doubled f-pawns).

What confuses me, however, is that I can be easily convinced (with what folks are explaining here) that gxf6 is better . . . but then I go look at other positions that *seem* similar, but gxf6 is not a very good move. So, how I need to go back and see how I can distinguish them. (This stuff can be hard for me . . . )

What confuses me, however, is that I can be easily convinced (with what folks are explaining here) that gxf6 is better . . . but then I go look at other positions that *seem* similar, but gxf6 is not a very good move. So, how I need to go back and see how I can distinguish them. (This stuff can be hard for me . . . )
The temptation is to think of every position as having some lesson or insight that you can generalize to understand a large class of positions... but that isn't always true. Some positions are too specific.
IMO this position is like that. You already know the key general idea (which is that Qxf6 is better in most positions). The lesson of this position is this is an exception to the rule. Don't try to morph this exception into another rule so to speak... is my advice anyway.
Maybe the "rule" (so to speak) you can learn from it is that doubled pawns aren't as weak as you thought. Maybe you could look at the position from white's side and try to find ways to attack black's kingside. The lesson is some things are optically weak, but ultimately if you can't bring pieces against the weak pawns/squares/diagonals/files then the weaknesses are an illusion.
In other words it can help you be more open minded about accepting a damaged structure for the right reasons without trying to create a lesson about the specific move gxf6.

@Sholom90 -- it all depends on the position. One slight difference in a piece placement can make the difference. So, how can you figure out what to play what when? My suggestion is that you take all the similar positions and line them up. Index cards are best, so you can shuffle and sort them, positive on one side, negative on the other.
Now study each stack? How are the positions similar or different? Assess both the attacking and defensive potentials. Write down any ideas you get. Compare the results for both stacks; are there any patterns. Draw your conclusions. Also, consider how comfortable you would be in each position. Do you know how to play from that position, or are you lost? If you are lost in a better position, and the difference in computer score is minor, go with the one you feel more comfortable with. Playing something you do not understand easily leads to a blunder, and you find that you are -3 instead of -.5.
Can someone help me?
White just took my knight, Bxf6. I naturally took back Qxf6. Engine says that gxf6 is 0.5 better. What?! Is this an "engine line"? Or an "IM/GM line"? (or "every Russian schoolboy knows"?) And, at my level (rapid mid-1200's) is this something that I should even worry about?