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Why play French rather than Caro-Kann (as Black)?

1. e4 e6 seems kind of similar to 1. e4 c6.

Both are solid openings, lead to more positional games etc. In the French, however, Black's light square Bishop gets blocked and as I understand it, it's a thematic problem in this opening. One can try and trade it off on a6 etc., but there's no guarantee it will work.

Meanwhile in Caro-Kann it's quite easy to let the light square Bishop out of the pawn chain and only close it with e6 afterwards. This is where Caro-Kann clearly seems more convenient, even though they can lead to similar positions otherwise (or am I wrong).

My question is, why would someone play French rather than Caro-Kann? What are the benefits of 1...e6 that 1...c6 misses?

Thanks for any insights
In the Advance Variation of the Caro-Kann (1. e4 c6 2. d4 d5 3. e5), black cannot play the c5 break as easily as he can in the French:
First of all, because black played c6 on move 1, playing c5 later will cost him 1 tempo. And secondly, as long as black hasn't played e6 yet, white can answer an early c5 (e. g. 3. ... c5!?) with dxc5 and black cannot immediately recapture the pawn.

Also note that if black chooses to develop the queen's bishop to, say, f5 before playing e6, this bishop could eventually become a target - white can try to harass it with early g4 & h4 advances. (And developing this bishop early also leaves b7 weak.)

In the French Advance (1. e4 e6 2. d4 d5 3. e5), it is much easier for black to get quick counterplay against white's center, with the natural move 3. ... c5, usually followed by Nc6 and possibly Qb6. Which is why the Advance Variation is not as popular against the French as it is against the Caro.
For me it's mostly about specifics.

One thing that's nice about the French is that most positions are idiomatic if black wants them to be. Tarrasch, classical, advance - they're all thematically very similar. For other things like the Winawer it's black's decision whether or not to allow the insanity. And all these variations are also mutually dangerous. If white plays even a little bit sloppy he can get into losing positions surprisingly fast - of course so can black.

In the Caro Kann by contrast black has to be prepared for a very wide range of concrete ideas that all have very different and very nuanced handling. The advance variation and the Panov-Botvinnik couldn't be more different, yet they're both dangerous and complex ideas that black needs to be able to handle. And then there are a wide array of slower attacking ideas like the exchange variation with h3. When/if/how black should play g6/Bf5 there and all these other complexities are enough to make your head explode in that variation alone. And that's just a part of the attacking stuff. Obviously the mainline Capablanca variation type stuff and various other more positional approaches are also putting black under substantial pressure.

I mean this is a serious amount of work! And it's not like white is living on a razor's edge. It's hard for white to go too wrong against the Caro Kann. Even if he does then he's more like to just end up in an insipid position than to end up in real trouble.
Played CaroKann myself for years, and quite successful....but finally dropped it. "OhNoMyPants" described the practical drawbacks: lots of different types of positions, some really dangerous lines you have to know, and quite often you end up with positions without winning chances - esp. against better rated opponents winning gets more or less impossible....Sicilian or Spanish is in the long run the same learning/experience effort with better results.
(Exaggeration 1: CaroKann lives like other inferior defences from the fact that many white don't know it well and fail to make the best of their positions.
Exaggeration 2: look at the database statistics. With French Black gets in any line close to 50% (better than average), while in CaroKann Black mostly gets only 40% (worse then average)).

Some final "chessic thoughts": yes, e6 shuts in the bishop c8. But what is c6 doing? It's extreeemely slow: does nothing to develop the king side, takes the best field from the knight b8, in the main lines with Bf5 this becomes an immediate target,...
c6 "supports the center with a wing pawn", but there is definitely a price to it!
@Vibov, which variations appear similar to you in Fr and Ck? I fail to find some...e.g. advance variations have nothing in common but a white pawn going to e5; exchange variations, "dull draw" in french, fully and interesting play in Ck, ....
@gurkenzug "look at the database statistics. With French Black gets in any line close to 50% (better than average), while in CaroKann Black mostly gets only 40% (worse then average))."

10% difference, thats indeed an Exaggeration ;)

my database statistic says:
French, 2...d5 (300 000 games):
+39%/=30%/-31%

Caro Kann, 2...d5 (150 000 games):
+38%/=32%/-30%

So Caro Kann has a slightly higher drawing rate. If you go into lines, go into the lines i play with white. You will see, that the best case is that that statistic does not change :) Edit: i should correct me: the best case is that it goes to fifty fifty. Edit two: also, the best lines often just have not been played yet.

For the records:
Sicilian, 1...c5 (1 100 000 games) (scores best):
+37%/=28%/-35%

Modern, 1...g6 (80 000 games) (scores second best):
+38%/=27%/-35%

Open Games, 1...e5 (650 000 games) (score not very impressive):
+42%/=28%/-30%
@selfmateman
Indeed, the overall objective numbers are like that. My database gives the same results :-)

Interesting....the "50-40" holds true for my games, which i re-checked. Here the white's more often had an edge in the CK compared to my FR attempts.
Probably related to my style or the particular (main-) lines i played: in my CK positions finally reached after a few "out of book moves" white often had a wider choice of good moves/plans, while in FR they more often landed in situations with limited good options (and of course misplaying more often then).
Seems i was correct only on a *very* personal basis ;-)
That's why, answering to french, I've been trying something like this: 1. e4 e6 2. d4 d5 and then simply 3. exd5 and no "french positions". I don't know if that's a good strategy... french defense is so hard to play, oh my god.
@gabrr82 #8 play it with black and see what happens :)

Remember Petrosian: "if i look at it with white, its even, if i look at it with black its advantage."
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