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Recently I (rated ~1900 "classical" on Lichess) played the following opening: 1.d4 Nf6 2.Bf4 g6 3.e3 Bg7 4.Nf3 O-O 5.Nbd2 d6 6.c4

[FEN "rnbq1rk1/ppp1ppbp/3p1np1/8/2PP1B2/4PN2/PP1N1PPP/R2QKB1R w KQ - 0 6"]

Upon playing c4, the stockfish analysis goes from a score of 0 to a whopping -1.1, as if I've already blundered a pawn. I've noticed this in a lot of my games - when black avoids developing his queenside and putting pawns in the center, I'm tempted to play c4, planning Nc3, castling kingside, taking up space on the queenside and if black is passive, perhaps pushing for a central pawn break with c5. But in these situations stockfish usually strongly dislikes c4.

Why? Stockfish's response is usually suggesting black play c5 pretty quickly, but this allows d5 giving me a lot of kingside space instead, and I can imagine a nice eventual pawn break with e5. I'm perhaps not at a level where I should be focusing on the opening so much, but I feel like I'm missing a big strategic idea here.

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It may be to the fact that you are making his bad Bishop into a Monster. After 6...c5, 7. d5 Nh5! and the dark square bishop is free to roam.

[FEN "rnbq1rk1/pp2ppbp/3p2p1/2pP3n/2P2B2/4PN2/PP1N1PPP/R2QKB1R w KQ - 1 8"]
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    That's not the main reason. In the diagram you posted Black wins the b2-pawn or gets to play ...Nxf4.
    – Inertial Ignorance
    May 31, 2019 at 22:11
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    @InertialIgnorance The Main Reason is because the dark square Bishop has the a1-h8 diagonal at its disposal (the main drawback of playing the KID is gone in this position!) Which allows winning the b2 pawn once White decides what to do about his Dark square bishop.
    – gtgaxiola
    May 31, 2019 at 22:15
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    The bishop having access to the long diagonal is not a sufficient reason for the winning the pawn on its own. In the Benoni the bishop enjoys this throughout the whole game. Black wins a pawn in the diagram because of a specific tactic involving White's f4-bishop and the loose pawn.
    – Inertial Ignorance
    May 31, 2019 at 22:25
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If you want to play c4 against the King's Indian, it's better to go "all in" by having your e-pawn on e4 (so playing a main line against the KID). With the pawn on e3 you're sort of dipping your toe in the water with c4. It's not nearly as effective.

There's also an important tactical reason for why c4 is bad (probably why Stockfish gave -1). After 6...c5, if you push 7.d5 then Black has 7...Nh5, attacking your f4-bishop and the hanging b2-pawn. You'll have to give up the pawn or settle for Black playing ...Nxf4 and giving you doubled pawns. You could avoid pushing d5 but then after ...Nh5 (again) your d-pawn is under heavy fire since it doesn't have any support from your c-pawn.

If your c-pawn were on c3 then the d4-pawn would have more support, and there would never be any issues with the b2-pawn hanging.

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    It is actually very reasonable to play against the KID with c4, Bf4 and e3 but then White needs her knight on c3, while in the line of the OP it is already committed to d2, where it is passive and interferes with protection of d4 along the file.
    – Evargalo
    Jun 1, 2019 at 6:55
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I don't think the problem is with any c4 in this type of position altogether. I think that if you go for a line like 5.c4 and 6.Nc3 your position is just OK.

The particular position you post is maybe a different story as the knight is a bit misplaced on d2 (this leaves the d4 pawn a bit exposed. Many of the moves suggested are right, and exploit this fact in one way or another.

I am surprised, however, by how much the chess community has changed! In both responses, the writers believed the engine's evaluation and tried to justify it. I'd rather think Stockfish is exaggerating here! For how long have you let it think? (Please beware of the use of computer analysis in the opening. When no tactics are involved, it can be quite misleading!) If we trusted machines for the opening, we would be playing 1.Nc3 all the time. But how many games have you seen with that move?

The line with 6...c5 pointed out by @Inertial_Ignorance is strong, but I don't think Black is more than slightly better after 7.d5 Nh5 8. Qb3 Nxf4 9.exf4. By the way, you can also just play 7.Nb3 or 7.bxc5 instead continuing your development with a reasonable position.

One (correct) argument is that the sequence is bad as a whole as you'll never get anything more than equality, but I don't see any other way to play that leads to an advantage for White, with or without c4. With correct play, you will reach an equal position that is (maybe) a little more comfortable for Black

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