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The Slav Defense: Chameleon Variation (help)

This situation occured in one of my recent games when I was trying out this defense as black:

1. d4 ... d5
2. c4 ... c6
3. Nc3 ... Nf6
4. Nf3 ... a6
5. Bg5 ... dxc4
6. e3 ... b5
7. a4 ... e6
8. axb5 ... cxb5 exactly the pawn structure that I was looking for.
9. Nxb5

And I couldnt take the night because of the hanging rook.

When I analised it later it turned out that I had the advantage and had to let him take my rook (9...axb5 10.Rxa8), but I just couldnt see why since a few moves later I was still down an exchange.

Can you guys help me? (I sorry for not posting the board with the game, I dont know how to do that)

Thanks

After bishop 10.. b4 11.knight d2 11...Bishop b7 12.Rook a1, maybe e5, and white is standing difficult. Stockfish wants break the lock with 13.Bishop takes c4. Black has more space for his pieces, the bishop pair and the Dynamik pawn duo. And last but not least the better piece Koordination.Thanks L Fernandez for this interesting Opening, and good luck by playing this move order next time.( By the way, 11.King e2 is also playable) P.S.Sorry for my bad english.
Here is a game that transposes into our variation of interest.


After 9.Nxb5 axb5 10.Rxa8 Bb4+ 11.Nd2 Bb7 12.Ra1 e5, Black has more than enough compensation for the exchange, as is shown by the three main lines that stem from this variation :

1) 13.Be2 Qd5 (in the game Black plays exd4?!) 14.Bf3 e4 (14.f3? exd4 and d3-+) 15.Bxf6 exf3 16.Qxf3 gxf6 (16.Bxg7? fxg2 and Black is even better) 17.Ke2 f5 and after a queen trade, Black's bishop pair dominates a rook and a pawn, as is almost always the case (two bishops are even stronger than a rook and two pawns in at least 50% of the cases).

2) 13.dxe5 Bxd2+ 14.Qxd2 Qxd2+ 15.Kxd2 Ne4+ 16.Kc2 Nxg5 and Black has two knights against a rook and a pawn, that's enough to hold the balance but not more. Therefore, against 13.dxe5, Black is tempted to look into the third line, which is more ambitious.

3) 13.dxe5 Qd5!? 14.Bxf6 gxf6 15.exf6 Nd7. Right now, Black is an exchange and two pawns down, but White cannot develop anything. Black is threatening to win a piece with Nc5-e4xd2, restoring material equality with a crushing position. Komodo suggests a reasonable line starting with 16.Rc1, but let's first consider Komodo's second and third choices :

3a) 16.Bxc4 bxc4 17.Ra4 Qxg2 18.Rxb4 Qxh1+ 19.Ke2 Qc6 20.Qa4 Qxa4 21.Rxa4 0-0 22.Nxc4 with advantage for Black in the endgame.
3b) 16.Ra7 Nxf6 17.Ke2!? Qd3 18.Ke1 with a clear advantage to Black again.
Both lines are pretty desperate (Ke2 was certainly a computer surprise), so we can safely focus on the main continuation.

3c) 16.Rc1 Rg8 17.Rc3 Qe5 (17.Rg1 Nc5 and Rc3 is necessary anyway) 18.Be2 Bxg2 19.Rg1 Nxf6 20.Bf1 Fxc3 21.bxc3 Bxf1 22.Rxg8 Nxg8 23.Kxf1 Qxc3 and again Black's advantage is clear, but not as big as in 3a or 3b.

It's definitely a line that is difficult to play for both sides. One small slip, and Black has no compensation at all. The Noteboom variation (dxc4 earlier, without a6) is similar and to me, it seems easier to play for Black.
Excellent analysis by @A-Cielbleu, though I disagree with the final conclusion. All given lines offer black an advantage, so this whole defence is much recommended for black rather than the Noteboom variation. In fact it looks like a trap white falls into. White is better adviced not to take 9 Nxb5, exactly the opposite of what the original poster @LFernandes was thinking.
Some improvements:

In #1 7...Bb7! which prevents Nxb5.

Therefore better 6.a4 or 6.e4!?

In #3 3) white can improve with 14.exf6:



This has already been on board up to 19...Nd4 in the corr game Krimbacher - Laube from 2017.
Thanks very much everybody!

@A-Cielbleu thats a really insightful analysis, thats what i was looking for. It is indeed a extremely dangerous and complicated line for black, although, I agree with @tpr

@tpr I knew (because of Stockfish) that black had the advantage there. I just didn't understand why because I'm quite a beginner and being behind in material is still scarry for me.

@pemikan also helpful, thanks for explaining black's advantages (I think you mean 10... Bb4)

@nh78 Thanks for the alternative moves!

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