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What is Black's best line in the Nimzo-Indian Rubinstein
It depends on what result you want :)
Perhaps the most correct is the Karpov Variation but it tends to be drawish (a result of being correct perhaps).
How about if I want to play for a win?
A quick rundown on the key characteristics of those variations would also be much appreciated.
I play the white side. There are a lot of playable lines for black after e3, I don't think you should think of any one as a "best" line. ...c5 is probably the sharpest. ...d5 could catch the routine Nge2 players unaware since its an infrequently played line, and stumbling along with the N to e2 puts white in a unconfortable position when black follows up with dxc4. I think 0-0 is currently the elite favorite. There are other lines. No one is considered best.
So what you are saying. Give me the lines of the Nimzo Indian ? I suggest you get a book because it is a bit too much for a post :) The following book is very good !
http://www.newinchess.com/The_Strategic_Nimzo_Indian-p-969.html
Look there is also a wikipedia page with the different variations !
https://en.wikipedia.org/wiki/Nimzo-Indian_Defence
I like (as Black) the Karpov, and against 4.e3 0-0 5.Nge2 (recommended in two recent repertoire books by Watson and Schandorff) the rather rare (yet) but excellent 5...c6!?
So what you are saying. Give me the lines of the Nimzo Indian ? I suggest you get a book because it is a bit too much for a post :) The following book is very good !
http://www.newinchess.com/The_Strategic_Nimzo_Indian-p-969.html
Look there is also a wikipedia page with the different variations !
Not "give me the lines" but more "recommend me a line to play"
I like (as Black) the Karpov, and against 4.e3 0-0 5.Nge2 (recommended in two recent repertoire books by Watson and Schandorff) the rather rare (yet) but excellent 5...c6!?
Thanks.
With a system as huge as the Nimzo, you'll nail down something against the Rubinstein only to find everyone plays the Saemisch or the Leningrad or the classical...
It's like the Sicilian of the Q-pawn openings.
I like (as Black) the Karpov, and against 4.e3 0-0 5.Nge2 (recommended in two recent repertoire books by Watson and Schandorff) the rather rare (yet) but excellent 5...c6!?
Could you please post the titles of the books? I have sought them invane over the Internet. Thanks! 
They are 2 books writen from the white perspective of the Nimzo.
Watson: https://www.newinchess.com/A_Strategic_Chess_Opening_Repertoire_for_White-p-7092.html
Schandorff: https://www.newinchess.com/Playing_1_d4___The_Indian_Defences-p-7095.html
As a matter of theory, what is currently the best line for Black in the Nimzo-Indian Rubinstein (4 e3) variation?
I know that there are many playable lines here. Some lines that come to mind are the Karpov Variation, the Huebner Variation, the Tal/Petrosian/Classical Variation, and the Romanishin-Psakhis (spelling?) Variation. There might be others whose name I had forgotten. Just wondering which line is best.