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Some comments below. Corrections from stronger players would be most welcome.
4...Nc6 is suspect, because it blocks the c-pawn, the advance of which (to put pressure on White's center) is usually important in the Nimzo-Indian and many Queen's Pawn openings.
6.Bd3 seems a bit better to me, delaying the development of the dark-squared bishop, since if Black captures on c3, then playing the bishop to a3 might be a better option.
11. dxe5: I like this better than the 11. d5 that was suggested as an improvement, because I think given White's development advantage and more active pieces, he does better to open things up a little, which gives him more opportunity to attack, rather than closing the center and giving Black time to catch up in development.
14. Qe2: it seems better to develop the queen somewhere else and break the pin. White shouldn't be so scared of letting Black capture and double his pawns on the f-file, as Black can't make much of it. The extra pawn on the f-file may be useful to put pressure on the center, and the semi-open g-file provides a nice route for a rook to the black king.
15. e4: this is a positional blunder, as it gives Black the opportunity to dominate the d-file. The d4 square also becomes very weak, and after Black gets rid of the white knight on f3 and the dark-squared bishop, that may become a great outpost square for the black knight, which White will have no way to challenge at all (without any knights or a dark-squared bishop). Lastly, this moves cuts off the diagonal for White's light-squared bishop, which will become an extremely bad piece later in the game and be totally dominated by the black knight.
20...Rxd4: 20...cxd4 seems better, as it secures a protected passed pawn that will be a huge advantage in the endgame. White isn't forced to capture the rook after ...Rxd4, so Black might not get an opportunity to create the passed pawn later.
22. Rxd4: this is a mistake, as it gives Black another opportunity to recapture with ...cxd4, which would have been much superior to the ...Qxd4 that Black actually played.
27. fxe5: another mistake, since after Black captures the e5-pawn, he has much more of an advantage due to White's weak isolated pawn. A better plan than f4 and fxe5 would have been to focus on defense and and aiming for a draw, giving Black the opportunity to overpress and make a mistake if he really wants to fight for a win.
Lastly, White erred in letting the queens get exchanged so easily, as after that, Black has both the superior pawn structure as well as the hugely superior minor piece -- Black's knight runs rings around White's sorry bishop after this in a textbook case of good knight versus bad bishop.
Thank you sapientdust, I agree with you mostly, but what do you suggest in place of 15.e4? consider that 15.g4 is also very dubious...
There are many other moves, because Black's threat of ...e4 isn't yet dangerous. White can play Qc2, which threatens Bxf6 followed by Qxh7# if Black plays ...exf3.
It would have been much better though if White had avoided pinning his queen though by not moving it to e2 in the first place.
I meant that White can play Qc2 on the next move if Black plays ...e4, so White really doesn't have anything to be afraid about yet that would force him to play e4 himself.
Even after 15. Qc2 Bxf3 16. gxf3 though, White is doing fine:
He has the bishop pair in an open game and is slightly better.
But what about the last move? it wins a pawn..
17. Qf5, and if Black plays ...Qxc4, then 18. Bxe5 and Black is much worse than before 16...Qe6.
fair enough, thanxsapientdust
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