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I don't know whether 5.Nc3 is best, but I don't like it. The resulting pawn formation is similar to the Spanish exchange with color reversed. The difference is that, in the Spanish exchange, in return for the damaged pawn structure, Black receives a compensation which is the possession of two bishops and open center. In this particular game, White does not receive a similar benefit. So I think 5.Nc3 is inferior.
Tell it to Anand
Top players play all kinds of sub-optimal moves. Their purpose is to avoid the opponent's preparation. Just because Anand plays it, it doesn't mean that the move is the best.
I whole-heartedly agree with you.
To make this a peaceful conversation: 5.d4 and 5.Nc3 both do not lead to a white win, objectively speaking (if both sides play correctly, the game ends in a draw; I guess this is at least the opinion of the majority of GMs).
The question which one of the two moves raises more positional problems for Black is - from this point of view - less important.
On the other hand, even if my impression that 5.d4 is 'better' would be a valid statement , it is perhaps not true from the practical point of view:
The defense tools against 5.d4 have been demonstrated in many games of the leading world players, who play often the Petroff with both colours.
I dare to say this is not true for me.
I meant that I have no fear to play with Black against the plan with Nc3.
The Petroff does appear to mostly be a draw. I had just been studying it, but I forgot about the queenside castling. If I were to castle queenside, the doubled c pawns would be an advantage in the middle game because it would add protection to the king. Also, 3. Nxe5 is main line Petroff, so I'm not sure what that is about.