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Qd4 and you lose your e4 pawn, once you block the check qxe2 and youre the one who actually loses castling rights.
why play the exchange variation. there are much more advantageous lines.
The exchange variation followed by d4 can be good. If white can survive the middlegame against blacks 2 bishops, he will win in the endgame, since white will be able to create a pawn majority on the king side, while black won't be able to do the same on the queen side. But again, the middlegame is usually better for black. All in all, it is not a bad opening, but there are more advantageous lines for white.
I think the OP is actually asking how to play the Exchange Variation as black after Nxe5. I second Qd4.
Best for black is 5 ... Qd4, 6Nf3 Qxe4+, 7Qe2 QxQ+, 8KxQ Bf5, 9d3 (as per NimzoRoy) o-o-o -----5... Qg5 and 5 ... Qe7 regain the pawn but not as advantageously.
If Qd4 then 6. Ng4 Qxe5+7. Ne4You won't lose your castling here, but is this really worth it?
5.Ne5? is a mistake. That's why masters don't play it. I only found one game with it in my DB out of 5.5 million games.
Here's a master game in fact Chigorin was ranked #7 in 1900 according to http://www.edochess.ca/players/p388.html 5...Qd4 worked for Chigorin, however I never heard of Hellbach and suspect he was way out of his league here, and playing a 3rd-rate move like 5.Ne5 only made things worse for him.
My line is better. Now if I can only find a way to get back to the 19th century...
Best for black is 5 ... Qd4, 6Nf3 Qxe4+, 7Qe2 QxQ+, 8KxQ Bf5, 9c3 o-o-o -----5... Qg5 and 5 ... Qe7 regain the pawn but not as advantageously.
9.d3 is better than 9.c3 in your line, because the QN can go to c3 since the KN isn't pinned by 8...Bg4 like Chigorin played. If you were intending c3 and d4 for White that justs reduces the mobility of his QB and increase the mobility of Black's QB. BUT if you worked this line out on your own I'm impressed - you had the same overall plan as Chigorin inc ...0-0-0 but excluding 8...Bg4
12/10/2013 - Easterwood-Williams 2004
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