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Center Counter Defense
White normally continues 2.exd5 when Black has two major continuations: 2...Qxd5 and 2...Nf6.
After 2...Qxd5 White normally attacks the queen with gain of tempo with 3.Nc3 when 3...Qa5 is most common. (3...Qd8 and 3...Qd6 are also seen, while 3...Qe5+!?, the "Patzer Variation", has recently attracted some interest.) A typical continuation might be 4.d4 Nf6 5.Nf3 Bg4 (or 5...Bf5) 6.h3 Bh5 7.g4 Bg6 8.Ne5, after which White often fianchettos his bishop on g2.
With 2...Nf6, Black delays recapturing the pawn for another move, believing that capturing with the knight rather than the queen will avoid the loss of time inherent in developing the queen so early. White may defend the pawn with 3.c4; now 3...e6 is the relatively little-explored Icelandic Gambit, in which Black gives up a pawn for quick development. 3...c6 is more common; if now 4.dxc6, then Black has sufficient compensation for the pawn after 4...Nxc6, with a development lead. White instead often plays 4.d4, which transposes to the Panov-Botvinnik Attack of the Caro-Kann Defense after 4...cxd5.
Also important is 3.Bb5+, which can lead to very tricky play after, for example, 3...Bd7 4.Bc4 Bg4 (4...b5!? is also an option) 5.f3 Bf5 6.Nc3 Nbd7 7.Qe2 Nb6 8.Bb3 Qd7 9.d6!. In these variations Black generally can't count on regaining the pawn, but can usually get compensation.
Normally after 2...Nf6, however, white does not defend the pawn, but instead plays 3.d4 Nxd5 and then either 4.Nf3, developing normally, or 4.c4, taking a larger piece of the center and attacking the knight. Black can also try 3.d4 Bg4!?, the Portuguese Variation, with play similar to the Icelandic Gambit.
Alternatively, White may avoid all the Center Counter theory and play 2.d4, transposing into the Blackmar-Diemer Gambit.
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