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After 1.e4 c5 2.Nf3 d6, White's most important alternative to 3.d4 is 3.Bb5+, known as the Moscow Variation or Canal–Sokolsky Attack. Grandmasters sometimes choose this variation when they wish to avoid theory; for instance, it was played by Garry Kasparov in the online game Kasparov–The World. Experts in this line include GMs Sergei Rublevsky and Tomáš Oral. Former World Champion Magnus Carlsen has also played this variation extensively. Black can block the check with 3...Bd7, 3...Nc6 or 3...Nd7. The position after 3...Nc6 can also be reached via the Rossolimo Variation after 1.e4 c5 2.Nf3 Nc6 3.Bb5 d6.
Most common is 3...Bd7, when after 4.Bxd7+ Qxd7, White can either play 5.0-0 followed by c3 and d4, or 5.c4 in the style of the Maróczy Bind.
Moves: 1. e4 c5 2. Nf3 d6 3. Bb5+
The move Bb5+ is considered an Anti-Sicilian, and is the most commonly seen thereof. White develops his bishop with a tempo, enabling kingside castling, and may seek to develop rapidly along similar lines to the Ruy Lopez in order to meet Black's later attack head-on, or simply to control d5 by playing c4 but, not wishing to have the king's bishop stuck behind the c4 pawn, exchanging it off first. However, Black's own development can carry on unhindered and he tends to get an equal game. This opening gives white a good game.
Black has three replies, assuming no sentient being would block the check with the queen.
3...Nc6 leads to a Lopez-type setup in which Black has already played the useful c5.
This is the Rossolimo variation
3...Nd7 a more defensive variant of the above considered to grant White a minor advantage
3...Bd7 wins a tempo by compelling the exchange of bishops but gives White more options. This is the main option in Chessbase Live Book.
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When you have gained a basic understanding of the lines above we can explore the games games played by GM Magnus Carlsen.