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Chess Opening Theory/1. e4/1...c6/2. d4/2...d5/3. Nc3/3...dxe4
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Caro-Kann defence B15 Caro-Kann → 3. Nc3
3...dxe4
Black has taken White's e-pawn and denied them the classical two-pawn centre. By taking the pawn, Black frees up the space it controlled and creates new possibilities for their piece development.
4. Nxe4, recapturing the pawn is the natural and most common response, which usually leads to one of three main lines, 4...Bf5, the classical variation, 4...Nd7, the Karpov variation, or 4...Nf6 5. Nxf6+ exf6, the Tartakower variation.
White may choose to gambit the pawn with 4. f3 or 4. Bc4 for a development advantage. White doesn't receive full compensation for the pawn, but the lines can be sharp.
4. f3 is the Rasa-Studier gambit. White offers Black the f-pawn to remove the problematic e-pawn so that they can recapture it by developing a new piece, 4...exf3 5. Nxf3. This leads to positions resembling the Blackmar-Diemer gambit.
4. Bc4 is the Von Hennig gambit, though this comes with the same idea to play f3 and the two gambits usually converge after 4...Nf6 5. f3 exf3 6. Nxf3. If Black declines to take the f-pawn there are other original lines.
Theory table
all 4. Nxe4 Bf5 5. Ng3 Bg6 6. h4 h6 7. Nf3 Nd7 8. h5 Bh7 9. Bd3 Bxd3 10. Qxd3 e6 Caro-Kann defenceleading to the classical variation + 4. ... Nd7 5. Ng5 Ngf6 6. Bd3 e6 7. N1f3 Bd6 8. Qe2 h6 9. Ne4 Nxe4 10. Qxe4 Qc7 Karpov variation + 4. ... Nf6 5. Nxf6+ exf6 6. c3 Bd6 7. Bd3 O-O Tartakower variation + 4. f3 exf3 5. Nxf3 Nf6 6. Bc4 Bf5 7. O-O e6 Rasa-Studier gambit -- 4. Bc4 Nf6 5. f3 exf3 6. Nxf3 Von Hennig gambit(transposes)
References
See also
Caro-Kann