Chess Opening Theory/1. e4/1...e6/2. Nf3/2...d5/3. e5/3...c5/4. b4/4...cxb4

Now leaving opening theory: This page represents a rare sideline. Before making new pages for following moves, please consider line notability.

Black accepts White's gambit.

White usually continues with the immediate 5. a3, hoping for Black to take the pawn and allowing White some open lines. However, Black doesn't have to take and can simply develop with 5...Nc6 with the idea to recapture on b4 with the dark-squared bishop. This does help White by letting them build up their centre with tempo, so after 6. axb4 Bxb4 7. c3 Be7 8. d4 White gets a space advantage in the centre in exchange for a pawn and allowing Black a passed pawn on the a-file.

Black can choose to take back the a3-pawn too with 5...bxa3. White can simply continue with 6. d4 to build up the centre and delay taking the pawn for now.

White doesn't have to offer up the a3 pawn immediately, they can simply build up the centre with 5. d4. These lines are likely to transpose back into lines with 5. a3.

1. e4 e6 2. Nf3 d5 3. e5 c5 4. b4 cxb4

Wikipedia has related information at French Defence.