I'd absolutely play 4. d4 against that. It's actually stronger than it would be normally, because it hits the bishop. The d4 pawn is supported 3 times and attacked 3 times, so it's safe. After the pretty much forced pawn trade on d4, white has a strong center with dual pawns, which is exactly the point of this opening, and black has to move his bishop. Bb6 and Bb4+ seem like black's best options, and white has natural development from there ie Nc3 against the check. I'd take the white side of that any day.
ponziani opening
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I was studying the ponziani opening and wondered what the best option for white is if black plays bc5. would the best response be to play d4? thanks in advance