I keep losing at my chess club to the Bishop's Opening:
[FEN ""] 1. e4 e5 2. Bc4
I have no idea what to play after that, any help?
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The Bishop's Opening often transposes to the Italian, so black's response depends on which line he wants to play after 1.e4 e5 2.Nf3 Nc6 3.Bc4: 3....Bc5 or 3....Nf6. The former allows the Evans Gambit (4.b4), while in case of the latter, black should be ready for 4.Ng5.
According to the GameDatabase of ChessTempo, after 1.e4 e5 2.Bc4, the most popular responses are 2....Nf6, 2....Nc6 and 2....Bc5.
The most popular and probably the most aggressive move is 2....Nf6. Now, white's main options are
If black wants to play 3....Bc5 against the Italian, then 2....Bc5 against the Bishop's Opening is definitely an option. However, white has the option transpose to the King's Gambit with 3.f4.
If black doesn't want to bother with all the possible transpositions, then he can consider 2....Nc6.
[StartPly "3"] [FEN ""] 1.e4 e5 2.Bc4 (2.Nf3 Nc6 3.Bc4 Bc5 (3...Nf6 4.Ng5) 4.b4) Nf6 (2...Nc6) (2...Bc5 3.f4) 3.d3 (3.d4 exd4 4.Nf3 Nc6 (4...Nxe4)(4...d5)(4...Bb4+)) (3.Nc3 Nc6 (3...Nxe4)) Nc6 (3...c6 4.Nf3 d5) 4.Nf3
I have played this in the past, and always had trouble with the following line:
[FEN ""] 1. e4 e5 2. Bc4 Nf6 3. d3 c6 4. Nc3 d5
You can also play Bc5 on move 2, to prevent the Urusov Gambit, 3. d4, and likely transpose either into the Italian Game, or white may continue as above into a King's Gambit Declined setup.
You can go and convert it into a Giuoco Piano chess opening with the moves:
[FEN ""] 1. e4 e5 2. Bc4 Bc5 3. Nf3 Nc6
Now you have transposed into a regular opening line and can carry forward from there.