3...Nd4? is a bad move. You play an already developed piece a second time. If they fall into the trap 4 Nxe5? you get a free win from which you learn nothing, but if they do not fall into your trap and play 4 Nxd4 or 4 c3 or 4 O-O then black is in a bad position.
Much better are 3...Nf6 or 3...Bc5.
How to play against Italian game as black

Hi.
Today we are going to learn how to play against Italian game as black 🖤
1.What is Italian game ?
This is Italian gameÂ
2. How to play against this opening as black 🖤
In this case they didn't fall in our trap.
If they capture our pawn then they will fall in our trap
Let see how
You know how to play against Italian game
But what if they capture our rook ♜
Let's see how
This is the problem when your opponent capture our ♜ rook
Now you are ready to play against Italian game as black
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Next: English opening as white
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If Black wants an alternative to the well known 3. ... Nf6 or 3. ... Bc5, then he can just play the Hungarian defense. 3. ... Be7 (preventing 4. Ng5).

Jobava plays it as Black.
You've heard of the Jobava London, yes? That guy.
Areshchenko vs Jobava (2017) TCh-ESP Div Honor 2017 (365chess.com)

3...Nd4? is a bad move. You play an already developed piece a second time. If they fall into the trap 4 Nxe5? you get a free win from which you learn nothing, but if they do not fall into your trap and play 4 Nxd4 or 4 c3 or 4 O-O then black is in a bad position.
Much better are 3...Nf6 or 3...Bc5.
4.Nxe5? is bad of course, but not losing.
White gets back the piece after an eventual d4-d5, but he will be a pawn down and his compensation (some advantage in development) is probably not enough. Still, it's a game.

i recommend 3.d6 agaisnt the italian if you want to avoid well known territory. The lines can actually get quite unique.
after 3.bc4 d6!? here is how i play it
4.d4 is met with exd4, 5.nxd4 g6
4.c3 f5!? is a sound an agressive line and believe it or not, after 5.d3 qf6 intending f4-f5 with an early pawn storm is sound. c3 took away the square for the queen knight so no nd5 to worry about
4.0-0 bg4, and black will play nf6, be7 qd7 and castle either side.
4.nc3 na5!? if 5.be2, c5! as the c3 knight blocks c3-d4, if 5.bb5+ c6 and either b5 if ba4 or transpose with be2, c5.
4.d3 na5 and win bishop pair.
Hi.
Today we are going to learn how to play against Italian game as black 🖤
1.What is Italian game ?
This is Italian game
2. How to play against this opening as black 🖤
In this case they didn't fall in our trap.
If they capture our pawn then they will fall in our trap
Let see how
You know how to play against Italian game
But what if they capture our rook ♜
Let's see how
This is the problem when your opponent capture our ♜ rook
Now you are ready to play against Italian game as black
For more openings like these please Click here to join our club
Thank you
Next: English opening as white