The Hungarian Defense is a variant of the Italian Game, a very rich opening system.
Those two conditions make 3… Be7 worth considering, at the very least. But this move also gives White some choice in the next move.
4. c3: Trying To Get The c3-d4 Pawn Center
In the Open games in general, and in the Italian game in particular, White is often trying to achieve a strong d4-e4 pawn center.
To be honest, we know that in those positions similar to the Philidor defense, Black’s issues are not solved once Black has played exd4, so there is still a lot to play for here, as we will see later.
But again, maybe White wants to get the c3-d4-e4 center. Is that possible ?
So here is what happens in a nutshell: White is forced to play d3 soon and we come back to a sort of Giuoco Pianissimo usually arising after the Two Knights defense. Here White’s advantage is very small albeit real. Hence, the move 4. c3 does not help White to build a strong pawn center.
Playing 4. O-O
As 4. c3 does not completely work to establish a strong pawn center, White often tries something else. Castling short is another attempt for White to claim an advantage. This is indeed probably better.
Then after Nf6 , if White wants to protects the pawn, d2-d3 has to be played and you come back to the same sort of Giuoco Pianissimo arising after the Two Knights defense. Good, but maybe you can get better.
So, probably, O-O followed by d2-d4 is a good way to play against the Hungarian defense. But then, why not play d4 before Black gets the opportunity to attack the center with 4. Nf6 ?
4. d4: the Main Move in the Hungarian Defense !
We have seen that c2-c3 and O-O transpose to some lines of the Italian game in which White only has a small plus. So, let’s see now the strongest reply for White.
Black Protects the Pawn with d7-d6
Here, there is no forced win for White. But this endgame is clearly better for White. So you should really choose this variation with White if you are looking for a safe and long-lasting advantage.
This variation is better for Black here than in the Scotch game (where it was losing !)
Be careful with Black ! The previous line shows that you can quickly get into trouble after just one inaccuracy.
So dxe5 is the first possibility to play this position with White, it gives a favorable endgame. However, if White wants a sharper position, there is another way to play this position.