1.d4 Nf6 2.c4 e5 is the Budapest gambit. Black takes a side-line by sacrificing a pawn temporarily and avoids almost all mainline set-ups that occur in the queen’s pawn opening.
White is almost forced to accept the gambit because as we will see later on, other moves don’t make much sense. The main goes 3.dxe5 Ng4 4.Nf3 Nc6 and here white can play either 5.Bf4 or a quiet move 5.e3.
White plays 5.Bf4
After 5.Bf4, white is threatening to play h3 and kick the black knight away. Therefore black has to keep putting pressure on the e5 pawn. Black plays 5…Bb4+ 6.Nbd2 Qe7. And now white has no way to defend the e5 pawn, therefore the e5 pawn has to be given up.After 7.a3 black plays 7…Ngxe5 setting a nice trap.
White can’t take the bishop with 8.axb4 because of Nd3#. So after 8.Nxe5 Nxe5 9.e3 Bxd2 10.Qxd2 d6 we reach the position below.
White has slight advantage because of his two bishops and slightly open position. But this advantage is very minimal and very hard to convert because black’s position is solid without any weaknesses.
Instead of 6.Nbd2, white can also play 6.Nc3, with an attempt to keep his extra pawn after 6…Qe7 7.Qd5
Black cannot regain the pawn in this line, but gets a really good compensation after 7…Bxc3+ 8.bxc3 f6 9.exf6 Nxf6.
The game can go for example: 10.Qd3 d6 11.g3 0-0 12.Bg2 Bg4 13.0-0 Rae8 14.Re1
And black has good compensation for the extra pawn which are doubled at the moment. The open e and f file combined with well placed minor pieces make it hard for white to expand his forces. But for the long term, white obviously keeps an advantage of two bishops and extra pawn.
White plays 5.e3
Another alternative is to play 5.e3, giving back the pawn immediately. After 5…Ngxe4 6.Be2 Bc5 7.Nc3 0-0 8.0-0 d6 the game is almost equal.
White will play b3-Bb2 and try to either expland on queenside with a3-b4 or simply occupy d5 square with Nd5 and complete this development. Black is fine with no immediate danger here. Therefore if white is looking for advantage, 5.Bf4 is a much better choice.
White plays 4.e4
Instead of defending the e5 pawn, white can focus on his fast development with 4.e4. After 4…Ngxe4 5.f4 Nc6 6.Be3 Bb4+ 7.Nbd2 Qe7 8.Bd3 Na6 we reach the position below.
White has a strong center but it is coming under fire soon as black plays …Nc5. For example after 9.Nf3 Nc5, black is already threatening to take on e4 and white has a difficult time coordinating his pieces.
Black plays 3…Ne4
Another line for black is to play 3…Ne4, but in this line black doesn’t regain the pawn. In fact, it doesn’t make much sense to play Ne4 here. After 4.Nf3 Bb4+ 5.Nbd2 Nc6 6.a3 Bxd2 7.Bxd2 Nxd2 8.Qxd2 Qe7 9.Qc3 b6 10.e3 Bb7 11.Be2 0-0-0 12 0-0-0 g5
Black is trying to put pressure on the e5 pawn with the idea of playing …g5-g4, kicking away the defender knight. However, in this position white is just a pawn up and black’s compensation doesn’t seem to be enough.
Therefore 3…Ng4 is much better.
Budapest gambit declined
If white declines the pawn sacrifice, black is very happy because he got the …e5 break early in the opening without much hassle. For example after 3.d5 Bc5 the position is already equal because white has neither initiative, nor better development nor extra control on the center which he may aim to achieve in the opening.
Also after 3.e3 exd4 4.exd4 d5 5.Nc3 Bb4 6.Nf3 0-0 black should be completely alright with the opening outcome.
Game Played with Colle System
Here is classic game played between Aronian, Levon (2809) vs Ivanchuk, Vassily (2757)
It turns out that even though not the most popular opening, the Budapest gambit is a good choice for black to try sometimes because white can only hope to have a minimal positional advantage. There are no sharp lines and black mostly regains the pawn or gets a very strong position as a compensation. The best way for white is to accept the gambit, because by declining the e5 pawn, white gives black equality for nothing.