The Budapest Defense, sometimes called the Budapest Gambit, was first played in 1896, but has never found favor among the world's top players. It is rather easy to play against by white players who have some idea of what they are doing.
My approach has been to not try to hang onto the gambit pawn, but to play for development, and pressure on the d-file. A game I played today on chessbase illustrates this theme. It began 1 d4 Nf6 2 c4 e5?! 3 de Ng4 A trappy line is 3...Ne4, but if white knows to simply play 4 a3, it comes to nothing. I rarely, if ever, face 3...Ne4. White's moves with his king's knight in the Budapest violate basic principles against moving the same piece twice in the opening. The trick for white is to be patient and not try to capitalize violently on this violation on black's part.
4 Nf3 White can also play 4 Bf4, 4 e3, or 4 e4, all of which score in the 60%+ range.
4...Bc5 5 e3 Nc6 6 Be2 0-0 7 0-0 Nxe5 8 NxN NxN 9 Nd2 9 Nc3 is the overwhelming favorite here, but I like the d2 square, preparing to go to f3 and oppose the black knight on e5.
9...a5 10 b3 Ra6 This "rook lift" is actually a major idea in the Budapest, although I wasn't really familiar with it before this game.
11 Bb2 Qe7 12 Nf3 NxN+ 13 BxN Rg6 14 Qe2 d6 15 Rfd1 Qh4 16 g3 Qh3 17 Bg2 Qf5 18 Rd5 Qe6 19 Rh5 Rh6 20 Bh3! I offer black a rook and bishop for his queen, an offer which he wisely declines.
20...Qg6 21 RxR QxR 22BxB RxB 23 Qd4 Rg8 24 Rd1 Bxe3? Black, unable to realize anything from his king-side pressure, unwisely sacs his bishop for two pawns. Patience is the virtue he lacks.
25 fe Qxe3+ 26 Kh1 g6 27 Qd4 27 Bd4 was objectively better, but I choose to simplify into an easily won endgame.
27...Qf3+ 28 Kg1 f6 29 Rf1 1-0 In a position in which white has complete control of the board, black ran out of time.
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