Budapest Gambit

The Budapest Gambit appears after White has advanced the queen pawn and c-pawn, Black has developed the knight that starts next to the king, and Black then advances the e-pawn to e5. White can capture that pawn. A gambit is a deliberate offer of material, usually a pawn, in return for activity or another advantage. Black's point is that accepting the offer displaces White's queen pawn and gives Black developing moves that attack the pawn now sitting on e5.

In the main continuation, Black's knight jumps to g4 and attacks the e5-pawn. Black often combines that pressure with rapid bishop development and frequently wins the pawn back. The Budapest therefore does not always aim to remain a pawn down for the whole game. The initial sacrifice buys time, activity, and disruption of White's center.

The Budapest trades a pawn for development with threats

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...e5 tries to deflect White's d4-pawn so the time spent capturing can be converted into active development.

...e5 offers the central pawn

Black attacks d4 before occupying the center with the d-pawn and accepts that White may capture.

1. ...e5 tries to deflect White's d4-pawn so the time spent capturing can be converted into active development.

White does not need to cling to the extra pawn at any cost. The priorities are completing development, stopping concrete threats, and keeping a healthy center. If Black regains the pawn without extracting further concessions, the position can settle down; if White spends too many moves defending material, Black's initiative, the ability to create threats that demand answers, can become the more important factor.