The Budapest Gambit, 1.d4 Nf6 2.c4 e5, is a different beast from the Vienna Gambit. First of all it's a weapon from Black's arsenal. It's an interesting side-tracking device for Black which can be used to counter or even discourage the Queen's Gambit. When you see White start with 1.d4, very often you can expect to see the Queen's Gambit. If you play something like 1...d5 it's not quite inevitable but very likely.
If you don't like playing the Black side of the Queen's Gambit you can begin instead with 1...Nf6 which is practically a waiting move. You can transpose into just about anything from there so you're keeping your options open. White may abandon his Queen's Gambit plans, he's more likely to do so in the face of 1...Nf6. But if he presses ahead undeterred and plays 2.c4 anyway you then have the opportunity to play 2...e5, entering the Budapest. This gambit takes up two ECO entries, BG Declined (A51) and BG Accepted (A52).
The earliest known deployment of this gambit took place in 1896 in the Adler-Maroczy game, played in Budapest. Maroczy's success went unnoticed as his opponent was not considered particularly strong. The gambit didn't manage to gain traction. However some of the local Hungarian masters who either saw the game or heard about it began to work on the gambit, developing theory on it. Guys like Istvan Abonyi, Zsigmond Barasz and Gyula Breyer established the themes and concepts of the gambit and strengthened the lines.
In 1918, 22 years after it's original appearance, the gambit claimed it's first major scalp. The Austrian- Hungarian master, Milan Vidmar of Ljubljana, now the capital of Slovenia, was due to play with Black against the brilliant Polish master, Akiba Rubinstein. He needed a novelty to crack the armor of the Pole. He was pondering what to do with his pal Abonyi. His friend suggested the Budapest and showed Vidmar how to play it. Vidmar went out the next day and recorded a crushing victory over Rubinstein. The Budapest Gambit had arrived and enjoyed it's Golden Age in high level chess for 10-15 years before fading away again.
The Budapest Gambit is probably not objectively strong enough to withstand the stress of top level championship chess. It is however more than a viable option for the amateur playing blitz online or OTB on the local scene. It's true that you can only play it if White allows you to. But these Queen's Gambit players are determined and may sometimes play 2.c4 anyway. Yes even if you play your king's knight instead of the queen's pawn on your opening move. It will never be one of your main weapons but it's an interesting sideline if you have the time and inclination to study it.
Remember those 1.d4 players are more than likely looking for a safe and sure positional game. When you get guys like that it never hurts to complicate things a bit. Take a look at the Budapest G Analysis using Fritz. Although the samples are small Black has a fair record in many of the lines played out in these games. Because the Budapest is not a widely used opening, there is not a plethora of famous games. There is one however, the first in the following series of five, the Vidmar-Rubinstein clash. The other four while not famous are certainly interesting and entertaining Budapest games.
The Budapest is a fine supplementary weapon to have in your locker. There are plenty of opportunities for White to trip himself up and even with best play from White, Black while standing not quite as strong, can still salvage a playable position.
Some of the fancier traps include the Kieninger Trap when Black leaves a bishop hanging as bait. His knight is ready to pounce with a Smothered Mate should the bait be taken. The remarkably flat Black pawn formation in some lines allow for the possibility of a rook lift with the queen's rook coming to a6 before sliding right across to h6 mounting a huge threat on the White king's position.
Blitz chess is fun when you mix it up with a variety of ideas like the Budapest. Another good sideline to consider for casual online chess would be the Belgrade Gambit.
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