(2) A name given, like most, by Richard Sharp, to a particular group of Austrian opening moves in Spring 1901, all of which share in common the order A Bud-Ser (and usually F Tri-Alb). The name explains it all: a "Gambit" is a move that risks loss in one area for a hopefully better chance of gain elsewhere, in this case the Balkans. It is a commitment by Austria to taking up two centres in the south (Serbia and Greece) and is thus generally regarded as anti-Turkish. There are several variations, mostly involving A Vie, of which the Trieste, Budapest and Galicia versions traditionally account for a significant proportion of Austrian opening moves - indeed, Balkan Gambits are widely regarded as the only "sensible" alternative to the "Southern Hedgehog"). Notice should also be taken of the so called "Houseboat" variation of the Balkan Gambit, in which F Tri- Holds instead of moving to Albania.
The Balkan Gambit is most commonly defined as *any* Austrian opening which includes the moves A Bud-Ser & F Tri-Alb. In the 1960's it was common to see the Budapest variation (A Vie-Bud), an attempt to take three centres. In the early 1970's Italy often opened A Ven-Tri and accordingly the Budapest variation lost favour with the Trieste variation gaining in popularity (A Vie-Tri). The Balkan Gambit is a risky opening: if both Italy and Russia attack Austria in Spring 1901 it is unlikely that Austria will live to tell the tale. A commonly seen variation is the Galician (A Vie-Gal) which offers Austria some defense against most hostile openings. In the 1980's Italy has moved towards opening A Ven-Tyr, A Rom-Ven. Accordingly some Austrian players have used the rarely-seen Tyrolian variant A Vie-Tyr which, if Russia is friendly, gives Austria a strong position provided Italy has opened to Tyr and not Tri. Postal play has, on occasion, seen the Bohemian variant but this has nothing to commend it to Austrian players; even if England/France/Italy & Russia have all agreed to attack Germany. Finally in the early 1970's the A Vie H option attracted support from Don Turnbull, I presume as a result of FTF experience as this opening has not (to my knowledge) been played in a British postal game.
Here the object of distrust is Italy. A Tri can still defend against Russia if she moves to Galicia. As in Opening 1a, however, the defense is primarily a guessing game.