Green’s Dictionary of Slang

big store n.

also big joint
[note Maurer, The Big Con (1940): ‘The big store An establishment against which big-con men play their victims. For the wire and the pay-off, it is set up like a poolroom which takes race bets. For the rag, it is set up to resemble a broker’s office. Stores are set up with a careful attention to detail which makes them seem bona fide. After each play, the store is taken down and all equipment stored away’]

(US Und.) a fake casino or broker’s office, in which victims are subjected to an elaborate large-scale swindle.

[US]W. Irwin Confessions of a Con Man 13: I dallied with all the games – phony poker, three-card monte, gold bricks, big joint, wire-tapping [etc.].
[US]G. Henderson Keys to Crookdom 397: Big Store. Wealthy gambling house or dive.
[US](con. 1905–25) E.H. Sutherland Professional Thief (1956) 61: The first ‘Big Store’ of any consequence was opened by the Gondorf Brothers in New York about 1906.
[US]D. Maurer Big Con 4: The big store, a fake gambling club or broker’s office, in which the victim is swindled.
[US]C. Hamilton Men of the Und. 320: Big store, A fake gambling or bookie establishment used by confidence men.
[US]M. Salovesh in Comments on Etymology Feb. 16: The con men at my favorite bar loosened up while I was around [...] That’s how I learned about the ‘big store’: a false-front operation set up for the purpose of separating a wealthy victim from a lot of cash.