Brewer's: Green Baize Road
(Gentlemen of the). Whist players. “Gentlemen of the Green Cloth Road,” billiard players. (See Bleak House, chap. xxvi. par. 1.) Probably the idea of sharpers is included, as “Gentlemen of the Road” means highwaymen.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894