Slang.

This is old slang for a habitual thief, drunkard, or hustler. Less-commonly used to refer to someone with general experience, as in "old-timer". In poker, a career player, the opposite of a "sucker."

As the Webster's definition implies, "rounder" is derived from the phrase "to make the rounds."

Supreme Court Justice William O. Douglas used the word in his biography: " . . .It was a moving, eloquent plea: he had a mother to support; he was poor as a church mouse; he was not a "rounder" or a "boozer." Vol. I, p.99. (1974).