That is, the most common of the many alternate names for the sleight-of-hand swindle in which an operator palms a pea or pellet while appearing to cover it with one of three walnut shells, thimbles, cups, bottle caps, whatevers, shuffles the shells, and bets a mark that they can't tell where the pea is. It's an old con, but when it exploded in popularity in the late 19th century, thimbles were the common cover -- the -rig being using an old slang sense of a trick or scheme, as in a rigged game. Which this is. Even if the operator is working alone -- which he won't be, as he'll have partners posing as audience members -- you can't win this one so don't try.
Thom lost all his paycheck to thimblerig before he even got to the first bar, the idiot.