Green’s Dictionary of Slang

faro-bank n.

(US Und.) a form of cheating whereby the victim is allowed to win, but never as much as he loses; also as v.

implied in faro-banker
[US]D. Maurer Big Con 296: faro-bank. 2. To take a mark’s money by allowing him to win and lose, always losing more than he wins. Also to bankroll.
[US]Goldin et al. DAUL 67/2: Faro bank. (Carnival) The process of letting swindle victims win at a crooked game often enough to keep interest high.

In derivatives

faro-banker (n.)

a confidence trickster specializing in this.

[US]Night Side of N.Y. 39: A couple of well-known Broadway ‘faro-bankers’ follow the procession, for the body was one of their craft.