In Comp City, Max Rubin, who was a dealer, floorman, pit boss, casino manager, and a big-time blackjack player, and knows whereof he speaks, tackled this very question. Here are his conclusions.
If the dealer makes a mistake, say something like, "That’s why they make erasers," and tell him how amazed you are that he doesn't make more, considering how many hands he has to deal every day.
If a dealer makes a mistake and overpays you, overlook it. [Editor's Note: There's no law against this that we know of. It seems like it would be impossible to enforce.]
If the dealer makes a mistake that's going to cost you money, stop the hand.
If the dealer forgets to give a player a card, or doesn't give herself a hole card, or forgets to give you your double down, take your time before deciding what to do. If you have a clear advantage, continue the hand. If it looks like you're about to get whipped, try to bail out.
Say you've doubled down on ten and the dealer's got a five up. She forgets to give you a card. She turns over a ten in the hole. Let her hit out. If she busts, demand to be paid for the double. If she makes a hand, it'll probably be called dead.
What if she forgets to give you a card and turns over a five in the hole? Let her draw out. If she draws your face card, demand to be paid. If she busts, demand to be paid. If she draws out a multi-card hand, let them call "No hand."
After she's made a hand, never let them go back and give you a card. You're better off pulling your money back.
If they give you the option of continuing or 'got a big card and you don't have squat, fold. If she's got a little card up and you’'e got a total of 10 or 11, double. When in doubt, bail out.
Just to check on the legality of all this, we put in a call to the Gaming Control Board. The Chief over at the Enforcement Division confirmed that if the casino makes a mistake in over paying you and draws your attention to their error, then to keep the money would be theft. If they don't notice an over-pay in your favor, it's up to your own conscience and whether you're an intrinsically honest person and care about the possible consquences for the cashier/dealer stemming from your accident good fortune, or not.
