The only Casino game that I know of that this is possible to achieve (without cheating of course) is Black Jack (counting cards), but now days with continuous shuffle this is no longer possible.
Take a look at strikesapphire.com. Their blackjack was very beatable until recently (dealing 65% to 75% of the way through 6 decks before shuffling and allowing a spread from $0.10 to $5.00) and probably still is, but to a much lesser degree.