I'm not sure I follow. You're right in that this is what gambling houses do. I'm told that casinos calculate their expected earnings for a given table thus:

Revenue = House Edge * Bets.

Where "bets" is the total money put down and "house edge" is the probability that the house will win any given bet.

So from a Casino's point of view, the gambler's fallacy would encourage me. If I were to walk the floor and see someone winning twenty hands of blackjack in a row, I would first send Vinnie and Louis the Louse to ensure he wasn't cheating. Once I was sure this really was the result of blind luck, I'd let him continue playing. After all, the laws of probability can't be mocked forever. If he keeps playing at that probability, not only will I eventually win it all back but I'll get his starting stake too. It may not happen on the next hand or the next twenty hands. It may take several years, but it will happen. Meanwhile the winnings will encourage OTHER people to put down money at bad bets, resulting in even more cash for me.

How am I , as the Casino owner, not succumbing to the gambler's fallacy?

This leads up to my sure-fire foolproof system to winning at gambling: Buy a casino and make the laws of probability work for, rather than against, you :).

Respectfully,

Brian P.