Actually there is a basis for it in blackjack and how to card count. That said I'm not sure what casino's are doing these days ever since the card counting was figured out.

They use a decent size shoe of several decks and reshuffle more than just in between rounds. Furthermore, the dealer only deals from a subset of the shoe IIRC.

I figured they had a way to break up the benefits of card counting - thanks for informing me!

Certainly not in the sense of the gambler's fallacy, but you can be sure that someone's fortunes from playing casino games will exhibit mean reversion in the sense that the next game is always more likely to bring their cumulative winnings closer to the house edge rather than further from it. Not so with the stock market. The stuff about card counting is basically impossible to do these days but can alter the house edge, and also doesn't apply to the market.