Writer confuses the gambler's fallacy with the law of large numbers. The gambler's fallacy concerns individual coin flips, which are obviously independent. The law of large numbers concerns the average of many coin flips, which will converge given enough flips. But that doesn't make the gambler's fallacy any less fallacious - particularly in a casino, where the averages are deliberately set up to favor the house, and the house gets a much, much larger number of trials than the gambler.