I don't understand why the author wastes time with his particular beef, but arguably, Gambler's Fallacy is not a fallacy in the sense that it is neither a logical (formal or informal) fallacy nor a mathematical fallacy. A fallacy is the employment of faulty reasoning, but when committing the Gambler's Fallacy, it isn't reasoning that is flawed, but a lack of knowledge of statistics, or Discrete Mathematics such as combinations and permutations, or, conversely, Gambler's Fallacy is instead merely cognitive bias towards inaccurate expectations.
