Yeah I think this is confusing the gambler's fallacy with something like the hot hands hypothesis. The former has to be true by definition, assuming everything

Yeah I think this is confusing the gambler's fallacy with something like the hot hands hypothesis. The former has to be true by definition, assuming everything is as it should be, and there's no deceit or malfunction; the latter might be true empirically in reality. I do think there's an interesting question that's raised by the essay though, which is at what point does a string become so inconsistent with a certain probability distribution that you have to question whether things are as they are assumed? That is, let's say you go into a casino and you keep getting wins. At what point do you say "this is so improbable under X probability of wins that something is off"? Gaming regulators must have some definition of this.