The gambler's fallacy fallacy (fallacy)

The gambler's fallacy is the irrational belief that prior outcomes in a series of events affect the probability of a future outcome, even though the events in question are independent and identically distributed. In this paper, we argue that in the standard account of the gambler's fallacy, the gambler's fallacy fallacy can arise: The irrational belief that all beliefs pertaining to the probabilities of sequences of outcomes constitute the gambler's fallacy, when, in fact, they do not. Specifically, the odds of the probabilities of some sequences of outcomes can be epistemically rational in a given decision-making situation. Not only are such odds of probabilities of sequences of outcomes not the gambler's fallacy, but they can be implemented as a simple heuristic for avoiding the gambler's fallacy in risk-related decision-making. However, we have to be careful not to fall prey to a variant of the gambler's fallacy, the gambler's fallacy fallacy (fallacy), in which we do not calculate odds for the probabilities of sequences that matter, but rather simply believe that the raw probability for the occurrence of a sequence of outcomes is the probability for the last outcome in that sequence.