Common probabilistic fallacies and putative paradoxes are surveyed, including those arising from distribution repartitioning, from the reordering of expectation series, and from misconceptions regarding expected and almost certain gains in games of chance. Conditions are given for such games to be well-posed. By way of example, Bernoulli's "Petersburg Paradox" and Hacking's "Strange Expectations" are discussed and the latter are resolved. Feller's generalized "fair price, in the classical sense" is critically reviewed.

Decision theory aims to provide mathematical analysis of which choice one should rationally make in a given situation. Our current decision theory norms have been very successful, however, several problems have proven vexing for standard decision theory. In this paper, I show that these problems all share a similar structure and identify a class of problems which decision theory overvalues. I demonstrate that agents who follow current standard decision theory can be exploited and have their preferences reordered if offered decision (...) problems of this class. I show that preference reordering is a serious problem, which motivates my search for a decision theory which is immune to exploitation. I find Dr. Nick Smith’s theory of Rationally Negligible Probabilities cannot be exploited in this way and discuss why agents should adopt it. (shrink)