The Sleeping Beauty problem remains controversial with disagreement between so-called Halfers and Thirders, although the Thirders appear to be leading these days. I analyze three popular arguments for the Thirder position, including the long-run frequency argument, Egla’s ‘symmetry’ argument, and new-information arguments, and find problems with each. The long-run frequency argument is almost unequivocally thought to strongly support Thirders, but in formalizing the argument for an arbitrary number of repetitions, I show that the expected proportion of Heads-Awakenings for a single-trial (...) experiment is unambiguously 1/2. My criticisms of Elga’s symmetry argument and the new-information arguments point to subtle misalignments between the narrative/causal description of thought-experiments and the mathematical probability expressions and theory we use to describe these narratives. I end with distinguishing two varieties of possibility—a dynamic forward type and static historical type—that help clarify the Sleeping Beauty problem, nullify the main criticism against Lewis’s Halfer argument, and have applicability to probability theory in general. (shrink)