Abstract
Some random processes, like a series of coin flips, can produce outcomes that seem particularly remarkable or striking. This paper explores an epistemic puzzle that arises when thinking about these outcomes and asking what, if anything, we can justifiably believe about them. The puzzle has no obvious solution, and any theory of epistemic justification will need to contend with it sooner or later. The puzzle proves especially useful for bringing out the differences between three prominent theories; the probabilist theory, the normic theory and a theory recently defended by Goodman and Salow.