Safety accounts of knowledge intend to explain why certain true and intuitively justified beliefs fail to be knowledge in terms of such beliefs falling prey to a modal veritic type of luck. In particular, they explain why true and intuitively justified beliefs in “lottery propositions” (highly likely propositions reporting that a particular statistical outcome obtains) are not knowledge. In this paper, I argue that there is a type of case involving lottery propositions that inevitably lies beyond the scope of any reasonable safety account of epistemic luck. I offer counterexamples to accounts of epistemic luck in terms of safety conditions that involve both “locally” and “globally” reliable ways of forming beliefs in nearby worlds. All such counterexamples present a lottery case illustrating the next possibility: the process of selecting the lottery winner might be such that any world in which it delivers a different outcome is extremely far away from the actual world. In addition to being a case of safe ignorance, this type of lottery case shows that, ultimately, either veritic epistemic luck is not unsafe true belief or beliefs in lottery propositions are not epistemically luckily true.