How to co-exist with nonexistent expectations

We address the problem that gambles having undefined expectation pose for decision theory. Observing that to place a value on such a gamble exposes one to a finitary diachronic Dutch Book, we defend a variant of Mark Colyvan's ``Relative Expected Utility Theory'' ({\bf REUT}), noting that it has the property of never preferring a gamble $X$ to an identically distributed gamble $Y$. We demonstrate, however, that even {\bf REUT} subscribers succomb to diachronic incoherence should they assign infinite expectation to a gamble they actually confront. In a final section, we use basic principles of anthropic reasoning (as formulated by Brandon Carter) to show why one needn't ever do so