 Pollock (1983) offers the following puzzle. You have a bottle of Ever-better wine, which keeps improving as it ages: the later you open it, the better it will be. When should you open it? There’s a good sense in which any time is too soon: opening it slightly later would be better. But the worst option is never to open it, and to avoid this it must be opened at some time. This decision problem has uncountably many possible actions, but we could easily make them denumerable by adding that the bottle can only be opened at discrete times—e.g. on the hour. You would gladly perform an action that has maximal utility, but here there is no such action! This problem displays an intriguing feature that Bartha, Barker and Hájek (2013) call discontinuity at infinity: “an infinite sequence of choices, each apparently sanctioned by plausible principles, converges … to a ‘limit choice’ whose utility is distinct from, and typically much lower than, the limit approached by the utilities of the choices in the sequence” (630). Their paper discusses other decision problems with this feature. For more discussion of this kind of phenomenon, see Chow, Robbins, and Siegmund (1971) and Seidenfeld (1981).