 So you might object that the utilities are bounded. (See e.g., Hardin 1982.) However, unbounded quantities abound—length, volume, mass, curvature, temperature, and so on. Why is utility unlike them in this regard? Moreover, one might imagine a case in which utilities are intimately linked to another such quantity—e.g., the further away you get from some undesirable place, the better—and an unbounded function might link them. Moreover, as we have noted, probability theory is already shot through with infinitude; we need a principled reason why this kind of infinitude should be shunned. (See Nover and Hájek 2004 for further discussion.) And perhaps it is not crazy after all to value the St. Petersburg game infinitely. After all, it dominates each truncation of the game, which pays nothing if heads has not come up after \(n\) trials (for each \(n\)): the St. Petersburg game’s outcome is equally good in finitely many states, and strictly better in infinitely many. Plausibly, then, it should be preferred to all these truncations of the game (Hájek and Nover 2006, 2008)—its desirability is greater than \(n\), for each \(n\).