Pascal's wager attempts to provide a prudential reason in support of the rationality of believing that God exists. The wager employs the idea that the utility of theistic belief, if true, is infinite, and in this way, the expected utility of theism swamps that of any of its rivals.

Not surprisingly the wager generates more than a good share of philosophical criticism. In this essay I examine two recent objections levelled against the wager and I argue that each fails. Following this, I argue that a transfinite version of the wager – one using the idea of an infinite utility – is incompatible with standard axiomatic constructions of decision-theory and, as a consequence, the Pascalian would be well-advised to give up the idea of an infinite utility and employ only a finite version of the wager. The consequences of limiting the wager to finite utilities are also explored.