1) There is a non-zero possibility of receiving an infinite reward (everlasting joy in heaven) if and only if you believe in God.
2) Infinity multiplied by any non-zero real number is still infinite.
3) Since Expected utility = Reward * Probability, the expected utility of believing in God is infinite, whereas the expected utility of disbelief will be finite. [From 1 & 2]
4) As a matter of practical reason, you ought to act in such a way as to maximize your expected utility.
C) Therefore, you ought to believe in God (or act in ways that will help you to develop such a belief).
The first problem I want to highlight is that the formula in premise (3) should probably only apply to finite values. Strange and implausible things happen when you start playing with infinity, e.g. the St. Petersburg Paradox. [Update: more here.]
But the real problem is with premise (1).
I don't mean to suggest that it's impossible to receive an infinite reward, though that is one response that could be made - especially if one thinks theism is inconsistent and so could not possibly be true, or if one denies that infinity as such could actually exist. But those are not my complaints here. Rather, I think it is absurd for the theist to suggest that it's impossible for a non-believer to receive an infinite reward.
The problem is that they have set up a false dichotomy between atheism and Christianity. But of course there are all sorts of other theological positions one could consider here. For example, perhaps some god exists, but has a twisted sense of humour, causing it to send all believers to hell (for infinite suffering), whereas all non-believers will receive an infinite reward (heaven). This is extremely unlikely of course, but it at least seems possible (if traditional theism is). So, since it comes with a non-zero probability, we can run through an analogue of Pascal's argument which yields the opposite conclusion.
So premise (1) is false. This alone is enough to immediately refute Pascal's Wager, if treated as the deductive argument shown above. Perhaps one could modify it though, to form a slightly weaker version based on the premise that believing in God is more likely to yield infinite utility. I'm not sure how one would establish that though. Probably the best one could do here is try to offer an infinite-utility-involving scenario that sounds more plausible than any other. Consider the following from Jeremy Pierce (which I'm taking slightly out of context here):
What if God does exist and won’t reveal this to anyone with any certainty unless they’re genuinely seeking God through religious practices, and only then when they try hard enough and seek in the right ways (whatever those ways might be)? If this is true, then could a nonbeliever be innocent in not seeking God? One might argue that a nonbeliever needs to have pursued God through the worship, prayer, reading of scriptures, genuine efforts to see and evaluate oneself in the way a perfect God would want us to, entering into a community of faith to see life through the eyes of faith, and so on. Simply learning about religion isn’t enough, because that’s not what God is looking for in us. Only if we enter into religious practices, genuinely seeking God, would God give us this assurance. If this is possible, then it may be that the atheist or agnostic doesn’t have all the evidence that a theist has. This is an interesting possibility that should at the very least give pause to those who think the lack of convincing arguments for believing in God is a good enough reason for not believing in God.
It sounds vaguely plausible that God might want that. But I don't think a truly benevolent deity would impose an infinite punishment on honest non-believers. I don't find that even remotely plausible.
And consider this alternative scenario: What if God does exist, and happens to value epistemic integrity and rationality? He wants people to believe what they are epistemically justified in believing, rather than blindly embrace dogma. Perhaps some theists are justified in their beliefs, due to the 'special evidence' God reveals to them. But certainly many atheists are also justified in their beliefs, given the evidence that's available to them. So God is happy with all these epistemically responsible people, and rewards them all appropriately. However, he is repulsed by the opportunistic dogmatist who ignores the evidence and irrationally adopts faith hoping for salvation. So God does not reward such irresponsible people. Therefore, if this were true, one should follow the evidence and ignore all these 'pragmatic' arguments for belief.
I think my honest deity sounds at least as plausible as the traditional theistic one, and probably more so. So, as a matter of practical reason, you ought NOT believe in God (presuming this is what the evidence otherwise advises), lest ye suffer the wroth of mine honesty-besotted deity!
Lastly, one might argue that - quite apart from the silly practical advice of Pascal's Wager - atheists have an epistemic obligation to seek out all the evidence for theism, including the special 'experiences' that we are told occur only to those 'inside' the worldview. To quote Jeremy again:
It's easy to find different perspectives that compete to explain our experience. The question becomes how to look at those different perspectives and judge between them about what we should believe. It may be that you can’t understand the theistic framework without having tried to live, think, and feel from that orientation. The claim would then be that someone who hasn’t done this hasn’t given oneself the opportunity to look at the evidence in a balanced way.
Given the vast variety of worldviews on offer these days, it would be absurd to suggest that one has an unconditional epistemic obligation to 'try them all out', just in case doing so might yield some new/unexpected evidence. Surely we should only go to such extreme lengths if we have some prior, independent reason to find the worldview plausible.
Suppose I believe that Santa Clause is real. Moreover, he is omnipotent (how else could he deliver all those presents on time?), omniscient (he knows whether you've been naughty or nice) and at least moderately benevolent too (he gives us presents!). Now, after you die, you get to turn into an elf and spend eternity in joyful union with Santa - but only if you believe in him! If you don't believe, your rotting corpse gets fed to the reindeer, and your soul's energy is captured within a special battery to help light up Rudolph's red nose. Now, I know this all sounds rather silly, from your limited worldview, but trust me: if you just take a leap of faith, and immerse yourself within my merry religion for a while, you too will see the light.
Presumably nobody feels any compunction to take me up on my offer. We have no epistemic obligation to try out a belief in omni-Santa. But I find Christianity no less implausible. (Really, I don't. I could go along with some sort of deism, perhaps, like the one I described earlier. But theism, with its revealed texts and lovingly vengeful God, really does strike me as ludicrous. No offence intended to any theists who might be reading this - your circumstances and evidence may, after all, differ from mine.) So, absent any compelling reasons to the contrary, the rational atheist surely has no epistemic obligation to take theism seriously. If anything, he's obliged not to. (See also Clayton's comments in the linked-to post.)
Update: What I'm here calling "Pascal's Wager" differs from Pascal's original argument. For a reconstruction of the latter, see Siris.
Update 5 Dec: John Holbo sums up (something like) my central objection here in a single sentence: "What are the odds that any one possible one true jealous God is the one true one true jealous God, after all?"