Before I begin, let me mention that there are much better reasons for worshiping God than Pascal’s Wager, especially as Pascal posed it. It would be far, far better for a person to take their time investigating the truth than to choose, indifferent to the truth, a course based solely on the mathematically expected value of the outcome. But since most New Atheists (Horsemanites, as I’ve heard them called) seem rather indifferent to the truth anyway, they might as well at least make a sensible bet with their lives.
A very brief version of Pascal’s Wager, which will suffice for this discussion, runs as follows:
God either exists or he doesn’t and you must live as if one of those two alternatives is true. If God does exist and you live that way, you can be infinitely happy. If you do and God doesn’t exist, you lost out on at most a finite amount of happiness. If you don’t and God does exist, you lose out on infinitely much happiness. If you don’t and God doesn’t exist, maybe you gained a finite amount of happiness.
At this point the standard objection is “but that’s true of any god, and since this argument gives you no way to pick between them, the odds of you picking correctly are tiny, so after we cancel all the infinities atheism seems like the best bet”. (Theists who dismiss Pascal’s Wager will usually omit the last part.)
Leaving aside that it is mathematically invalid to cancel infinities (∞ – ∞ is undefined), there is both a major and a minor problem. The minor problem is that you can break this down to: believe in any god vs. atheism, then it holds for any god, at which point it might be true that you have no better method than rolling dice to pick. Even if this objection were true, atheism would still be the worst choice possible.
The major problem with this is that it is a category error in comparing God with gods. God is self-existent, eternal, unchanging, perfectly happy, and the creator of everything that is (which we can interact with, at least). Moreover, these traits are not separable. God cannot lack for nothing and be unhappy. God cannot be the cause of his own existence and lack for something. And so on; it is beyond the scope of this blog post to explain why all of these are connected. If you’re interested, you’ll have to read the Summa Theologica or find a friend who can understand it and have them explain it to you. (There are other philosophers besides Saint Thomas Aquinas who can explain it, but he’s the best.) Thus anyone who posits a God with any of these attributes really posits them all. These attributes also uniquely define God, so whatever name one might apply to God, it names the same thing.
Thus there are three categories of choices: a self-existent creator, a contingent but powerful being in the universe, and nothing beyond human beings.
Contingent gods, that is, powerful beings who exist because something made or begot or otherwise caused them, have the problem that they have no way of granting infinite happiness. How they lack this ability depends on whether they are temporal or aeveternal (in a created eternity, like angels).
If the gods are temporal, they can’t give infinite happiness because true happiness cannot come from changeable things. It’s complicated to prove in detail, but the very short version is that continual novelty gets old, and if you try to appreciate things for what they are, they won’t be those things for long. Worse, nothing in time is really itself because the moments of its existence are disconnected, so its reality is at best completely inaccessible because it is shattered across time. You can only love what you can know, and you can’t know what you have no access to.
If the gods are not temporal, but rather aeveternal, it is more complicated to show that they cannot give infinite happiness, though it is also academic because no one has ever claimed the existence of an atemporal but contingent god. I suspect that this is because an atemporal contingent being immediately points to what it is contingent upon and an infinite logical regress is too obviously absurd since it can’t be hidden in the separate moments of time. Still, the core of the proof lies in the nature of free will (if one doesn’t believe in free will, this whole discussion is moot because there is no choice to make, you must do what you must do). Free will, which is a contingent substance that can originate causality, cannot depend for its existence on another contingent thing, since non-contingent things do not have the ability to create ex nihilo, and so the contingent aeveternal god would not have the power to convert our souls into aeveternal souls, thus its possibility for happiness cannot be transmitted—by its own power—to us.
Since contingent gods cannot give infinite happiness, they are properly in the same case as atheism: they too are a bad bet, since the maximum payout is only finitely much happiness. Thus we are really only left with two categories: God, and no God. Little-g gods are just a distracting sub-category of no God.
Properly considered, then, Pascal’s Wager does evaluate in favor of betting on God, the Father almighty, creator of heaven and earth, of all things visible and invisible. There are much better reasons to believe in God, but since even the devil should be given his due, so too should this argument.