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In his famous Wager, Pascal contemplates whether one should choose to believe in God. (Maybe we can't directly choose to believe in God any more than we can simply choose to believe that the Sun is purple; but we can choose to expose ourselves to conditions, such as regular association with devoted theists, that are likely to eventually lead us to believe in God.) Although there's some debate about how exactly Pascal conceptualizes the decision, one interpretation is this:

• Choose to believe: If God exists, infinite reward; if God does not exist status quo.
• Choose to not to believe: If God exists, infinite punishment; if God does not exist status quo.

Suppose that your antecedent credence that God exists is some probability p strictly between 0 and 1. Employing standard decision theory, the expected payoff of believing is p * ∞ [the expected payoff if God does exist] + (1-p) * 0 [the expected payoff if God does not exist] = ∞. The payoff of not believing is p * -∞ + (1-p) * 0 = ∞. Since ∞ > -∞ (to put it mildly), belief is the rational choice.

Now maybe it's cheating to appeal to infinitude. Is Heaven literally infinitely good? (There might, for example, be diminishing returns on joyful experiences over time.) And maybe decision theory in general breaks down when infinitudes are involved (see my recent discussion here). But finite values also work. As long as the "status quo" value is the same in both conditions (or better in the belief condition than the non-belief condition), the calculus still yields a positive result for belief.

If not believing is better in the absence of God, it's a bit more complicated. (Non-belief might be better in the absence of God if believing truths is intrinsically better than believing untruths or if believing that God exists leads one to make sacrifices one wouldn't otherwise make.) But if Heaven would be as good as advertised, even a smidgen of a suspicion that God exists favors belief. For example, if life without belief is one unit better than life with belief, contingent on the non-existence of God, and if Heaven is a billion times better than that one-unit difference and Hell a billion times worse, then the expected payoff for believing in God is p * 1,000,000,000 + (1-p) * -1, and the expected payoff of not believing is p * -1,000,000,000 + (1-p) * 0. This makes belief preferable as long as you think the chance of God's existing is greater than about one in two billion.

So far, so Pascalian. But there's God and then there's the gods. It seems that a more reasonable approach to the wager would consider theistic possibilities other than Pascal's God. Maybe God is an adolescent gamer running Earth in a giant simulation. Maybe the universalists are correct and a benevolent God just lets everyone into Heaven. Or maybe a jealous sectarian God condemns everyone to Hell for failing to believe the one correct theological package (different from Pascal's).

If so, then the decision matrix looks something like this [click to enlarge and clarify]:

In other words, quite an un-Pascalian mess! If the positive and negative values are infinite, then we're stuck adding ∞ and -∞ in our outcomes, normally a mathematically undefined result. If the values are finite but large, then the outcome will depend on the particular probabilities and payoffs, which might be sensitive to hard-to-estimate facts about the total finite goodness of Heaven or badness of Hell. And of course even the decision matrix above is highly simplified compared to the range of diverse theistic possibilities.

But let me suggest one way of clarifying the decision. If God is not benevolent, all bets are off. Who knows what, if anything, an unbenevolent God might reward or punish? Little evidence on Earth points toward one vs another strategy for attaining a good afterlife under a hypothetical unbenevolent deity. I propose that we simplify by removing this possibility from our decision-theoretical calculus, instead considering the decision space on the assumption that if God exists God is benevolent. Doing that, we can get some decision-theoretic traction: a benevolent God, if he/she/it/they reward anything, should reward what's good.

This, then gives us mortals some (additional) reason to do whatever is good.

Here's something that's good: apportioning one's beliefs to the evidence. The world is better off, generally speaking, if people's credence that it will rain on Tuesday tends to match the extent of the evidence that it will rain on Tuesday. The world is better off, generally speaking, if people come to believe that cigarette smoking is bad for one's health once the evidence shows that, if people come to believe in anthropogenic climate change once the evidence shows that, if people decline to believe in alien abductions given that the evidence suggests against it, and so on. Apportioning our beliefs to the evidence is both a type of intellectual success that manifests the flourishing of our reasoning and a pragmatic path to the successful execution of our plans.

This is true for religious belief as well. Irrationally high credence in some locally popular version of God doesn't improve the world, but in fact has historically been a major source of conflict and suffering. Humanity would be better off without a tendency toward epistemically unjustified religious dogmatism. Nor should a benevolent God care much about being worshipped or believed in; that's mere vanity. A truly benevolent God, with our interests at heart, should care mainly that we do what is good -- and this, I suggest includes apportioning our religious beliefs to the evidence.

The evidence does not suggest that we should believe in the existence of God. (We could get into why, but that's a big topic! We can start by considering religious disagreement and the problem of evil.) If a benevolent God rewards or at least does not punish those who apportion their belief to tge evidence, a benevolent God should reward or at least not punish non-believers.

If God does not exist, we're better off apportioning our (non)belief to the (non)evidence. If a benevolent God exists, we're still better off not believing in the God. If God exists but is not benevolent, then decision-making policies break. Thus, we can flip Pascal's wager on its head: Unless we reject decision theory entirely as a means to evaluate the case, we're better off not believing than believing.