Does Pascal's Wager Work?

When discussing the intersection of faith and reason, Pascal’s Wager often surfaces as a go-to argument for Christianity.

Blaise Pascal proposed that, when faced with the uncertainty of whether God exists, one should “wager” on belief because the potential reward—eternal life in heaven—infinitely outweighs the possible loss. On the surface, this pragmatic approach might seem like a compelling case for Christianity, but does it really hold up under scrutiny?

As a Christian apologist, I understand the desire to present faith in a logical and reasoned manner, yet I find Pascal’s Wager falls short of its intended goal.

While it offers an enticing proposition—bet on belief to avoid infinite loss—its actual effectiveness in leading someone to genuine faith is questionable. Beyond its limitations in fostering belief, Pascal’s Wager raises deeper issues when examined more closely.

In this article, I will outline why Pascal’s Wager fails to provide the kind of rational or spiritual conviction necessary for meaningful belief, and how it ultimately undermines its own argument.

Pascal’s Wager

Pascal’s wager can be summarized as follows:

In the case of Christianity, it is either true or else it is false.

It is also the case that either one believes in Christianity or they do not.

These create four possible outcomes:

1. Christianity is true and one believes it

2. Christianity is true and one does not believe it

3. Christianity is false and one believes it

4. Christianity is false and one does not believe it

So what are the results of each possible outcome? (respectively)

1. Infinite gain in Heaven

2. Infinite loss in Hell

3. No gain/loss

4. No gain/loss

To show this more visually, here is a two-way table:

	Christianity is True	Christianity is Not True
One Believes in Christianity	Infinite Gain in Heaven	No Gain, No Loss
One Does Not Believe in Christianity	Infinite Loss in Hell	No Gain, No Loss

Then Pascal concludes, given the weighted mean, one should wager on Christianity.

There are several common critiques of Pascal’s wager:

This might show it a safe wager to believe in Christianity, but it does not give one the insights necessary to actually come to said belief.

It has no claim to uniqueness; that is to say that many other religions can posit the same exact wager.

Truthfully at the heart of the second critique is that Pascal has committed a fallacy, the fallacy of a false dichotomy

Let me expand on this in a way that I have not seen, and I believe that we will see that Pascal’s wager has little to no merit at all.

Given that there are multiple theistic beliefs that can posit such an argument, we may consider them in two possible ways. Either, we consider each religion individually and factor it into our arithmetic, or else we consider theism in a generalized sense and then apply our arithmetic.

For the former, consider each religion individually

Let us consider, for simplicity’s sake, that there are only three, mutually exclusive, religions which can utilize Pascal’s wager. Let’s call these religion A, religion B, and religion C. Let us again consider the resulting 2-way table.

	Religion A is true	Religion B is true	Religion C is true	All Religions Are False
One Believes only in Religion A	Infinite Gain	Infinite Loss	Infinite Loss	No Gain, No Loss
One Believes only in Religion B	Infinite Loss	Infinite Gain	Infinite Loss	No Gain, No Loss
One Believes only in Religion C	Infinite Loss	Infinite Loss	Infinite Gain	No Gain, No Loss
One Believes in None of The Religions	Infinite Loss	Infinite Loss	Infinite Loss	No Gain, No Loss

Attempting to do a proper weighted mean, with multiple ways to win or lose an infinite sum, is an exercise in mathematical futility. So rather than demonstrating a weighted mean for the results, I will simply show the probability of each outcome. (Notice, I am structuring this as probability of winning vs losing, not probability of being right or wrong. If one has no gain and no loss, I am not classifying that as a win or a loss, but neutral. For that reason, the sums in the following table do not add to 1, as they are missing the neutral cases).

	Probability of Winning	Probability of Losing
Believing Religion A	¼	½
Believing Religion B	¼	½
Believing Religion C	¼	½
Not Believing Any	0	¾

What is made clear here, is that if all cases are equally likely, then it is more probable that one will lose (receive infinite loss) than that they might win (receiving infinite gain). In considering the other religions that have justified claim to Pascal’s Wager, the only thing that Pascal’s Wager can conclude is that it is more advantageous to place your wager on an arbitrary belief than it is on no belief at all. But any individual religion is actually a non-advantages bet (as it is more likely to lose than it is to win).

So, if we choose to consider each religion individually, Pascal’s Wager is not helpful in choosing where to place our bet. One must, necessarily, learn more about the religions and the evidence for them in order to receive some advantage in placing their bet and increase their probability of winning.

For the latter, theism in a generalized sense

For conversation’s sake, let’s consider general theism to be the belief that there is a higher power that has created this universe, but no more particular beliefs than that. A general theist is not necessarily a diest (a deist believes that the creator does not interact with the creation), but simply lacks any convictions on any particulars other than that there is a creator. This is what is meant by the notion of “theism in a generalized sense.”

Unfortunately, the main shortcoming of generalized theism is that many (if not all) of the particular religious beliefs have unique requirements to receive their particular claim to “infinite gain.” For that reason, it seems most reasonable to me that the beliefs of a “general theist” would stack up as follows:

	A Particular Theistic Belief is True	No Particular Theistic Beliefs are True
General Theist	Infinite Loss	No Gain, No Loss
Atheist	Infinite Loss	No Gain, No Loss

As you can see, the general theist has the same exact potential outcomes as the atheist.

We have shown that if we consider each religious belief in particular, then Pascal’s Wager is unhelpful in determining where to place our bet

And that
If we attempt to consider the generalization of Theism vs Atheism, then Pascal’s Wager serves to show that both camps are equally bad bets.

Now, I personally believe that the proper way to do the arithmetic is to consider each religious belief individually and that Pascal’s Wager is simply unhelpful. To prove this claim is beyond the scope of this article, but something that I may attempt in a future article.