Pascal's Wager Explained: Why Belief in God is a Good Bet

Confession: It’s hard to prove God exists. Arguments for God’s existence are less than conclusive. Pascal agrees, “God is, or He is not. But to which side shall we incline? Reason can decide nothing here.” To get around this problem, Pascal shifts the target of thinking. You’ll learn about this new target and how he thinks he hits it, in this video. You’ll also learn a powerful objection to Pascal’s Wager.

Pascal's New Target = The Utility of Belief in God

Pascal’s new target is not rational belief, which is based on evidence. Remember he thinks the evidence is mixed on that score when it comes to God. Instead, Pascal’s target is rational choice. He shifts from truth as the goal to utility. Is it rational to choose a religious life? That depends on the value of the payoffs for living such a life and how likely you are to get them.

Decision Theory Illustrated

Pascal was ahead of the game. His Wager relies on a now standard theory of rational choice called decision theory.

To see how decision theory works, let’s imagine I’ve decided to take a vacation to a ski resort. I need to decide whether I’ll ski or snowboard. If it recently snowed, it’d be better to snowboard because snowboarding in powder is the best. But, if it didn’t recently snow, it’d be better to ski because I’m a better skier than snowboarder and I can enjoy more of the mountain. I don’t want to rent skis or snowboards, and I don’t want to lug around more equipment than I need. I’d rather not fly with equipment. So, I’m going to ship one week ahead either my skis or snowboard. Let’s represent these outcomes in what’s called a decision matrix.

The four possibilities are bring skis, bring snowboard, it snows, and it doesn’t snow.

If I bring my snowboard and it snows that’s worth a value of 100. I’ll get to carve some sweet turns on my board in powder. If I bring my snowboard and it doesn’t snow, that’s a value of 20. I’ll be stuck snowboarding parts of the mountain that are icy, and I won’t be able to enjoy the steepest terrain on the mountain. If I bring my skis and it snows, that’s worth a value of 70. I can still enjoy the mountain and the powder, but it’s not as good as snowboarding powder. If I bring my skis and it doesn’t snow, that’s a value of 50. I can enjoy steep parts of the mountain, and maybe even jump off some cliffs.

The last thing we need to know is how likely it is that it will snow within 24 hours of me hitting the slopes. It’s 7 days until my first day on the mountain. The weather report shows a 35% chance of snow the day before I ski or snowboard.

Let’s calculate the expected utility of bringing my snowboard. First, we use the probability that it snows, which is 35% times the utility of bringing my snowboard if it snows, which is 100. We add that to the probability it doesn’t snow times the utility of bringing my snowboard if it doesn’t snow.

The result 0.35(100) + 0.65(20) = 35 + 13 = 48.

The utility of bringing my skis is: 57.

According to decision theory, a rational agent always takes the choice that maximizes her expected utility, so I should ship the skis to the resort and get ready for catching some sweet air off some cliffs.

With the heavy machinery of decision theory in mind, let’s relate this to Pascal’s Wager.

Why You Must Bet & The Payout is Infinite

Because you’re alive you already have skin in the game, so to speak. You have a life to bet on God or not. As he says,

What is the everything you win, “an infinity of infinitely happy life.” If you bet your life on God and become a true believer, and it turns out God exists, you win an infinite reward. Why?

Pascal thinks if God exists God is utterly unlike us. God is simple, without parts. We are riddled with parts that break. God is extensionless, as spirit. We are extended in space as material beings. We are limited and finite. God is limitless and infinite. So, if, upon death, we are rewarded with union with God in the afterlife, that reward is infinite. It is eternal. God is wholly good, so the reward is infinite bliss, an infinity of infinite amounts of happiness. That’s one heck of a payout. We can represent it with the infinity symbol.

What if you choose to believe in God and God doesn’t exist? You lose a finite reward. You could have engaged in a whole lot more sex, drugs, and rock and roll and not wasted your time doing boring religious stuff.

The Power of Pascal's Wager

What about the probabilities. Mathematically, infinity is a funny thing. Contemporary math theory allows for bigger and larger sizes of infinite numbers of things. This comes from the worl of Georg Cantor. He developed a way of doing math with transfinite numbers.

When Pascal wrote The Wager such a system of math wasn’t around. So, the infinite number involved in The Wager is governed by two assumptions:

"For any finite number n, n + infinity = infinity, and For any positive number n between 0 and 1, n times infinity equals infinity." (Rosen et. al)

As long as the probability that God exists is non-zero, The Wager works. Pascal assumed it’s 50/50 that God exists, but any positive number or probability multipled by infinity results in infinity. This is the power of The Wager. If you think it’s even remotely possible that God exists, then The Wager makes it rational to risk everything on belief in God.

Objection - I Cannot Will Myself to Believe

But, wait. I can’t just decide to believe in God in order to potentially get an infinite payout upon death. Wouldn’t God see through my inauthentic belief? This is why Pascal commends you to take religious action. It’s the fake it until you make it view of religious belief. People start out skeptical and as they do more religious stuff, their believef comes on the scene or gets stronger.

Additionally, as a deep insight into human psychology, Pascal thinks people resist the reasoning of the wager due to their emotions, what he calls their passions. You simply don’t want to believe because you want to live how you want to live and you know if you did come to believe in God things in your life might change.

As Pascal responds to such an objection from inability to freely bring about genuine belief, “You want to cure yourself of unbelief, and you ask for remedies: learn from those who were tied like you and who now wager all they possess. These are people who know the road you would like to follow; they are cured of the malady for which you seek a cure; so follow them and begin as they did—by acting as if they believed, by taking holy water, by having masses said, and so on. In the natural course of events this in itself will make you believe, this will tame you. “But that is just what I fear.” Why? What have you to lose? If you want to know why this is the right way, the answer is that it reduces the passions, which are the great obstacles to your progress.”

Objection - Many Gods

There are several objections to Pascal’s Wager. One of the biggest is the “many Gods” objection. Pascal is assuming something like the Christian God. He assumes there’s an eternal, loving God that rewards believers with a blissful life of eternity with him. But, There might be a perverse God that rewards unbelievers with infinite good stuff just to be, well, perverse. If so, then not believing in God and it being the case that the perverse God exist result in an infinite payout. We need some independent reason to favor the God Pascal supposes. Doing so might require arguments for God’s existence—a God that’s wholly good. But doing so defeats the purpose of pascal’s argument, which targets practical reasons for belief. Looking at truth-focused reasons only puts us back in the quagmire Pascal’s Wager sought to avoid.

What are your thoughts about The Wager? Leave your thoughts in the comments.

Watch a video version of this post below.