What Is Pascal's Wager?

What Is the Argument?

Pascal's wager, found in the fragments assembled as the Pensees, is one of the most famous arguments in the philosophy of religion, and it's distinctive because it's not an argument that God exists. It's an argument about what to do when you can't settle whether God exists. Pascal writes for a particular reader: the educated Frenchman of the seventeenth century who finds the evidence for and against God inconclusive and is deciding how to live. The wager tells that reader that, given the inconclusive evidence, believing in God is the rational bet.

The argument has a decision-theoretic structure. You face a choice: believe in God or don't. You don't know whether God exists. If God exists and you believe, the payoff is infinite—eternal happiness. If God exists and you don't believe, the loss is infinite—eternal separation from God. If God doesn't exist, the cost of believing is finite (some sacrifices of earthly pleasure, some practices), and the cost of not believing is also finite (you avoided those sacrifices). The expected value of belief, then, is infinite, because infinite payoff times any non-zero probability is infinite, and that swamps the finite cost. The expected value of disbelief is either infinite loss or finite gain, which is worse than infinite gain plus finite cost. So belief is the rational bet.

The Original Context

Pascal wrote the wager in the context of a larger apologetic project. He was a Jansenist Catholic, and he held that human reason is damaged by sin, that the evidence for God is real but easily suppressed, and that the proper response to God is not just intellectual assent but a transformation of the heart. The wager is meant to break through the reader's complacency: even on a cold calculation, belief is the better bet. But Pascal is clear that this is a first step, not the last. The wager can get you to seek God; it can't by itself produce the genuine faith that saves. That requires practice—prayer, the sacraments, the disciplines of religious life—which gradually reshape the heart.

This context matters for the wager's interpretation. Pascal isn't arguing that you should calculate your way to a "belief" that you then hold instrumentally. He's arguing that the rational response to inconclusive evidence is to commit yourself to the practices that, over time, can produce genuine faith. The wager is a door into a way of life, not a one-off decision. This is why Pascal devotes attention to what we'd now call habituation: "custom" is his word for the discipline that turns external practice into inward conviction.

The Expected-Value Reasoning

The wager's logic is proto-decision-theoretic, and modern philosophers have formalized it carefully. The expected value of an action is the sum of the values of its possible outcomes, weighted by their probabilities. For belief in God, the possible outcomes are: God exists and you gain infinite happiness (probability p, value +∞); God doesn't exist and you bear the finite cost of religious life (probability 1−p, value −c, where c is finite). The expected value is p·(+∞) + (1−p)·(−c). As long as p > 0, this is +∞. For disbelief: p·(−∞) + (1−p)·(+c), which is −∞ as long as p > 0. So belief wins on expected value, regardless of how small p is, as long as it's positive.

This structure is what gives the wager its force. It doesn't require strong evidence for God; it requires only that the probability of God is non-zero. And it doesn't require that the payoff of heaven be certain; it requires only that the expected payoff is positive infinity, which any non-zero probability of infinite reward yields. The argument is a piece of practical rationality, and its force comes from the asymmetry between infinite and finite stakes.

The Many-Gods Objection

The most famous objection is the "many-gods" problem. Pascal's wager assumes the choice is between the Christian God and no God. But there are many candidate gods: the Christian God, the Islamic God, the Jewish God, the gods of various polytheisms, and any number of hypothetical gods (a god who rewards disbelief and punishes belief, for instance). If you bet on the wrong god, you may suffer infinite loss. The objection is that the wager doesn't tell you which god to bet on, and that the expected-value calculation, applied to the whole space of possible gods, doesn't obviously favor any one.

Defenders of the wager have several replies. The first is that Pascal's wager was offered in a particular historical context, and the relevant comparison was between Christianity and the naturalistic alternatives available to his reader; the proliferation of hypothetical gods is an artificial expansion of the choice. The second is that, among the actually-existing religions, some have higher expected payoff than others, and Christianity might still win, especially on certain theological views about the fate of the unevangelized. The third is that the Bayesian structure of the wager can be generalized: you weigh each candidate god by its probability, and the calculation can still come out in favor of some belief over none. The many-gods objection is serious, but the SEP entry treats it as a challenge rather than a refutation.

The Sincerity Objection

A different objection asks whether belief chosen as a bet is the genuine faith that religion requires. If you believe because the expected value is high, you don't believe because you take God to be real; you believe because belief is useful. And a God who rewards faith might not reward this kind of instrumental belief. The objection is that the wager, if it produces belief at all, produces the wrong kind of belief.

Pascal's reply, in the fragments, is that custom can transform outward practice into inward conviction. You begin by acting as if you believe—attending Mass, praying, taking the sacraments—and the practices gradually reshape your disposition until you believe sincerely. The wager gets you to start; the practices do the rest. Whether this reply succeeds depends on your view of how belief works and whether God would reward belief produced by this route. Modern philosophers have developed the point further, distinguishing doxastic voluntarism (the view that you can choose what to believe) from the kind of indirect control Pascal relies on.

Why It Matters

Pascal's wager matters for several reasons. It's an early and sophisticated contribution to decision theory, anticipating the formal treatment of expected value by two centuries. It's a serious attempt to address the practical question of what to do when the theoretical question (does God exist?) is inconclusive—a question that ordinary believers and skeptics actually face. And it forces the reader to confront the stakes: if the choice between God and no God is as Pascal describes, then sitting it out isn't an option, because disbelief is itself a choice with consequences.

The wager also matters as a model of practical reasoning in religion. Most arguments for God try to show that God exists; the wager tries to show that belief is rational even if you can't show that. This is a different kind of argument, and it has analogues elsewhere—in pragmatism (William James's "will to believe"), in existentialism (the choice to commit), and in contemporary philosophy of religion (the "practical" arguments). The wager is the ancestor of a whole family of views that take the question of God to be, at bottom, a question about how to live.

Sources

• Stanford Encyclopedia of Philosophy, "Pascal's Wager" — https://plato.stanford.edu/entries/pascal-wager/
• Stanford Encyclopedia of Philosophy, "Pascal" — https://plato.stanford.edu/entries/pascal/
• Stanford Encyclopedia of Philosophy, "Philosophy of Religion" — https://plato.stanford.edu/entries/philosophy-religion/

Related Topics

• Does God Exist? — the theoretical question the wager presupposes unsettled.
• What Is the Argument from Religious Experience? — the experiential companion.
• What Is the Moral Argument for God? — the value-based companion.
• Philosophy of Faith — the wider framework.