Definition
Pascal's Wager
Pascal’s wager is Blaise Pascal’s practical argument that, under uncertainty about God’s existence, one should pursue belief in God and a religious life because the possible infinite reward outweighs any finite worldly cost.
Let
be the state in which God exists and grants eternal happiness for the religious commitment , and let be the alternative of not making that commitment. In a simplified model, assume , , and all other payoffs are finite. Then the expected utilities satisfy The principle of maximum expected utility therefore favours
within this model, however small is. The wager is not a proof that God exists. Its recommendation depends on the assumed rewards, the available religious alternatives, and whether infinite utilities admit a meaningful comparison. Pursuing belief also need not mean that belief can be chosen directly.