Pascal’s Wager

Pascal’s argument (written in the 1600’s) went like this: Suppose you concede that you don’t know whether or not God exists and therefore assign a 50 percent chance to either proposition How should you weight these odds when decided whether to lead a pious life? If you act piously and God exists, Pascal argued, your gain – eternal happiness - is infinite. If, on the other hand, God does not exist, your loss, or negative return, is small – the sacrifices of piety. To weigh these possible gains and losses, Pascal proposed, you multiply the probability of each possible outcomes by its payoff and add them all up, forming a kind of average or expected payoff. 

In other words, the mathematical expectation of your return on piety is one-half infinity (your gain if God exists) minus one-half a small number (your loss if he does not exist). Pascal knew enough about infinity to know that the answer to this calculation is infinite, and thus the expected return on piety is infinitely positive. Every reasonable person, Pascal concluded, should therefore follow the laws of God. Today this argument is know as Pascal’s wager. 

Pascal’s wager is often considered the founding of the mathematical discipline of game theory, the quantitative study of optimal decision strategies in games.

Leonard Mlodinow, The Drunkard's Walk: How Randomness Rules Our Lives