Blaise Pascal said that you couldn't ascertain the existence (or lack thereof) of God by pure reason. Reason, he said, was fallible and uncertain. Still, he continued, optimally you should believe in God. His argument laid the first brick of the foundation of decision theory.
Imagine that you are a believer and God does not exist. You die and fade into oblivion, a neutral outcome that can be assigned a zero. If God does exist, though, you will be taken unto Him. The payoff is infinitely positive. Now assign any probability to God's existence, as large or as small as you can imagine. Say, p. What is the expected payoff of a believer's strategy? It would be p * Inf + (1 - p) * 0 = Inf.
Now, let's say you are an atheist. If God doesn't exist, you die and fade into oblivion, an outcome that can be assigned a zero. If God does exist, though, He is unlikely to forgive your transgressions, and it's off to Hell with you, my friend. The payoff then is infinitely negative. Under the same probabilities of the existence of God, your expected payoff would be p * -Inf + (1 - p) * 0 = -Inf.
Dude, you are totally stuffed if you are a disbeliever. But you have the potential for infinite positive payoff if you are a believer.
Therefore, Pascal concluded, it is more optimal to act as though God existed.
Of course, his mathematics made sense only if the probability p of God's existence was not zero (multiplying 0 by infinity is nonsense mathematically). And yet, who can prove categorically that He doesn't exist?
You might quibble that the going to Heaven is so fraught with tedium (imagine all those people in white robes playing harps constantly: who is to say they are any good? I'm leaving aside the 72 virgins for the moment) that the believer's infinitely positive payoff may not be so at all. If the payoff is not infinite, Pascal's argument breaks down.
Pascal was born into a devout Catholic family that detested the Jesuits, the intellectual arm of the Church. Indeed, his scientific study caused him no end of self-loathing because Bishop Jansen, the head of the sect that he belonged to, considered science a corruption and an unholy pastime, a lust that needed excision from society. Initially at least, his lust outweighed his devotions, and he came up trumps in a variety of scientific fields: probability theory, geometry, algebra, hydrostatics and atmospheric physics. Eventually, though, he went back to his faith, and gave up mathematics for the rest of his life (except for one strange incident when after a sleepless night occasioned by illness, he sat down to some mathematics; his pain disappeared and he concluded that God didn't mind him working on the subject).