Pascal's Gamble Revisited

Pascal's Gamble has always sparked my interest because it soundly rejects a norm I've always detested-- that the theory which is most likely true should always be preferred as utterly superior. In fact, choosing to believe with rational intentions requires knowledge of the probability of many competing theories, with the best choice being, oftentimes, "inferior."



For those unfamiliar with the gamble, it goes as follows:
1. When you die, one of two things is true: God is real, or God is not real.
2. If you believe in God and He is real, you will be rewarded infinitely.
3. If you believe in God and He is not real, you will have been inconvenienced in only a finite way.
4. If you do not believe in God and He is not real, you will have lost nothing and gained nothing.
5. If you do not believe in God and He is real, you will be punished infinitely.
6. It is, therefore, rational to believe in God.

Given assumptions 1-5, 6 is true for any probability of God's existence as the rewards and punishments imposed by God are infinite-- so the theory goes. To illustrate, if we were to calculate the value of each belief as measured by (probability of outcome) times (result of outcome), and suppose that the liklihood of God's existence is but .0000001, it would look something like:

Belief in God: .9999999(-100) + .0000001(infinity) = infinity
Non-Belief in God: .9999999(0) + .0000001(negative infinity) = negative infinity

Though his theory has received many critiques, Pascal has been unfairly accused in many respects. For example, that God would find your belief unworthy if formulated in such a manner is pretty obviously inane-- there's no reason to so postulate.

The one that stands out is that, given no evidence, the probability of God's existence is infinitesimal, and further, that the existence of "counter-gods" whose moral requirements antagonize God is of equal likelihood. So if you believe in one god with a list of requirements, it may turn out, when you die, that a different god exists who punishes you for abiding by those requirements.

Consider that but one thing is required to nullify this demur: God's existence having *some* evidence, and likewise a likelihood greater than a God that would "counter" Him.

I pose that perhaps this evidence is found in the numerous testimonies and witnesses of His existence. Even though these can be explained in perfectly reasonable ways that exclude God's existence, one is hard pressed to argue that the odds He exists are not even remotely increased as result of them. If we give that this evidence lends the probability God exists as being higher than infinitesimal, Pascal's Gamble, it seems, holds.


A few more ideas on the subject: first, perhaps the rewards of heaven and pains of hell are not actually infinite or negatively infinite respectively. Perhaps because it is inconceivable and understandably logically impossible to experience, at any given time, "infinite pain" or "infinite happiness", and because we will never experience an infinite length of time- we can only have an infinite length of time ahead of us- the calculation with regards to religion deals with finite numbers and, though large, are multiplied by exceedingly slight probabilities, thus, at least possibly, resulting in non-belief as a more rational choice when belief is an inconvenience.

Another possible refutation concerns the nature in which such a calculation- when infinite- seems unreasonable. Consider if you are presented with two religions, religion A and religion B. You know the chance that religion A is correct is 99.9%, and that the chance religion B is correct is .1%. If you are rewarded infinitely for believing in the religion that so happens to be correct, calculating (reward) times (possibility of reward) results in infinity in both cases, despite that it seems clear to choose religion A.