"Pascal's wager is exactly like this [betting] game, except that it uses a different set of envelopes: Christian and athiest. (Actually, Pascal only analyzed the Christian case, but the athiest case is the logical extension.) For the sake of argument, imagine for a moment that there's a 50-50 chance that God exists. (Pascal assumed that it would be the Christian God, of course.) Now, choosing the Christian envelope is equivalent to choosing to be a devout Christian. If you happen to choose this path, there are two possibilites. If you are a faithful Christian and there is no God, you just fade into nothingness when you die. But if there is a God, you go to heaven and live for eternity in bliss: infinity. So the expected value of being a Christian is:
1/2 chance of fading into nothing 1/2x0 =0
1/2 chance of going to heaven 1/2xinfinity =infinity
-------------------------
Expectation= infinity
After all, half of infinity is still infinity. Thus, the value of being a Christian is infinite. Now what happens if you are an athiest? If you are correct--there is no God--you gain nothing from being right. After all, if there is no God, there is no heaven. But if you are wrong and there is a God, you go to hell for an eternity: negative infinity. So they expected value of being an athiest is:
1/2 chance of fading into nothing 1/2x0 =0
1/2 chance of going to hell 1/2x negative infinity =negative infinity
---------------------------------------
Expectation= negative infinity
Negative infinity. The value is as bad as you can possibly get. The wise person would clearly choose Christianity instead of atheism.
This seems to always be the case, even if its a one in one billion chance that God does indeed exist. The only exception is zero.
If there is no chance that God exists, Pascal's wager--as it came to be known--makes no sense. The expected value of being a Christian would then be 0x infinity, and that was gibberish. Nobody was willing to say that there is a zero chance that God exists. No matter what your outlook, it is always better to believe in God, thanks to the magic of zero and infinity. Certainly Pascal knew which way to wager, even though he gave up mathematics to win his bet."
--from the book Zero: The Biography of a Dangerous Idea by Charles Seife | 
