## Pascal's Wager

Setup: The utility of going to heaven is infinite, so if there is a chance that God exists, then decision theory tells us that the expected utility of believing in God is greater than the expected utility of not believing.

The problem here is that two different levels of probability are being confused. The statement "God exists" is either true or false. Therefore, the probability that God exists is either 0 or 1. When we say that there is a slight chance that God exists, we mean to say that there is a slight chance that the probability that God exists is 1. If we assign the value of this slight chance directly to the probability that God exists, it is effectively saying that when you die, somebody is going to roll some dice to determine whether God should be born or not. Therefore the paradox is resolved because the decision theory matrix splits into two cases, one where the probability that god exists is 1 and another for a probability of 0. The chance that you give that God exists simply determines which of these two matrices you look at.