Pascal's Wager sounds convincing at first, but if you think clearly about it, the wager quickly reveals itself as deeply flawed logic.

In short, the wager says that

1. If the Christian god is real, then you either receive eternal reward (+infinity) or eternal punishment (-infinity) based on belief.
2. If the Christian god is not real, then you do not stand to gain or lose much by believing in the Christian god (say, +1/-1).

The wager concludes that not believing in the Christian god is too risky for the modest potential gains.

However, the second point is not at all true. There are infinitely many possibilities that could completely change the expected value of the wager. Here are a few examples:

• There exists a god that punishes only Christians and rewards everyone else.
• There exists a god that punishes people who believe in him based on probabilities (such as Pascal's Wager).
• There exists a god who punishes everyone who is not an atheist, and rewards atheists for not believing in him.

For Pascal's Wager to really hold up logically, one has to show that the Christian god is more likely than any of the infinite other possibilities. There is no a priori reason to expect that. The reason that Pascal's Wager sounds so convincing at first is that the Christian paradigm was common among Pascal's peers (and still is many places), hence the Christian god seemed plausible whereas other possibilities were not considered equally plausible.

Pascal's Wager sounds convincing at first, but if you think clearly about it, the wager quickly reveals itself as deeply flawed logic.

In short, the wager says that

1. If the Christian god is real, then you either receive eternal reward (+infinity) or eternal punishment (-infinity) based on belief.
2. If the Christian god is not real, then you do not stand to gain or lose much by (not) believing in the Christian god (say, +1/-1).

The wager concludes that not believing in the Christian god is too risky for the modest potential gains.

However, the second point is not at all true. There are infinitely many possibilities that could completely change the expected value of the wager. Here are a few examples:

• There exists a god that punishes only Christians and rewards everyone else.
• There exists a god that punishes people who believe in him based on probabilities (such as Pascal's Wager).
• There exists a god who punishes everyone who is not an atheist, and rewards atheists for not believing in him.

For Pascal's Wager to really hold up logically, one has to show that the Christian god is more likely than any of the infinite other possibilities. There is no a priori reason to expect that. The reason that Pascal's Wager sounds so convincing at first is that the Christian paradigm was common among Pascal's peers (and still is many places), hence the Christian god seemed plausible whereas other possibilities were not considered equally plausible.