Pascal's wager is an argument that asserts that one should believe in God, even if God's existence cannot be proved or disproved through reason.
Blaise Pascal's original wager was as a fairly short paragraph in Pensées amongst several other notes that could be considered "wagers".[1] Its argument is rooted in game theory and that the best course of action is to believe in God regardless of any lack of evidence, because that option gives the biggest potential gains. Pascal's original text is long-winded and written in somewhat convoluted philosophy-speak,[2] but it can be distilled more simply:
If you believe in God and God does exist, you will be rewarded with eternal life in heaven: thus an infinite gain.
If you do not believe in God and God does exist, you will be condemned to remain in hell forever: thus an infinite loss.
If you believe in God and God does not exist, you will not be rewarded: thus a finite loss.
If you do not believe in God and God does not exist, you will not be rewarded, but you have lived your own life: thus a finite gain.
The gains and losses associated to outcomes 3 and 4 can be thought of as the opportunity costs of feigning belief and living in accordance with religious norms, since these are typically more restrictive than secular laws. These costs are finite because of human mortality. Mathematically, a finite gain or loss is negligible compared to an infinite gain or loss as would be incurred during an eternal afterlife. Therefore, Pascal concluded that it was a much better choice to believe in God rather than not. The Wager can also be seen in table form and it becomes clear that belief gives you a reward or
(practically) nothing, while disbelief gives you punishment or nothing:
Pascal's wager makes a number of assumptions about reality, and a number of theological assumptions about the god it argues for. If any of these can be shown to either be false or undesirable, then the power of the Wager for determining one's actions and beliefs is severely weakened - indeed, the argument of the Wager can be reversed in some cases and it can argue for non-belief. These mostly stem from the theological implications of applying the Wager to belief in God, rather than the Game Theory attributes and decision making process presented.
Evil
There are several ways in which the Wager can be said to promote evil.
Total self-interest
The Wager assumes that a believer will only care about maximizing their own gains.
More troubling than this are occasions where you might theoretically be called upon to hurt someone else to advance your worship of the superior entity. This forms a flip side to the argument that Pascal's Wager emphasizes belief over worthiness in that it suggests that outright evil people can gain reward and avoid punishment simply through belief.
In the Old Testament there are numerous instances when worshipers had to kill and hurt others as commanded by God. In fact, there are occasions in which God was extremely displeased that they didn't take the abuse of fellow humans far enough. Even with the Pascal's Wager metric in place, one could argue that it's more moral to resist these commands for the sake of others even if it results in an infinite loss for you.
Again, it can be demonstrated on Earth that bad people who do bad things can still profess belief—Pascal therefore suggests they are worthy of infinite gain, and atheists cheekily suggest that being around those people in heaven isn't selling the whole belief thing to them very well.
The moral case for dead children
If you ask most Christians whether children who die when they are very young will go to heaven, they will say yes.
So it would be most reasonable to kill your children while young (especially since children today are much more likely to become atheists), rather than risk them leaving the Christian faith.
Problem of evil
If, as Pascal's Wager must assume, God is willing to punish good people simply for a lack of belief, this would preclude God being "good" by any sense that we understand the concept of "good" — and "good" is a necessary property of God, at least as understood by Christianity. As it can be demonstrated on Earth that no single specific religion has a monopoly on good and moral people, a God that causes Pascal's Wager to be valid cannot be focused on spreading good around the world.
Various responses to Pascal's Wager involve pointing out that to be at the constant beck and call of such a clearly evil being would be less preferable to hell, and so it is favorable to disbelieve.
Multi-theism
The biggest irony of Pascal's Wager as far as Christian apologetics go is that even if it was otherwise completely sound it should then suddenly become a huge disincentive for convincing an unbiased party to worship YHWH specifically. By definition worshiping the Judeo-Christian God requires the worshipper to actively reject the existence of every other deity or potential deity thanks to the intolerance that is the First Commandment. In the absence of evidence for a specific deity, the theist-to-be would be better off directing some worship to one or more proposed deities that do not require exclusive worship. Pascal's Wager being a lynchpin of Christian apologetics (rather than being a shibboleth that must be denied at all costs) can be viewed as a case of cognitive dissonance engendered by Christian privilege.
Infinite number of gods
In Bayesian terms, this can be stated as saying non-believers attribute uniform prior probabilities to the existence of any particular god; all equal, and all infinitesimal. Pascal's Wager alone cannot update these probabilities as the reasoning applies only to the One True God out of an infinite number of possible gods.
Without any further information to whittle this down, the odds of inadvertently worshiping the wrong god is a practical certainty. Only when the probability of a particular god existing increases does Pascal's Wager become useful, i.e., if one god could be assigned even a mere 1% chance of being the One True God, Pascal's Wager would present a clear benefit. Hence for anyone constrained by a bias towards a particular god, the Wager is far more clear cut and supportive of their belief.
Anti-gods
If one is willing to accept that an infinite number of deities exist, then Pascal's Wager leads to a very interesting conclusion.
First: There can be an infinite number of possible gods. Why? There are an unlimited number of attributes that a god can have. If two gods have different attributes then they are different. For example, God A hates bananas, while God B likes bananas, while God C is indifferent to bananas, while God D likes bananas half as much as God B, while God E likes bananas twice as much as God B. A different attribute means a different god; there is no limit to the size of the set of divine attributes; thus, the size of the set of all gods infinite.
Second: Of the infinite set of gods that can possibly exist, there necessarily is a god that fits any and every system of rewarding/punishing people in the afterlife. This is because, in the infinite set of gods, every possible attribute of a god must occur. (Otherwise, it wouldn't be infinite, as it would have some limit to the attributes gods can have (other than being possible).) It follows that, for every god n, there necessarily must exist a god -n, who rewards/punishes people for exactly the opposite of what god n does.
The modified Wager can be expressed in the following table
here,along with more on the topic