Pascal's wager
From RationalWiki

Pascal's original formulation of the wager was written down 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 somewhat convoluted philosophy-speak,[2] but it can be distilled more simply:

1. If you believe in God and God does exist, you will be rewarded with eternal life in heaven: thus an infinite gain.
2. If you do not believe in God and God does exist, you will be condemned to remain in hell forever: thus an infinite loss.
3. If you believe in God and God does not exist, you will not be rewarded: thus a finite loss.
4. 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.

Criticism

There are many problems with the reasoning in Pascal's Wager, as well as the unsavoury theological assumptions it makes. Like most arguments for the existence of God, it seems more about reassuring existing believers than converting non-believers. This is because in order to convince a non-believer, a theological argument must both prove that the god it argues for is the One True God and disprove all other possibilities. People lacking a belief can see the potential for multiple gods existing, in fact an infinite number, but believers are constrained by their existing view that there is their god or no god. Only in this latter case does the reasoning behind Pascal's Wager make any sense.

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.

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.

“Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?”