"Either God exists, or he does not exist," argued Pascal, "and since neither proposition can be proved, we must wager. If we wager that God exists and we are right, we win everything. If we wager that God exists and we are wrong, we lose nothing." "You would be impudent," Pascal said, "to wager that God does not exist." So Pascal infers that if you wager that God does not exist, and you are wrong, you will suffer eternally.
Here is a quote from article 233 of Pascal's Pensees, in which he presents his "Game Theory" approach to this question:"Let us examine this point and say, "God is, or He is not." ... What will you wager? ... Let us weigh the gain and loss of wagering that God is ... there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite ... every player stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty to gain a finite uncertainty, without transgressing against reason ... the uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss. ... And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and loss, and the infinite to gain. Take a look at the following Payoff Table:
| How to live: | If God exists: | If there is no God: |
| Live Life as if God exists | +J | -B |
| Live life as if God does not exist | -A | +G |
| +J = the Joys of Heaven | - an infinite payoff if you believe and God does indeed exist. |
| -B = the Burdens of a Disciplined Life | - a finite negative payoff if God does not exist. |
| -A = the Anguish of Hell | - a definite infinite negative payoff if God does exist but you do not believe. |
| +G = the Gratifications of Life | - a small positive finite payoff if there is no God and you do not believe. |
So how could any rational human being wager against the existence of God? You stand only to gain a very small payoff (the Gratifications of this life), but you have so much to lose (to spend eternity in Hell!). And yet if you do believe in God, you have everything to gain (the eternal Joys of Heaven), and really nothing to lose (living a good disciplined life should not be considered a negative payoff).
Lord Byron rephrased Pascal's argument as "Indisputably, the firm believers in the Gospel have a great advantage over all others, for this simple reason -- that, if true, they will have their reward hereafter; and if there be no hereafter, they can be but with the infidel in his eternal sleep, having had the assistance of an exalted hope through life..."
Denis Diderot observed that the wager applies with equal force to other major religions such as Islam.