Blaise Pascal (1623-1662) was a French mathematician and philosopher and religious thinker who played an important part in the early development of probability theory. He made lots of notes on pieces of paper, and thought of bringing them all together into a book. But he never did this. (They were brought together and edited after his death.) The famous "wager" was "written on four sides of a single folded sheet of paperclick to see photographs of the paper and contains paragraphs crammed into the text, others written vertically up the margins, and even upside down at the top of the page" (see Levi, Anthony, `Introduction' p. viii, in Pascal, Blaise, Pensées and other writings, Levi, Honor (trans), Oxford: Oxford University Press, 1995). Remember this as you read this text. It is an extract from a jumble of notes on a piece of paper which Pascal kept in his pocket. Notice that parts of the text are a dialogue. Pascal imagines that he is talking to someone who needs to be convinced, and puts in quotation marks the replies, comments and reactions of this imaginary interlocutor, to which he then replies in turn.
See Pascal, Blaise, Pensées et opuscules (Thoughts and minor works), ed. Brunschvicg, Léon, Paris: Hachette, 1922, III §233, p. 436 (translated by me - see also the translation mentioned above, pp. 152 ff, in which the paragraph number is §680):
infinity - nothing
................................
If there is a God, he is infinitely incomprehensible, since, having no parts or limits, he has no relation with us. We are therefore incapable of knowing either what he is or whether he exists. This being so, who would dare to undertake to resolve this question ? It is not ourselves, who have no relation with him.
So who will blame Christians for not being able to give reasons for their belief, those who profess a religion for which they cannot give reasons ? They declare, in explaining it to the world, that it is foolishness, stultitiam: and then you complain that they do not prove it! If they proved it, they would not be keeping their word: lacking proof is precisely not lacking good sense. -- "Yes: but even if this excuses those who offer such a belief, and removes blame from them for producing it without reasons, it does not excuse those who accept it." -- So let us examine this point, and say: "God either exists or does not exist." But which way shall we lean ? Our reason cannot help us: there is an infinite chaos which separates us. A game is played at the extremity of this infinite distance which will come up heads or tails. What will you bet ? By reason, you cannot do either one: by reason you cannot support either of the two.
So don't attack those who have made a choice, because you don't know. -- "No: but I shall blame them not for having made this choice, but for having made a choice at all. For the one who chooses heads and the other are equally at fault: the correct thing is not to bet at all."
-- Yes; but you must bet; it is not optional, you are in the game. So which one will you choose ? Let's see. Since you must choose, let's see what would be least in your interest. You have two things to lose: the true and the good, and two things to bring to bear, your reason and will, your knowledge and bliss; and your nature has two things to flee: error and misery. Your reason is not more wounded, in choosing one rather than the other, since it must necessarily choose. There is one point dealt with. Let us weigh the gain and the loss in choosing heads (that God exists). Let us work out these two cases: if you win, you gain everything; if you lose, you lose nothing. So wager that he exists, without hesitation. -- "That's very fine. Yes, it is necessary to wager; but perhaps I am wagering too much." -- Let's see. Given that there is an equal chance of losing or winning, if you stood to win two lives in place of one, you could still bet; but if there were three to win, you would have to bet (because you are obliged to), and you would be imprudent, when forced to play, not to bet your life to gain three lives in a game which has equal chances of loss and gain. But there is an eternity of life and happiness. This being so, if there were an infinity of chances with only one being winning, you would still be right to wager one to gain two, and you would act wrongly, being obliged to play, in refusing to play one life against three in a game in which you have just one winning chance out of an infinite number, if you stood to win an infinity of infinitely happy life. But in this case, there is an infinity of infinitely happy life to win, a chance of winning against a finite number of chances of losing, and what you bet is itself finite. This settles the matter: in each case involving the infinite, and in which there is not an infinity of chances for losing against the chance of winning, there is nothing to weigh up, you must give everything. In this way, when one is forced to play, it is necessary to give up the reasons for keeping one's life rather than gambling it, for the infinite gain which is as available as the loss of nothing.
Now it is useless to say that
it is uncertain whether one will win, and that it is certain what one is
putting at risk, and that the infinite distance between the certainty
of what one risks, and the uncertainty of what one would
win, equals the finite good which one certainly risks, to the infinite,
which is uncertain. This is incorrect. Every gambler bets something
certain to win something uncertain; and yet he is certainly betting something
finite for the uncertain gain of something finite, without being irrational.
And there is not an infinite distance between the certainty of what one
risks, and the uncertain gain: this is false. It is true that there
is an infinite distance between the certainty of winning and the certainty
of losing. But the uncertainty of winning is proportionate to the
certainty of what is risked, according to the proportion between the chances
of winning and losing. Consequently, if there are as many chances
on one side as the other, the game is to be played as equal against equal;
and thus the certainty of what is risked is equal to the uncertainty of
winning, so far from being infinitely distant from it. Accordingly,
our proposition has infinite force, when a finite bet in a game with equal
chances of winning and losing can win an infinite amount. That
is conclusive; and if human beings are capable of any truth, that is it.
-- "I admit it, I assert it. But is there no way of seeing the face
side of the cards ?" -- Yes, the scriptures, and the rest, etc.
-- "Yes, but my hands are
bound and my mouth is dumb; I am being forced to bet, and I am not free;
I am not released, and I am made in such a way that I cannot believe.
So what do want me to do ?"
-- "You're right. But
let us at least consider your inability to believe, given that reason leads
you to belief, but you are unable. So work, not at convincing yourself
by argumentation of the "proofs" that God exists, but at diminishing your
passions. You want to go towards faith, and you don't know the road;
you want to cure yourself of being faithless, and you ask for the remedy;
learn from those who have been constrained like you, and who now gamble
all that they have; they are people who know the path that you want
to follow, and cured of an ill which you want to cure. Follow the
way in which they began; that is, doing everything as though they believed,
taking holy water, having masses said, etc. Quite naturally,
that will make you believe, and make you like an animal.
--"But that's just what I'm afraid of !" -- Why ? What have you to
lose ?