QuestionsDoes God exist?The wager
Does God exist?TheismPractical reasons (the wager)

The wager

Blaise Pascal 1623 · 1662The heart has its reasons which reason knows nothing of.
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What it claims

One must wager that God is.

Why

If God exists you win infinite happiness; if not, you lose only something finite, and you cannot abstain from betting.

In short

"The wager" is an argument by Blaise Pascal (Pensées, B233) on the question "Does God exist?" (answer: theism). Its claim: One must wager that God is. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4). AskPhilosophy presents 6 objections, 5 of them with a documented reply, and the original text behind each premise, checked word for word.

Pensées, B233
Valid with an implicit premise

Pascal does not claim to prove that God exists: reason cannot settle it. He argues something else: since we must choose, it is more reasonable to wager that God is.

P1We cannot abstain: not choosing is already wagering against.
P2Reason cannot decide: there is a real chance that God exists.
P3Wager that God is: if you win, you win everything (infinite happiness); if you lose, you lose only something finite.
P4 · implicit premiseNo other option promises the same infinite gain: the choice comes down to "God is" or "he is not".
P5When forced to play, if an infinite gain has a real chance and only something finite is staked, one must stake on that gain.
Therefore one must wager that God is.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.
Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, the computer finds a case where we must play and an infinite gain has a real chance for a finite stake, but another option also promises infinity: the rule no longer picks out a single bet.
With its five premises the conclusion follows. Without P4 it no longer does: if another religion also promised an infinite gain, the calculation would not say which god to bet on. That is exactly where the most famous objection strikes.
Analogy. You are forced to buy a ticket. One costs little and gives a small chance of an unlimited treasure; the other pays almost nothing. Pascal says: take the first. The whole question is whether there is only one ticket of that kind.

Objections

6

Each objection is a conversation: click to see who replies and where the debate stands.

Objection anticipated by Pascal attacks premise 5

The gain is uncertain, the stake is certain: staking something sure for a doubtful gain is not reasonable.

Pascal replies
Pascal
Every gambler stakes a certainty for an uncertain gain without being unreasonable. What matters is the ratio between chances and stakes: against an infinite gain, a finite stake is worth it.
Where the debate stands (our summary)Pascal treats the wager as a game of chance, where one always stakes something certain against something uncertain. Today's disagreement is less about this analogy than about the value to give an "infinite" gain (see Hájek's objection below).
T
The unbeliever in the dialogue attacks the conclusion

I am willing to wager, but I am so made that I cannot believe: one does not decide to believe as one tosses a coin.

Pascal replies
Pascal
Begin by acting as believers do (practices, prayers): this lessens the passions, which are the real obstacle to faith.
Where the debate stands (our summary)Disputed: Pascal proposes acting as believers do so that belief follows; his critics (James, below) think a faith obtained this way lacks sincerity, and others ask whether one can really come to believe by habit. No consensus.
Diderot 1762 · attacks premise 4

The reasoning works for any religion: an imam could say exactly what Pascal says. So it does not tell us which god to bet on.

a defender replies
No reply possible: objection raised in 1762, after the author's death (1662).
W
William Lycan and George Schlesinger defender of the argument · 1989
Summary: among possible gods, not all are on a par. The traditional God, defined as absolutely perfect, is the simplest hypothesis; rival gods, being more arbitrary, are less simple and so less probable. The wager would therefore not be symmetrical between all religions.
J
Jeff Jordan defender of the argument · 1994
Summary: Jordan sets aside gods with no backing in any living religious tradition: they are not real options for an actual person. The wager addresses those for whom only a few options are serious, and a choice among those remains.
Where the debate stands (our summary)Defenders of the wager shorten the list of serious gods (simplicity, backing of a tradition), but several candidate religions remain: the wager alone does not say which to choose. The basic disagreement is about how to assign probabilities to different religions.
Voltaire 1734 · attacks the conclusion

My interest in believing something does not prove that it exists. The wager gives a reason to want to believe, not a reason to think it true.

a defender replies
No reply possible: objection raised in 1734, after the author's death (1662).
J
Jeff Jordan defender of the argument · 2006
Summary: the wager does not claim to establish that God exists; it gives a practical reason to believe. Jordan argues that when the evidence does not settle the matter, it is legitimate to form a belief for practical reasons, in the line of William James.
Where the debate stands (our summary)Both camps agree on one point: the wager proves nothing about God's existence. The disagreement is about whether it is legitimate to form a belief (or an acceptance) for practical reasons when the evidence does not settle the matter.
William James 1896 · attacks the conclusion

A faith adopted wilfully after such a mechanical calculation would lack the inner soul of faith's reality. If we were in God's place, we should probably take particular pleasure in cutting such believers off from their infinite reward.

no reply
No reply possible: objection raised in 1896, after the author's death (1662).
Where the debate stands (our summary)Open point: we found no widely accepted reply. Pascal himself presents the calculation as a starting point, before practice and the lessening of the passions, but whether God would reward a belief born of self-interest remains disputed.
A
Alan Hájek 2003 · attacks premise 4

Summary: if one computes expected gain, other choices also promise infinity. A mixed strategy (for instance tossing a coin and wagering on God only on heads) gives a positive, even if small, chance of the infinite gain: its expectation is therefore infinite too. Almost any action can be described this way, and the calculation no longer discriminates. The objection goes back to Antony Duff (1986).

a defender replies
No reply possible: objection raised in 2003, after the author's death (1662).
B
Bradley Monton defender of the argument · 2011
Summary: if the toss gives tails, one can toss again. By repeating, one almost surely ends up with heads, hence wagering on God. The mixed strategy does not dispense with the wager: it leads to it with probability 1.
S
S. Robertson 2012
Summary: some mixed strategies escape this reply: they can be built so that the probability of ending up wagering on God stays below 1.
See the rest of the debate (1)
K
Kenny Easwaran and Bradley Monton defender of the argument · 2012
Summary: considering a continuum of times at which one may toss, they maintain that Monton's reply still holds, and that mixed strategies do not evade the wager.
Where the debate stands (our summary)The technical debate remains open: it concerns what is rational when expected gains are infinite, and the assumptions (repeated tosses, uncountably many times) on which Monton's reply depends. There is no agreement on its validity.
What today's voices say
Defend it
William Lane CraigHe says that even if the evidence were equal, it would be irrational to prefer death, futility and despair to hope, meaning and life; but he thinks the evidence is not equal.
Criticize it
Ricky GervaisTo 'why not pray just in case?' he replies: 'why don't you hang garlic over your door in case there's a Dracula?'
Christopher HitchensHe compares a preacher pitching belief on those terms to a huckster trying to pull you into his parking lot.
Richard DawkinsHe says you cannot make yourself believe something, and asks what kind of good God would reward flattery over honest reasoning.
Alex O'ConnorHe answers it with an "Atheist's Wager": a just God would reward moral people, not mere believers.