Pascal's Wager Content from the guide to life, the universe and everything

Pascal's Wager

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What do you lose if you're a Christian and you're wrong?
Now, what do you lose if you're an atheist and you're wrong?
Based upon those arguments, which is objectively the safer bet?

History of the Wager

This is an old argument for belief in the existence of the Christian God and is known among philosophers and theologians as Pascal's Wager. The name is taken from that of Blaise Pascal (1623-1662), who formally wrote down the argument in his Pensées. However, the first recorded use of this argument was by the Roman Emperor Constantine, in 312 AD. Throughout his life he was the head of the cult of Sol Invictus, but he agreed to be converted and baptized on his death bed, as a precaution that the Christians had been right all along. His choice has been followed by many others and it is still the case that people are more likely to find or change religion as they draw closer to death.

While some critics may feel that Pascal's Wager is completely worthless, they should remember that we've had the benefit of 350 years of philosophy since it was formulated, and at the time it was cutting edge stuff - significantly advancing the fields of philosophy, theology, and effectively creating from scratch the field of probability. Pascal is often described as 'the father of probability', and with good reason.

Since Pascal died, people have continued to expand and evolve his Wager, exposing new possible weaknesses, finding new clearer ways to explain things, or showing how apparent problems can be resolved. There is no sign that this process has now stopped.

The Original

When the argument is presented as a definitive proof that people should believe in God, it normally takes the form of a decision matrix1. There are essentially three different ways to construct the matrix - Pascal used all of them in his writings. The first is as follows:

God existsGod does not exist
Wager for GodHeavenNo consequence
Wager against GodHellNo consequence

Naturally, Heaven is a better outcome than Hell. The first assumption of the Wager is that the only choice is between wagering for God and wagering against God. The entries in the decision matrix represent the second assumption. The third assumption is that the probability that God exists is not zero or infinitessimally small. If you accept these three assumptions, then to maximise your returns you should believe in God. That the correct thing to do is to maximise your returns is the fourth assumption. In logic, it's worth stating even seemingly trivial assumptions - better that than stand accused of hiding them. Of course, if you disagree with the logic of the Wager, then you can still believe in God - there are many potential arguments for God and this is merely one.


For some people, there is an immediate problem in that believing in God does have consequences if He does not exist, though they are almost certainly minor in comparison to eternal life or damnation. You may spend time in church that could be better spent helping others or yourself. If you become a martyr to your religious beliefs the consequences are huge if those beliefs are misplaced, as members of the Heaven's Gate2 religion may have found out. This is a worry about the second assumption.

Of course, in some situations, the opposite is true; belief in Christianity can enormously help you through life. It can give comfort, hope, and inner peace, and help you fit in with your society. Many Christians find that God helps them make sense of the world around them. It can even, if you become a religious adviser of some kind, give you power over your fellow man. It can do all this even if it happens to be incorrect. If you are in this situation, then the Wager becomes simpler still; whether God exists or does not, you are seemingly better off wagering for Him.

Equally, many Christians say that their lives are more fulfilling and generally more enjoyable and fun when they are living dedicated to God. It is difficult to say whether this is in fact true. Of course, it's easy to suspect that Christians believe this because it is essential to their religion - that it is believed in the same way that the resurrection is believed. It is worth noting, perhaps, that born again Christians in the USA are more likely to be convicted for drug-related offences than the rest of the population - evidence that some, at least, are enjoying themselves in their newfound life.

The Sequel

Realising these potential objections, Pascal went on to give an alternative formulation. This time, he made the claim that heaven is infinitely better than hell. This claim can be justified either by claiming that heaven is an infinitely good result, or that hell is an infinitely bad result, or both. This time the matrix is as follows :

God existsGod does not exist
Wager for GodHeavenSmall downside
Wager against GodHellSmall upside

Again, not everyone is happy with this second formulation. Finitists - those with the belief that the infinite does not occur in this universe - argue that an infinite reward is not possible. Others argue that even if Heaven is indeed infinitely good, or Hell infinitely bad, a finite human being can only experience a finite reward. Again, second assumption worries.

The other, more subtle, problem with this formulation occurs if the claim is that Heaven is infinitely good, while Hell is merely finitely bad. Clearly, the net reward for wagering for God is then infinitely good, while the net reward for wagering against him is finite. Now, suppose you choose to make the decision by flipping a coin, the net reward for this decision is also infinitely good. In fact, provided you ensure that there is any chance that you will believe in God in the future, your net reward will be infinite. Universal salvation, indeed!

On a similar note, if Heaven is infinitely good, and Hell is infinitely bad, then the net reward if you make the decision by flipping a coin is infinity minus infinity, which is undefined. The same thing occurs if there is any chance that you will end up believing, and any chance that you will end up not, which makes the fate of most real people effectively unknowable.

There are even those that claim that both Heaven and Hell would be infinitely bad, because both last for an eternity, and as such would eventually become excruciatingly boring. 'Oh no, not another day glorying in the everlasting majesty of the father.' Christians in general tend to claim that glorying in the everlasting majesty of the father would never become boring, which either shows their greater spirituality, or that they have no sense of adventure, depending upon which way you look at it.

The last problem of this type that has been raised is one that some people find offensive - the claim that God, as presented to them, is an immoral being, so if he did exist, they would not wish to support him. Whether these people have really understood the concept of God is, perhaps, somewhat doubtful, but their objection does make sense from their own point of view. If they knew that God existed they would morally have to become a devil-worshipper, and hence the pay-off for believing in God if he existed would also be Hell. Because of this, the Wager has completely the opposite effect for them.

Probability of God

The third assumption is that the probability that God exists is neither zero, nor infinitesimal, and is common to both the arguments so far. Many 'strong' atheists claim that the probability that God exists is indeed zero. There are a number of arguments they might use to justify this belief, such as the problem of evil, or the problem of unjustifiable suffering. Of course, none of these arguments hold any weight with those who do believe in God - religious consensus has long been seen as an impossible dream. Generally, few people are so sure of themselves as to accept this counter-argument, but there are some.

Alternatively, some agnostics might claim that the probability that God exists is completely undefined. We know so little about the universe in general, and God in particular, that any attempt to place a number would be irrelevant. As such, the Wager doesn't even get off the ground. The correct behaviour when faced with undefined probabilities is not obvious - some say that an assumption of 50% should be made, others that the correct behaviour must be deduced from other considerations, or that there is no 'best' decision.

Frequentism (or operationalism) is the mathematical standpoint that probability can only be defined on the basis of performing multiple experiments, and because there is no experiment to perform to determine the existence of God, it is undefined. The frequentist standpoint was undermined somewhat when it was pointed out that the only way a frequentist could determine the probability of the moon being made of blue cheese was to visit it a large number of times, and each time check whether it was made of a dairy product. Many people find this concept laughably dumb.

Worse still, some people find that Pascal's Wager itself is an argument that disproves God's existence. They say that Pascal's Wager could be used to require belief in any proposition P of the form: 'Belief in proposition P will bring an infinite reward and X'. This would lead to a large number of mutually exclusive beliefs, which would be irrational. Therefore, any such proposition must be false. This is not a totally sound logic, though, as it pre-supposes that the universe is, in fact, totally rational - a hotly contested viewpoint.

The Final Part of the Trilogy

The third formulation is less of a formal proof, but more of a dose of what seems to be plain common sense. Here, we don't sweat too much over whether Heaven is infinitely or merely finitely better than hell, but merely claim that the benefit from Heaven versus Hell is at least hundred times the cost of belief versus non-belief. Nor do we sweat overly about the exact probability that God exists, but merely claim that it is greater than 1%. With these two claims, the way to maximise expected returns is to once again believe in God.

Generally, the big variable with this is what you think the chances are that the various sets of God or gods exist. Part of the problem if you use the Wager to try and convince others of your cause is that probability varies wildly from person to person - a religious fanatic might say that the chance that God exists is 100% because he's seen him in a vision, and the chance that any other Gods exist is 0% because The Bible says so, and for that person Pascal's Wager is irrelevant. Meanwhile, an atheist might say that the chance that God exists is barely 0.1%, the chance of other gods is 1%, and for that person the Wager is not a valid argument at all.

However, for someone who is weak in their faith, perhaps placing the chance of God existing at just 20%, and other gods at around 5%, arguments along the lines of the Wager provide a powerful incentive to keep their faith, until they can find out more information. Whether this is a good or bad thing is, of course, a subject for fierce debate.

Bigger Tables

The issues to do with the first assumption (that there are only precisely these two rows and columns in the table) are common to all three formulations of the Wager, and some believe that they disprove all three of the Wagers at once. The most frequently claimed flaw of them all is that the Wager totally ignores other religions - if God doesn't exist, but some other gods or goddesses do, you could end up avoiding the wrong Hell. Effectively, this argument is subdividing the 'God does not exist' column into many columns, each containing the possibility that some other religion is true.

Discordianism has a superb example of this problem in its Hell Law which states:

Hell is reserved exclusively for them that believe in it. Further, the lowest Rung in Hell is reserved for them that believe in it on the supposition that they'll go there if they don't3.

In the unlikely event that Discordianism is correct, then Pascal's Wager is possibly the most dangerous idea you've ever heard!

Another potential flaw is that, in many religions, agnosticism is a lesser flaw than belief in false gods. This feature is included in branches of such dominant religions as Judaism, Islam, Christianity, Buddhism, as well as some dead religions, such as the pantheons of the Greeks, Egyptians, and Norsemen. If you choose religion on the basis of weighing up the odds, then perhaps the safest bet is to stick your fingers in your ears whenever religion is mentioned.

Certain people claim that the rewards are not the same for them as they are for others. For example, for some the prospect of salvation may not be appealing. Those who don't take religion seriously have even been known to argue that Hell would have better theme music, as all the best musicians have led lives of sin and excess.

This final objection with the first assumption of the Wager is one that probably has as many subscribers among Christians as non-Christians. They argue that if you believe in God for the mercenary reasons that Pascal proposes, then this belief is not proper belief, and will not get rewarded as would belief through faith. Faith is a very important part of mainstream Christianity, and one that many believe is not optional.

Acting Illogically

The fourth assumption - that we should act so as to maximise our returns - seems, at a glance, to be totally obvious - why would anyone act any different? However, there are objections here too. The first is practical insomuch as well as maximising returns, it is worth minimising risk. If Hell is not particularly bad - as in the case where God is claimed to be benevolent even to non-believing sinners, or where Heaven can be entered based on works, the less risky option is to not believe. Of course, the opposite is true in that if God is claimed to be a fire and brimstone lover, where Hell is horrendous, and Heaven is just vaguely nice - then the less risky option is to believe. However, normally God is presented as a kind, forgiving deity, so the former is, perhaps, more likely.

Some people don't really find it possible to choose to believe in something one doesn't think is true. For such people, the Wager is an unpleasant fact of life, which can no more be changed than the discovery that tall men are viewed as more attractive can change someone's height (unless one wears high heels). Pascal had thought of this objection, and his response was that though it might be difficult to change one's belief directly, one could try to act in such a way that it would change later. One can spend time in church, reading holy texts, praying, meditating, and so forth. Gradually, acting as though one believes something is supposed to be likely to lead to eventually believing that thing. Modern psychology theories partially support him in this idea, as do the experiences of countless believers around the world.

There is also the question of morality - some have argued that it is somehow immoral for God to give special favour to those who believe in Him despite there being no good evidence for Him. In fact, good evidence for God could be the subject of a whole new entry. In which case taking advantage of God's act would make the believer complicit in immoral behaviour. This is a very combative stance to assume, since it effectively states that all Christians are immoral, and is generally understood to be inappropriate in polite company.


Pascal's Wager was originally conceived as an argument for the Christian God and that is how this entry has treated it. However, it is worth bearing in mind that it could be seen to apply to a fairly large range of religions. Any religion, in fact, where belief in the religion gets you a large benefit, and non-belief a large penalty - which includes a good number of them. The changes that need to be made to the arguments are fairly obvious, and the same objections can be raised along the way. Christianity, however, is possibly the religion for which Pascal's Wager is most effective, with elements such as 'only way to the Father', 'salvation through belief', 'eternal life', and 'eternal damnation'.

Aside from religion, arguments along the lines of Pascal's Wager can also be used to argue against predestination, solipsism, and relativism, among other philosophical discussions. In these rather more formalised settings it is perhaps a little more successful.

Whether Pascal's Wager is a reason to believe in God is extremely personal - while it may convince some, others will find it totally irrelevant. This means it is not the best way to try and convince someone to believe in God because what seems perfectly logical to you may sound like utter madness to the person you are talking to - and vice versa. Be grateful if it works for you, but try no harder.

1A simple tool used in probability.2A cult called Heaven's Gate committed mass suicide in San Diego a couple of years ago, when the comet Hale-Bopp passed through. They were convinced that there were no gods but aliens, using the comet as camouflage for their ship. The aliens were coming to pick up the faithful, who could only catch a ride after 'shedding their earthly bodies'. The males had all been ritually castrated, and everyone donned purple Nike jumpsuits and track shoes, and proceeded to imbibe poisoned Kool-Aid.3From The Gospel according to Fred, 3:1 and the Principia Discordia, page 37.

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