Pascal's wager

"While men are gazing up to Heaven, imagining after a happiness, or fearing a Hell after they are dead, their eyes are put out, that they see not what is their birthright." -- Gerrard Winstanley, The Law of Freedom, 1652


The life of the great mathematician, physicist and religious philosopher Blaise Pascal (1623-1662) is interesting and full of paradoxes. Pascal was a genius who, at young age, started to solve mathematic problems. He was a very intelligent man, who based all his considerations on logic and reason, but an accident with a carriage in 1654 changed his life dramatically.

Pascal got into religious ponderings and started to live as a guest at the convent Port-Royal, where his sister stayed. He would live there for the remaining eight years of his life. The Jansenists who ran the convent were strict moralists and logists, so Pascal never lost his rational basis for his beliefs.

One of Pascal's greatest contributions to mathematics was in the area of probability, much thanks to his friendship with the gambler Chevalier de Méré. The basis for his faith was a combination of the radical scepticism of the speculator Montaigne and an obsession for brobability calculus. Pascal's reasoning was that since nothing is known for certainity, the christian faith may be as good as any other belief, and since the possible gain from belief is so much greater than the possible gain from unbelief, christianity was the bet that gave the highest gain. This is what is referred to as Pascal's wager.

Another popular version of the wager is that if you are wrong, you will not lose anything from being a theist, while atheists who are wrong will go to hell. An atheist friend of mine said a while ago that if you were smart you would turn christian, because it would be so awful in hell. She does agree with me, however, that it is not a good argument, after I printed out this page and gave it to her :-). This version has the advantage of being more convincing (nobody wants to go to hell), but lacks the optimism and more happy view of God that Pascal's original version has.


  1. Missing possibilities
  2. The main problem with Pascal's wager is that it suffers from the fallacy of bifurcation. It only calculates with two options when there are, in fact, at least four alternatives: The christian God and afterlife, some other god and afterlife, atheism with afterlife, and atheism without afterlife. Therefore Pascal's wager is invalid as an argument.

  3. Avoiding the wrong hell problem
  4. Because of the multitude of possible religions, if any faith is as likely as the other, the probability of the christian being right is P=1/n where n is the number of possible faiths. If we assume that there is an infinite amount of possible gods (i.e. ideas of gods), the probability of you being right is infinitely small.

    Because Pascal's wager fails to tell us which god is likely to be the right one, you have a great probability that you picked the wrong religion and go to some other religion's version of hell. This is referred to as the "avoiding the wrong hell problem"

  5. Worse hells and greater heavens
  6. Pascal's wager is the product of the gain from a certain belief and the probability that it is the correct one (in Pascal's reasoning 50-50, but as mentioned above the probability is much less.) such as Win=Gain*P. This leads us to the conclusion that we should pick the religion with the worst hell and the greatest heaven. In that case we should chose to worship the Invisible Pink Unicorns (IPU) because they have an infinite bad hell and an infinitely wonderful heaven, unless, of course we can show that the probability of the existance of an IPU is exactly zero, i.e. you can prove for certainity that they don't exist. If it is only close to zero we still have infinite gain/loss since infinity times any positive value is still infinity.

  7. Atheist alternatives
  8. The argument is based on the false assumption that atheists don't gain anything efter they die. Most atheists don't believe that they do, but there are other possibilities than just going to heaven vs ceasing to exist, such as progression to a better plane, or hanging around as ghosts. Neither of those require the existance of gods to be possibilities.

  9. Detesting life?
  10. An example of a widespread atheist view on life after death is the Buddist belief in reincarnation. Personally I would suggest that this is the bet that gets the most gain, since it lets you play again, and again, and again... for eternity.

    Theists may say that the gain from heaven is greater than the gain from life on earth, so their faith is a better bet than belief in reincarnation. But they miss the point that living for eternity will give you infinite gain as long as the gain is positive, because infinity times any positive number is still infinity. Even infinity times infinity is still infinity, so the only possibility that would give theists better gain than Buddists is if the gain from life on earth is negative or exactly zero. Therefore you have to detest life and the world for the argument to be valid.

  11. Blasphemy worse than un-belief
  12. Believing in the wrong god has one additional problem. Most religions assure you that blasphemers will be more severely punished than un-believers. Once again, if we calculate with the rest of the possible gods, the chance of you being wrong is P=1-(1/n) so you both run a bigger risk than the atheist of being punished and risk the greater punishment.

  13. The loss from religion
  14. Pascal also made the incorrect statement that you would lose nothing from believing if you are wrong. This is not true either. Assume that you are wrong in being a theist. You will waste a lot of time and energy on going to church, praying and religious rituals. Imagine if all the energy that,throughout human history, had been wasted on such activities had been used to improve the world instead. Then maybe we would have had heaven here on earth instead.

    Imagine if all that energy had been used for science, arts and music. OK, there have been many christians who have devoted their life to that, but imagine how wonderful things they would have been able to do if they hadn't wasted their time on prayers and rituals. Imagine what Pascal could have done for mathematics and physics if he hadn't left science for God.

    Considering what religious belief has done to the world, it would be better if there was no religion. Religion is like a virus that changes people's minds into dogmatic thinking, rule following, and blind faith, qualities which do no good for the well-being of mankind. Consider how many people who have been burned, mutilated and tortured in the name of religion. Wouldn't it be better if we left the Dark Ages for once!?

  15. Believing what is probable
  16. The process of belief is not a bet, not based on hope for reward or fear of punishment. Normally you believe in something your sences tells you is likely to be true. No intelligent person would be convinced that god exists from Pascal's wager, and I question that this argument really was the reason why a genious like Pascal believed in god. I rather see it that he had lost the basis for his faith and that Pascal's wager was the last thread to keep him hanging on to christianity.

  17. Argument for theists only
  18. Pascal thought that theism and atheism were equally likely - that is, we cannot know which of the philosophies is correct. This is non-information, and, according to information theory, it is impossible to get information from non-information without any cost. Therefore it is impossible to conclude, from the assumption, that theists will gain more than atheists and the statement that if god exists you gain from believing in him must also be an assumption - not a conclusion. So what Pascal's wager basically says that "If you believe in God, you will believe that you gain from worshipping him". Not a very convincing argument for atheists.

  19. God rewarding only true believers
  20. The christian god is supposed to be omnipotent. If so, he will know who are the true believers and who worship him only to be on the safe side. Therefore it is not likely that a person who worships God because of Pascal's wager will go to heaven. This is sometimes called the Atheist version of Pasca'sl wager, since it says atheists will be better rewarded than theist hypocrites, and thus if you do not believe in god, you shouldn't lie and say you do.

  21. Is god just?
  22. Now if there is a god, and he is just, he would not send kind atheists to hell only because they can't believe in him. A just god judges people for who they are, not for what their minds tell them is likely to be true or not. Therefore a just god would still save atheists if they were good people.

    Like someone once said, "I would love to go to hell and meet people such as Einstein, Darwin, Russell and Voltaire." Is it really likely that these people were sent to hell, only because their great minds didn't find any evidence of the Christian god? In that case the word "just" is not applieable to god, and such a god is not even worth worshipping. To worship such a god would be like worshiping your worst enemy because you were afraid of his revenge if you didn't submit to his power.

  23. Theists being punished for their sins.
  24. I don't think there is an agenda in christianity that you are being rewarded for mere worshipping god. I think it is far more common among theists to believe that god rewards you for what you really are. In other words, God won't reward you for helping people if you do it only to please God, but he will if you do it out of compassion. Therefore it is quite likely that false people, who only worship god because they fear hell, or because they think it is the bet that gives the most gain, will go to hell. So believing in god and being a bad person will be as bad as being an atheist, if not worse because God mightn't like being surrounded for eternity by cringing hypocrites.

  25. Economics
  26. The original version of Pascal's wager fails to handle probabilities, since it states that both theism and atheism are equally reasonable. The problem with that approach is, as stated above, that it makes information out of no information, and hence is invalid as an argument. For the argument to be valid you will have to consider the probabilities of theism being right and the loss/gain from holding a religion.

    In order to convince an atheist, with Pascal's wager, theists need to convince him that there probably is some supernatural force, and that that supernatural force probably doesn't treat atheists the same as people of his religion, that that supernatural force probably doesn't treat people of his religion worse than atheists, and that either the probability of theism being right or theists reward is high enough to overcome the cost of following his religion in this life.

    Pascal's wager alone just doesn't cut it - you need to provide evidence of the supernatural, and reasons to think that the supernatural significantly rewards people of your religion, if you really want to convince people with the Pascal's wager logic.


  1. Anders Aspegren, Finns Gud?, Human-Etiska Förbundets småskrift Nr 14
  2. Kunskapens bok (a swedish encyclopedia from the 60:s)
  3. An E-mail posted to alt.atheism, by Abner J Mintz
  4. Dan Barker, Losing Faith in Faith - From preacher to atheist


  • Voltaire's notes
  • Invisible Pink Unicorns FAQ

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