The Wager

Blaise Pascal (1600s)


1.       Pascal assumes that we can’t know that God is or that he is not

          a.       God’s existence and nature is beyond human reason

          b.       Reason can’t decide this

2.       Appears the reasonable thing to do is not to take a position on God

          a.       Be agnostic: neither believe nor disbelieve

3.       But you must wager; you must choose

          a.       Which shall you choose


4.       If you wager that God is

          a.       “If you gain you gain all; if you lose, you lose nothing”

          b.       Plausible?


5.       “There is a finite stake in a game where there are equal risks of gain and loss and the infinite to gain”

          a.       The stake: Your belief and what it requires of you (this is finite)

          b.       Equal risks of gain and loss: Chances of God existing 50/50

                    i.        Even if there is only a small chance God exists the argument goes through

          c.       The infinite gain: Everlasting life and infinite happiness

          d.       You should wager for God


6.       Mathematical/expected value version

          a.       Rational to bet on the option with the highest expected value (or bet if the expected value is positive)

          b.       Expected Value= Amount of gain times its probability plus amount of loss times it probability

          c.       Example

                    i.        For $10 you get 25% chance of winning $100, should you do it?

                    ii.       $90 x 1/4 = 22.50, plus -$10 x 3/4 = -7.50 = 15$

                              (1)     Expected value (average gain/loss if repeated) is positive so you should bet

                    iii.      If wager cost $30, should not bet

                              (1)     1/4 chance of winning $70 (=17.50)

                              (2)     3/4 chance of losing 30 (-22.50)

                              (3)     Expected value is -$5.00

7.       Pascal's wager rational on these grounds because the expected gain is infinite, and expected loss is finite, and there is at least slight chance that God exists

          a.       For a finite sum, you get some chance of an infinite gain

          b.       No matter how small the chance (as long as there is some chance), one's expected gain is going to be infinite (because anything times infinity and anthing subtracted from infinity is still infinity)


8.       Four Square Version

  God exists

God doesn't exist


Infinite bliss

True belief


Sense of comfort

Clifford’s failed duty


Mistaken belief: (Is mistake on such a fundamental matter a serious loss?)

Sense of comfort

Clifford’s failed duty

Don’t believe

Eternal damnation

Mistaken belief

Avoid costs of being religious


True belief

Avoid costs of being religious



9.       General intuition behind the wager:

          a.       By believing you get a chance at infinite gain (with only finite loss)

          b.       By not believing you get a chance of infinite loss (with only finite gain)


10.     Infinite life pill

          a.       Would you take a pill that had some chance of giving you eternal life?


11.     Treating belief in God like a bet or gambling

          a.       Cold, calculating cost-benefit analysis

12.     Yes, if it isn't a live option

          a.       If it's dead for you

          b.       Believe there is no or little chance of its being true

          c.       Does seem crass, shallow, inappropriate

          d.       Irrational, believe something that you believe highly unlikely

13.     Not clear it is crass if wager is directed at those who already want to believe, but are finding it difficult to

          a.       A live option, a real and serious issue for these people

                    i.        E.g., 20% chance it is true

          b.       An additional reason that pushes you over the edge

          c.       Doesn't seem irrational, since you think it is quite possibly true



15.     No: God wouldn't give these people infinite gain (eternal life)

                    i.        God knows your motive

16.     Yes:

          a.       The wager will lead to sincere belief (transform the person)

          b.       No longer clear that God wouldn't go along and provide the benefit, even knowing the original motive

17.     Not clear God would object to the un-crass version of the wager

          a.       Your really wanted to believe anyway, just couldn't

          b.       You thought it was likely (or at least quite possible)

          c.       So you went to church, took holy water, prayed and ended up believing

          d.       Not clear that God would find this objectionable

          e.       E.g., Person wanted to trust you and placing trust in you was made easier by the gain it might provide


18.     Is the option really forced?

19.     What is a forced option?

          a.       Train analogy: Should I get on the train or not? To not decide is to let the train leave (is to decide)

          b.       Not a forced option:

                    i.        Believe Obama will be a good president or believe he will not be a good president

                    ii.       Shall I bike the bridge or not? To not decide leaves open the possibility of doing so tomorrow

20.     Is choice of God a forced option?

          a.       Why can't we wait until later in life?

          b.       Because you might die before you choose

          c.       William James’s idea that if it is true, we loose even now by not believing


21.     Agnosticism is a false option, as it gets lumped with atheism (failing to believe)

22.     Would God really treat agnostics and atheists the same?

          a.       One closed his/her mind, and actively disbelieves

          b.       Another remains unsure either way.


23.     Is belief under a person’s control?


24.     Not always rational to bet on expected value (in one time bets)

          a.       Wager your life savings ($100,000) for a 20% chance get $1 billion?

          b.       1B x 1/5 = 200 million (expected gain)

          c.       $100,000 x 80% = 80,000 (expected loss)

          d.       Expected gain exceeds expected loss ($200,000,000 versus $80,000)

          e.       If you can’t afford to lose your life savings, you should not bet it even if the expected value is positive.