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April 15, 2008 / Διαγόρας ο Μήλιος

Homer Simpson answers Pascal’s Wager

Χόμερ Σίμπσον 

Suppose we’ve chosen the wrong god. Every time we go to church we’re just making him madder and madder!

–Homer Simpson

.
“And what does that have to do with Pascal?” You may ask. Read on…

The famous French mathematician, physicist and philosopher Blaise Pascal (1623-1662) expressed the opinion, which was to be known as “Pascal’s Wager”, that the question of whether god exists cannot be answered logically, so we can only see it as a bet, but in this bet, belief in god is a much better choice than non-belief. Pascal’s statement can be very easily explained by the following table, which shows the available options, the available choices, and all four possible outcomes:

God exists God does not exist
You believe in god You go to heaven Nothing to lose
You do not believe in god
You go to hell Nothing to lose

.
As it is evident from the table, if you bet on the existence of god, the best thing that may happen to you is to go to heaven, and the worst is that you lose nothing. On the other hand, if you bet on the non-existence of god, the best scenario is that you lose nothing, while the worst is that you burn in hell.

From the above it is evident that:

Good gamblers always bet on god!

And another indisputable fact also becomes clear:

It takes some guts to be an atheist!

But I started this article with Homer Simpson, and I still need to show how he factors into the picture, so let us see the issue in a more mathematical way; let us give values to the various outcomes of the bet: we will consider the value of the “go to heaven” outcome as 100, the value of the “go to hell” outcome as -100, and the value of “nothing to lose” as neutral, that is, zero. Thus, we will be able to compute the value of each betting choice by computing the average value of its possible outcomes. So, the table looks like this now:

God exists
God does not exist Value of choice
You believe in god 100 0 (100 + 0) / 2 = 50
You do not believe in god
-100 0 (-100 + 0) / 2 = -50

So far so good; what Homer Simpson does with his quote, however, is to remind us of a little detail which must have escaped Mr. Blaise Pascal’s attention: and what happens with other gods?

In order to see what happens with not only the Judeochristian God Yahweh, but also with Zeus, we need to expand our table as follows: (Let us ignore, for the sake of argument, the fact that Zeus, in contrast to vindictive sadist Yahweh, would not send you to hell if you did not happen to believe in him, and let us also disregard the fact that the various Judeochristian sects want you burning in hell even if you happen to belong to the wrong sect.)

Yahweh
exists
Zeus
exists
No god
exists
Value of choice
You believe in Yahweh 100 -100 0 (100 + -100 + 0) / 3 = 0
You believe in Zeus
-100 100 0 (-100 + 100 + 0) / 3 = 0
You do not believe in god -100 -100 0 (-100 + -100 + -100) / 3 = -66.67

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Notice how the atheist’s position worsened by 16.67 points, while the position of either one of the believers worsened by far more, that is, 50 points!

Let us add Thor to the table:

Yahweh
exists
Zeus
exists
Thor
exists
No god
exists
Value of choice
You believe in Yahweh 100 -100 -100 0 (100 + -100 + -100 + 0) / 4 = -25
You believe in Zeus -100 100
-100 0 (-100 + 100 + -100 + 0) / 4 = -25
You believe in Thor -100 -100 100
0 (-100 + -100 + 100 + 0) / 4 = -25
You do not believe in god -100 -100 -100 0 (-100 + -100 + -100 + 0) / 4 = -75

.
Again, we see a worsening in the value of the atheistic choice, accompanied by a greater worsening of each of the god-fearing choices. As you can see, by adding deities to the table the value of all choices drops, and as the number of deities tends to infinity, the value of all choices, bar none, tends to -100. (That’s Calculus for you, an invention of the Devil, no doubt about it!)

Diagoras’ conclusion: if any god exists, humanity as a whole is done for!

Pascal’s wager in Wikipedia:
http://en.wikipedia.org/wiki/Pascal’s_Wager

More on Pascal in Wikipedia:
http://en.wikipedia.org/wiki/Blaise_Pascal

This article is also available in Greek.

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13 Comments

Leave a Comment
  1. John / Jan 5 2011 8:18 am

    I think there should be negative points for the case where you believe in god and god doesn’t exist since you just wasted your life, your one chance in all eternity for a life, on a falsehood. What if you suffered all sorts of torment and martyrdom to get to heaven and it doesn’t exist? Surely that is a negative.

  2. Διαγόρας ο Μήλιος / Jan 5 2011 11:11 am

    Sure, only the “wasted life” case is difficult to quantify and express in mathematical terms.

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  9. Abdullah Abdullah / Apr 22 2012 3:14 pm

    The big difference of course between the Christian God (Jesus Christ) as opposed to Thor, Zeus, or whomever is that the Christian God actually came down to our level when we couldn’t rise up to his, personally carried out His promise to forgive us of all our sins by dying in our room & stead on a cruel cross, healing us, and guaranteeing us an eternal home in heaven! Plus, plus, the Christian God arose from the grave as the all-victorious Savior with power to fulfill all His promises for those who believe in Him! Jesus Christ: 1; Thor, Zeus Combined: 0. The Christian God sure beats the atheistic religion’s twin-gods of :god Fat Chance” & his twin-god “Wholly Accidental!”

  10. Διαγόρας ο Μήλιος / Apr 22 2012 5:53 pm

    In other words, “Abdullah Abdullah”, the big difference between your christian god fantasy and those other fantasies is that your fantasy was designed to be more appealing to your ears. That’s no wonder, of course; it explains why your fantasy is the prevalent fantasy nowadays, while the other fantasies have died out. But that does not make it any more real: it is still a fantasy..

  11. Ibn Abdulla / Mar 9 2013 10:02 am

    What utter nonsense, written without a basic knowledge or understanding of discrete probability or calculus,which doesn’t apply to a probabilistic model anyways.

    “Notice how the atheist’s position worsened by 16.67 points, while the position of either one of the believers worsened by far more, that is, 50 points!” – Right there. Comparing two mutually exclusive events as if they were dependent events. If the first scenario is true, then the second cannot be and vice versa. Talking of comparative positions worsening between the 2 is fallacious.

    “As you can see, by adding deities to the table the value of all choices drops, and as the number of deities tends to infinity, the value of all choices, bar none, tends to -100.” Again, applying calculus to a discrete set of values. No matter the number of deities you add, even if one of them exists there is a 1 in “No. of Deities” chance that you are right whereas an atheist is never right in any of those scenarios.

    @misnomer xtian: “personally carried out His promise to forgive us of all our sins by dying in our room & stead on a cruel cross” : If the Jesus Christ you refer to (i.e as the son of God) is all powerful why not just forgive people in the first place and be done with it ? Why bother coming down as a man and in the process lose His everlasting attribute in a human form?

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  1. Suppose we’ve chosen the wrong God | Religion Poisons

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