Cthulhu's Wager measures the benefits/punishments of belief/non-belief in Cthulhu.
It follows logic thusly:
Cthulhu, if he exists, exists somewhere inaccessible to human beings, so we cannot be certain of his existence or nonexistence.
If Cthulhu exists, he will give a quick and relatively merciful death to those who have worshipped him and expressed their belief through self-flagellation and ritual sacrifice.
If Cthulhu exists, he will condemn those who have not worshipped him to an eternity of suffering and torment.
You may worship Cthulhu, and Cthulhu exists, in which case you get a swift death.
You may worship Cthulhu, and Cthulhu doesn't exist, in which case you gain nothing.
You may not worship Cthulhu, and Cthulhu doesn't exist, in which you gain nothing.
You may not worship Cthulhu, and Cthulhu exists, in which case you suffer infinite pain.
The following table shows the values assigned to each possible outcome:
Cthulhu exists (p)
Cthulhu does not exist (1 − p)
Worship of Cthulhu (EP1) < ∞ (finite pain) 0
Non-Worship of Cthulhu (EP2) = ∞ (infinite pain) 0
Now you must wager: do you choose to worship him or not?
So we can describe our calculus of pain, holding (p) as the probability that Cthulhu exists, and (1 − p) that he does not exist.
If you worship him, we assign X1 as the pain if he does exist, and X2 as the pain if he does not exist. X2 is less than X1 because in both instances you go through the pain associated with worshipping Cthulhu, but in X1,, you also get eaten, which is more painful.
If you worship him your expected pain (EP1) is some finite constant:
EP1 = p(X1) + (1 − p)(X2)
For the case where you do not worship him, we assign Y1 as the pain if he does exist, and Y2 as the pain if he does not exist. Y2 will be zero or negative, because you actually get pleasure if you don't worship him and he does not exist.
If you do not worship him, your expected pain is:
EP2 = p(Y1) + (1 − p)(Y2)
However, (Y1), the pain if he does exist and you don't worship him, is infinite. Therefore, expected pain is infinite if you do not worship him, no matter what the associated probability (p).
As infinite pain is always greater than any finite pain, EP2 is always greater than EP1.
Therefore, in order to minimize your pain, the only rational thing for you to do is to pick EP1, and worship Cthulhu through self-flagellation and ritual sacrifice. QED
source
http://uncyclopedia.wikia.com/wiki/Cthulhu
ph'nglui mglw'nafh cthulhu r'lyeh wgah'nagl fhtagn