I don't understand at all why you lump entertainment and religious purposes into a single hypothesis and treat evidence for one as evidence for the other. If we accept that our universe is being simulated for entertainment purposes, it would still not give us significant reason to believe that it's being simulated for religious purposes.
Talking about religious purposes was an afterthought. Nobody does that today. It's conceivable that religions in the future could tell people to run simulations. I wasn't really thinking of a player who wanted to be God; I was thinking of religions that might work things out in simulations for some reason, or have some occult beliefs about the relationship between the world and simulations, or believed it was their moral duty to emulate the Creator.
If the person running the sim wanted to be personally glorified within it, I would expect them to do a much, much better job of arranging it. I would adjust this one down several orders of magnitude.
I think you're saying something like, "What is the probability that we are in a simulation whose purpose is for the player to be a religious figure whom we worship and glorify?" Whereas I lumped that case in there as an afterthought, and am more interested in the higher-probability scenario that we are in a simulation that is supposed to be fun for the player, where the player get credit for playing well, but getting credit/glory is not supposed to be easy. It wouldn't be fun then.
If we imagine this is sim after the style of a game like Civilization, where the player is measured along multiple metrics of success and has competition from multiple other factions, I would substitute P(rel|sim) with P(rel|gamesim), the probability that religious veneration is one of the metrics in the game, but I would assign P(gamesim) a much lower probability than P(sim), because it occupies a very small part of the probability mass that I assign to a simulation. As before, a large part of the improbability would come from locating that particular typ...
Let P(chr) = the probability that the statements attributed to Jesus of Nazareth and Paul of Tarsus regarding salvation and the afterlife are factually mostly correct; and let U(C) be the utility of action C, where C is in {Christianity, Islam, Judaism, atheism}.
Two of the key criticisms of Pascal's wager are that
If, however, P(chr) is not infinitessimal, and U(Christianity) is merely very large, these counter-arguments fail.
Many poor arguments have been made that P(chr) > .1. But as far as I know, no one has ever made the best argument in favor of Christianity:
If you accept the simulation argument, then P(sim) > .99.
If you look at the fraction of computing power used for entertainment, I don't know what it is, but the top 100 supercomputer list for June 2011 lists a total of 4,531,940 cores in the top 100 supercomputers in the world; versus (rough guess) a billion personal computers and video game consoles, and a similar number of ordinary computers used at work. It would be reasonable to set p(ent|sim) = .5.
If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) is large. I originally set this at p > .99, but am now setting it to p = .5 in response to Jack's comment below.
We notice there are no obviously immortal world leaders on Earth (but see vi21maobk9vp's comment below). If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.
P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1. Given our observations of game-players here on Earth, it is not independent of p(ego), as players of self-glorifying games are likely to be young adolescent males, and so are people who enjoy burning insects with magnifying glasses.
We now have p(chr) > .99 x .5 x .5 x .25 x .1 = .0061875. As stipulated, your afterlife accounts for at least 99% of your utility if follow-thru (and hence chr) is true. If we suppose that the length of time for which God rewards us in Heaven or torments us in Hell has an exponential distribution, and we are considering only the part of that distribution where >= 99% of your utility is in the afterlife, then almost certainly p(chr) * U(Christianity | chr) > (1-p(chr)) * U(atheism | not(chr)). It now appears we should accept Pascal's wager.
(The expected utilities for Christianity and Islam are similar, and this argument gives no reason for favoring one over the other. That is of only minor interest to me unless I accept the wager. The important point is that they both will have expected utilities similar to, and possibly exceeding, that of atheism.)
You can argue with any of the individual numbers above. But you would have to make pretty big changes to make p(chr)(U(Christianity|chr)) negligible in your utility calculation.
(IMHO, voting this article up should indicate it passed the threshold, "That's an interesting observation that contributes to the discussion", not, "Omigod you're right, I am going out to get baptized RIGHT NOW!".)