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

• limit _{U(Christianity)→∞, P(chr)→0} P(chr)U(Christianity) is undefined, and
• invoking infinite utilities isn't fair.

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:

• Let P(sim) be the probability that we are living in a simulation.
• Let P(ent|sim) be the probability that this simulation was created for entertainment purposes, as opposed to purposes including scientific, economic, or governmental reasons.
• Let P(ego|ent, sim) be the probability that the person or organization running our simulation wants to be personally glorified within their simulation, and therefore created an avatar of themselves, or represented themselves in myth, or in some other way put some being into the sim whose status in the sim they identify with.
• Let P(chr0|ego, ent, sim, Earth) be the probability, given the observed history of Earth, that, of the various candidate religions or leaders or possible avatars, this egoist God is using Christianity.  (The same argument applies for Islam.  Judaism has a different payoff matrix.  I'm deliberately ignoring polytheistic religions.)
• Let P(follow-thru | chr0, ego, ent, sim, Earth) be the probability that our simulator God, on Earth, who is representing itself via Christianity, will follow through on promises of implementing Heaven and Hell - if not for an infinite time period, then for a long enough time periods that your utility is at least 99% afterlife.  Heaven and Hell could provide utility/disutility much greater than a human lifespan even if they run only until the end of game.  I imagine that pure torment could provide more than a lifetime's worth of disutility in a few days or weeks.
• Then P(chr) > P(sim)P(ent|sim)P(ego|ent,sim)P(chr0|ego,ent,sim,Earth)P(follow-thru|chr0, ego, ent, sim, Earth).

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!".)