Pascal is still wagering

I used to find Pascal's wager a particularly attractive idea. More recently, I have found its attraction again. Pascal wagered that he may as well believe in God; because if he was right, he gained eternal life and all the goodness with that, but if he was wrong, he lost nothing. So long as the chance of God existing ≠ 0, then it must be worth believing in God. This principle seems intuitively compelling, I think.

The first criticism of this argument is that there are lots of religions to choose from, many of which claim that they are the only way to achieve access to heaven. This does not actually damage Pascal's wager at all. It merely means that the probability of snagging the right religion is smaller; but since the payoff is heaven, it's still worth it. This will be explained in slightly more detail below.

The next criticism is that Pascal was wrong when he asserted that if he is incorrect about the existence of God that he loses nothing; in fact, believing in a certain religion usually requires a significant giving up of one's time and money, as well as being bound to follow a moral code. If the benefits of religion in this lifetime (such as satisfaction, lack of despair, etc) are outweighed by the negatives (such as the giving up of time and money and so forth), then, so the argument goes, it follows that if the chance of God existing is pretty tiny, we should not believe in a religion as we risk losing enjoyment in this life. This problem is slightly more damaging than the first criticism, but can be fairly easily sidestepped by some use of basic maths:
Imagine you are at a casino. The game you're playing is flipping a coin. You place a bet, flip a coin and if it comes up heads, then you get your money back + 50% of your bet (so a bet of £10 and a head would mean you receive back £15, a £5 profit - a return ratio of 1.5). Now, on average the amount of money you get back for every pound you put in can be found by this formula:
Average return = Probability of a head x Return ratio
For our example, your average return would be:
Average return = 0.5 x 1.5 = 0.75
So for every £1 you put in, you recieve back £0.75. You're not going to make money in the long run on that game.

However, if the return ratio was ∞, and you could choose to either bet all of your money or none of your money, then it would always be worth betting all of your money on the game (if money had constant returns to your happiness), even if the chance of you winning was 0.000001. In reality we would probably not choose to bet all of our money because we do not finding constant returns to happiness with money, and thus infinite money would not be that much better than our current amount of money, but zero money would be much worse than our current amount of money.

Let's place this strategy into Pascal's wager. Here, instead of betting money, we're betting the negatives of following a religion (time, money, following a moral code etc). The payback is not money but eternal life/heaven etc. This payback will last forever and thus is ∞, which also makes the return ratio ∞. We do experience constant returns to happiness here, because having eternal life in heaven is literally infinitely better than eternal damnation/annihilation (unlike the casino example above, where infinite money is not infinitely better than some money or no money).

Even if we considered the chance of any given religion being true to be very small (let's say 0.0000001), provided we did not consider the chance 0, we can see that it would be worth believing in a religion:

Average Return = 0.0000001 x ∞ = ∞

The average return is infinite; and since we have constant returns to happiness with regard to eternal life, it is certainly worth wagering on any religion rather than no religion, even if believing in the religion resulted in the most awful sacrifices in this world (the sacrifices would certainly not be infinitely bad, but the payoff would be infinitely good).

Thus, both of the first two criticisms against Pascal's wager can be avoided. The third, which for a while had me convinced, is that if we are considering all possible truths, perhaps it is the case that believing in God actually has negative eternal consequences. Any such situation can be dreamed up; maybe God does not like it that puny humans try to understand him and thus will punish them with eternal damnation, and reward atheists with eternal life since they did not commit such blasphemy. This leaves us right back in square one. However, this criticism too can be avoided. What this criticism does is to essentially just formulate another 'possibility', just as Christianity, Hinduism, Judaism, Islam etc. are all 'possibilities'. Thus, we can attribute probability values to each possibility, and then act accordingly. Maybe an atheist shall say that Christianity has a 0.0002 chance of being right, and Islam a 0.0001 chance - but he also has to attribute this 'atheist God' possibility a probability value. I'm pretty confident that even the most ardent atheist will not claim that the chance of Christianity being true is less than the chance of there being a God who rewards people who don't believe in him and damns those who do, since the evidence for the former (Evidence of the resurrection, 'religious experiences', historical validity of the gospels) is considerably higher than evidence of the latter (literally none). Thus, even Richard Dawkins himself will have to say that there's a better chance of Christianity than this imagined atheist God.
Therefore, this criticism leaves us only with choosing between another possible option, rather than damning the whole argument.

The final possible argument against the wager, which is no doubt the strongest one, is that in fact it does not matter which alternative we choose (including the atheist God alternative), because they all have infinite payoffs. This can be seen here:
Suppose we attribute Christianity a 0.5 chance of being right, Islam a 0.3 chance, Judaism a 0.1 chance and Atheist God a 0.05 chance*. Their average returns are as follows:

Christianity's Return = 0.5 x ∞ = ∞

Islam's Return = 0.3 x ∞ = ∞

Judaism's Return = 0.1 x ∞ = ∞

Atheist God's Return = 0.05 x ∞ = ∞
*The reason I chose those four religions is that all of them are exclusive. Under Pascal's wager, there's no point believing non-exclusive religions (such as Hinduism or Buddhism), since if they're right you've got eternal life regardless of your belief.

Therefore, it could be claimed that any alternative can be chosen - because the average return is always ∞! This could be a damning indictment of the wager. However, I think here that it would still seem that the best option is to choose the religion which we perceive as having the highest chance of being right. Given that all the religions will have an infinite average return, the only logical way to decide between them is to pick the one with the highest probability of being right.

Of course, the scope of Pascal's wager is limited to only what is rational to do. It is true that an atheist who understands and agrees with Pascal's wager may still be bound to being an atheist, because his belief is based on various factors about what he believes to be the true, rather than what he believes is best for him. We cannot 'choose' what we believe, essentially. This is true, and perhaps thus Pascal's wager is unhelpful as it only shows atheists that they are making the wrong decision, rather than enabling them to change it (as arguments for the existence of God do). Although, one thing can still be salvaged from the wager; its conclusion does show that atheists should do all they can to research and try to understand the arguments for God and religions, since this gives them the best shot at being able to make the most rational choice.