There is a well-known thought problem called X(z)eno's Paradox, or the Dichotomy Paradox. The essential base of Xeno's dichotomy is what I allude to, while the basic conclusions and premises behind the argument I push aside as they are not relevant.
The dichotomy is this, to travel any distance, say 10m, you must first travel half that distance before you can travel 10m. Thus you must travel 5m. To travel the remaining 5m, you must first travel 2.5m, and to travel the remaining 2.5m you must travel 1.25m first and so on. The gist of the argument is that motion is an illusion; one cannot travel, or begin to travel any finite distance without making an infinite number of smaller trips.
The interesting thing about Xeno's Paradox is that the more half-moves you make, the closer you move toward 0m until, at some point, the differentiation is pointless and from a pragmatic position, there is no longer a division between the remainder and 0.
How does this apply to Pascal's Wager?
The sliding scales of halving work in opposition to one another as you place your wager for god's existence and I place mine against. Since we know there are more possible gods than one, and since any argument in the absence of evidence applies equally to all gods, we like Xeno, must half the probabilities of a god existing, while increasing the possibility of no gods existing by a half.
So, if we allow the existence of gods an equal starting probability (50/50) and place our wagers, first through Pascal's method, then wager accordingly with the Dichtomy Paradox, it becomes apparent that non-existence quickly moves toward a probability of 1.0 and non-existence towards 0.
Yahweh + Jesus = 0.50/2 or 0.25
Vishnu + Shiva = 0.25/2 or 0.125
Allah + holy spirit = 0.125/2 or 0.0625
Brahma + Kali = 0.0625/2 or 0.03125
Ganesha + wu wei = 0.03125/2 or 0.015625
Considering if we counted or attempted to account for every variation of god that exists, we would likely end up some where over 4 billion possible deities. If that seems high, you must remember that:
- Most Christians have their own version of god with bits they like, bits they don't
- Hinduism would account for a large portion with official public deities and individual house hold deities
- You would also have to include every god that had existed, but are no longer worshiped
The number of 4 billion is entirely reasonable, but lets cut that in half just to give those positing god the strongest possible argument. That equates to:
0.50/2,000,000,000 = 0.00000000025
The number is so low, it might as well be zero. But lets be even more generous and include only those denominations within one religion, Christianity. Presently, there are somewhere between 38,000 to 55,000 versions, each claiming to be correct, and each claiming three separate gods exist, are equal but one. So lets not multiply their number of possible gods by three, even though we ought to since the chance of Yahweh existing is equal to the holy spirit existing as it is to Jesus existing as a man-god – don't believe me? Ask a Muslim or Jew.
So, best case scenario, using the minimum possible bets, we arrive at:
0.50/38000 = 0.0000131579
Not as improbable, but the resulting number is also close to, if not zero, pragmatically, which I will address later before moving on to the ontological apology.
0.50/38000 = 0.0000131579
0.0000131579 – 1.0 = .9999868421
Just in this case, we can see wagering against Pascal's gods, we come close to arriving at 1 without actually reaching it, nor can we ever, regardless of how many gods we might add. Example:
0.50/2000000000 = 0.00000000025
0.00000000025 -1.0 = 0.99999999975
This of course might embolden the agnostic or believer who insists god exists in the very small margins described, after all, if the chance isn't 0 and isn't 1, then there is a possibility, even if there is little to no probability.