Something struck me the other day as I was walking home from work. My apologies if this has been discussed in detail before.
Assuming that there is indeed no beginnings to the Wheel of Time, that means the Wheel of Time has turned forever, and the last battle at the end of the third age has happened infinitely many times. If so, that means the probability of the Dark One winning is literally zero. If there is a nonzero chance, then sooner or later the Dark One is going to break free, and the Wheel has already turned an infinite number of times, then he would already be free.
If, on the other hand, there was a beginning, and the Wheel has only turned a finite number of times, then there could be a small probability of the Dark One breaking free. In this case, he will of course eventually break free.
Moiraine repeatedly (I think) tells Rand something along the lines of "being ta'veren doesn't make you immortal", but for the Wheel of Time to keep turning forever, without the Dark One ever breaking free, this is in fact exactly what he would have to be.
There's a few ways one can get around the whole 'if something it finitely probable, after a long enough time it will eventually occur' because that phrasing is a simplification.
As an example, if something has a 10% chance of happening every minute, it will eventually occur, like on an order of less than an hour. However if the first minute it has a 10% chance, and the second minute a 5% chance, and the third minute a 2.5% etc then it is always possible for the event to happen, but it is not inevitable over an infinite time. As an almost-real life example, take gamma-sensitive switch and put it near a radioisotope, set to go off if it receives a gamma particle from the decay. Every half-life the number of particles, both of the radioactive sample and the gamma particles it emits, will decrease to half, lowering the probability of the switch being triggered in any given interval by one half. There will always be, at any given time, a finite probability of the trigger occurring, but the odds each moment decrease. Real world you'll eventually run out of particles, a sample of a trillion particles will reduce to one or two within 40 half lives, a quadrillion within 50, and so on until you're down to one particle with a 50% chance of disappearing each half life and ending the cycle, but that's a constraint of that example, rather than the mathematical concept. You can also run this concept backwards, with a steady source but a decaying risk, like an army besieging a castle that was having its walls steadily built up.
I'm sure RJ didn't miss that either, so he either had an explanation or considered it a legit handwave, and he does list the DO as lord of paradox.
We're also dealing with competing probabilities here too. The wheel isn't a passive system and the show and tell on the wheel is that it has the ability to play with probability. Explicitly and repetitively that taveren can never achieve an impossible result but regularly get improbable results. Finite chance inevitability gets a bit questionable when you have a situation where someone can play with probability itself.
Clearly Moridin believed it was a finite probability and thus inevitable, that's his character motivation. Rand might consider it so too but keeps going on since 101 turnings is better than 100.
- Albert Einstein
King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod
