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.