Alice may be right that there is really no chance in the world, and that the outcome is pre-determined. Sure, maybe the universe has already mechanistically pre-ordained The Day on which the 100-roll happens. However, Alice's optimism shouldn't logically follow directly from this pre-determination of the outcome - her optimism would only be warranted if the pre-determined day of the 100-roll were actually known to her and Bob.
If Bob and Alice knew that the 50th day would bring the release (say, as the story suggests, the jailer performed the dice rolls before the jailing, and he additionally let them know the results of these rolls), then every day would indeed bring them closer from a probability standpoint: probability of release for n<50 is 0, probability for n=50 is 1.
But without this knowledge, given what Bob and Alice actually know, the probability of release on a given day is just a cold 0.01, and the expected wait time until the good roll is 100 days. This 100 days expected value is always receding into the horizon as far as Bob and Alice are concerned. One failed day does not bring them closer. This is true given Bob and Alice's knowledge of the process, even if it is actually pre-sampled.
A roll other than 100 tells us nothing more than the fact that today is not their day. Even if the rolls are pre-sampled, and there is a finite N that they are actually getting closer to, as far as they are concerned it might as well be a daily, independent, and purely random dice roll.
One way Bob could convince Alice to see it his way: on the first day, ask her to somehow fix in her mind what this pre-ordained N is likely to be. Maybe just tell her to think of her best guess (like an average - the correct answer of which is 100) or a collection of values for N along with their respective probabilities (if she knows statistics, she'll think of the PMF of the geometric distribution). Now, every day that passes by without a 100-roll, Bob should tell Alice to shift that view of N up one day. If she thought that the pre-determined N was likely to be roughly 100, and it's been 20 days, Alice should now think that pre-determined N was probably close to 120 (that is, 100 away from today).
edit:
"It doesn't matter whether the jailer is rolling the dice every day, or has rolled the first 1 billion times ahead of time and just reads out the result each day. Because of this the Jailer knows on which day we'll be released (let's say day N), and so these failed days were necessary and each one takes us one day closer to our release. We are now 50 days closer to that release date"
Bob is much more pessimistic and re-inforces that after 50 failures they are statistically still no closer to release that on the first day they arrived.
A closer reading of the actual content of these arguments makes me think they're not actually that contradictory. Alice isn't actually saying that, given their own knowledge, they are more likely to reach the end any time soon if they haven't been released for n days. She is just saying that each failed day was necessary in the grand scheme of things. In fact, the first sentence of that selection is absolutely true: to Alice and Bob, it really doesn't matter from a probability perspective whether the dice rolls have already been made or if they are actually done daily. That's the point.
However, I think that the correct emotional response is: "it's unfortunate that the ultimate N is now at least one more than it would have been had we gotten lucky today" rather than "great, we're one day closer to being released." But if it helps her sleep at night, maybe focusing on this actual unknown fixed N shouldn't be critiqued too closely!
