If you’re trying to find out the probability of the next paper, as opposed to the ratio for all the papers, it works fine.
Suppose you have a printer that randomly prints “yes” and “no” at a certain ratio. Laplace’s rule of succession would work fine. If someone decided to turn it off after a certain number of papers, that wouldn’t change anything until then.
Technically, you have to adjust for the probability that there is no next paper, and the hat is empty.
If you’re trying to find out the probability of the next paper, as opposed to the ratio for all the papers, it works fine.
Suppose you have a printer that randomly prints “yes” and “no” at a certain ratio. Laplace’s rule of succession would work fine. If someone decided to turn it off after a certain number of papers, that wouldn’t change anything until then.
Technically, you have to adjust for the probability that there is no next paper, and the hat is empty.