[tomachello]

No, only one. Think about it this way - if the warden randomly generates their numbers, each prisoner has a 1/100 chance of guessing it right. So best case scenario is exactly one gets it right, which is actually possible.

[hollowpython]

Ooooh. The prisoners can't hear other prisoners' guesses then. Ok! But in your example, isn't the probability of winning 1-(99/100)*100?

I don't think your "best case scenario" comment is actually true

[tomachello]

They just need one prisoner to guess correctly - then they all win. Regarding the base case scenario - if each prisoner guesses randomly, each has a 1/100 chance of guessing correctly, and hence they have an expected number of exactly one correct guess. So no deterministic approach can give 2 correct guesses, since no prisoner actually has any real information about their number.