I don't think there's a set amount of trials you'll need tbh. The more trials you take, the closer you'll get to the answer.

>But can you assume the same from AABABBBABA? Or AABAB?

Ideally, you can't, as there's a slight chance that a third element (say C) didn't show up. If the sequence is only AABAB, I can assume A and B are the only elements and call it a day, as my statement "A and B are the only elements" makes sense as those are the only ones I saw + you told me that all elements have an equal chance of popping up. But, if the die did indeed have a C, I would be wrong. Eventually, as you increase the number of trials, the probability of C not appearing becomes extremely small, to an extent that you can assume it to be 0 (in other words, as you increase the number of trials, C is bound to appear in one of them). So, the more trials you do, the more likely every element shows up.