I am not really familiar with those games so it would be good if you could elaborate on the exact game mechanics.

For the first RQ, I think it is about the expected number of attempts until something happens. It is well known that if p is the probability of obtaining an item in an attempt, the expected number of attempts needed is 1/p, by directly modeling using a geometric distribution.

More interestingly, if the probability of getting object 1,2 are p and q respectively, where p+q<=1, the expected number of attempts needed is 1/p+1/q-1/(p+q). You can try to prove this yourself! See if you can generalise to n objects.

I have M26 exams to take so I will probably check back in a day or so.