Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?

We want to find the expected vaue of j - i, where i and j are the positions of the jokers.

We can compute that

\(\sum (j - i) = \frac{n^3 - n}{3}\)

So the expected value is (n^3 - n)/3/C(n,2). For n = 54, this is 110/3.