You have a standard 52-card deck of cards (13 values, 4 suites). Suppose all 52 cards are shuffled and layed on a table into a single row. A "special pair" of cards is the maximum number of non-overlapping consecutive pairs of cards where each pair has the same number written on both cards. For example, if the sequence "1 1 1" appeared in the row, it would count as one special pair of cards, and the sequence "1 1 1 1" would have a total of two special pairs of cards. What is the expected value of special pairs of cards of the row of the 52 cards?
I found the probability (not sure if I am correct) of one special pair of cards as 3/51 and the probability of two special pairs of cards as (3/51)(2/50)(1/49), but am not sure where to go from here.