Suppose a rook starts on the lower left-most square of a standard $8 \times 8$ chess board. The board contains no other pieces.
The rook randomly makes a legal chess move with every turn (directly vertical or horizontal). The rook cannot remain stationary during a turn. What is the expected number of moves for the rook to land on the upper right-most square?
I understand the rook has 14 possible moves for every turn. The problem seems to fit the concept of Markov chains, as the probability distribution of any given move does not depend on the previous. However, I do not understand how to approach this calculation.