Consider a standard chessboard with an 8×8 grid of possible locations. We define a Markov chain by randomly moving a single chess piece on this board. The initial location X0 is sampled uniformly among the 8 = 64 squares. At time t, the piece then chooses Xt+1 by sampling uniformly from the set of legal moves given its current location Xt. For a description of legal chess moves, see: http://en....