(c) now suppose that the piece is a king, with initial position
A chess piece is wandering around on an otherwise vacant 8×8 chessboard. At each move, the piece (a king, queen, rook, bishop, or knight) chooses uniformly at random where to go, among the legal choices (according to the rules of chess, which you should look up if you are unfamiliar with them). (a) For each of these cases, determine whether the Markov chain is irreducible, […]