What is the expected number of moves

Reference no: EM133651022

Question: A chessboard has 8 x 8 squares, and a knight moves by hopping two squares in one direction plus one in the perpendicular direction. Assume that a knight starts at its usual position, on an edge and one square from the corner, and at each step it choose a move at random from its legal moves. What is the expected number of moves taken before the knight returns to its original position? Hint: Treat the knight's location as a random walk on a graph with 64 vertices. Show that the chain is irreducible and find the stationary distribution.

Reference no: EM133651022

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