The average number of knight moves to return to A1

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The chess knight is on the A1 square and starts moving randomly (according to the rules of chess). What is the average number of moves it will need to do to return to square A1? How much of its endless life will it spend in each of the fields? I have tried to find probabilities for each move but there seems to be too many of them so I suspect that there is a simpler solution.