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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.

StubbornAtom
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Igor Igor
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    Does "radically" mean "randomly" ? – Peter Oct 07 '20 at 13:09
  • @Peter Sure thing – Igor Igor Oct 07 '20 at 13:42
  • When you say you've tried to find probabilities for each move, do you mean you've tried to construct the transition matrix directly and are looking for a 'trick' to avoid doing that? The following previous question may be helpful: https://math.stackexchange.com/questions/464049/what-is-the-probability-that-a-knight-stays-on-chessboard-after-n-hops?rq=1 – Sort of Damocles Oct 07 '20 at 14:07

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