# Torus Chessboard

Probability Level 5

A token is placed on the corner square of a $3 \times 3$ chess board. The token is moved either up, down, left, or right, with equal probability. If the token would move off the edge of the board it "wraps around'' the board and moves to the opposite side instead. For example, if the token was in the bottom right corner and moves down, it would move to the top right corner. What is the expected number of moves it will take for the token to end up on the center square of the board for the first time?

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