Erick stands in the square in the 2 nd row and 2 nd column of a 5 by 5 chessboard. There are \$ 1 bills in the top left and bottom right squares, and there are \$ 5 bills in the top right and bottom left squares, as shown below.
Every second, Erick randomly chooses a square adjacent to the one he currently stands in (that is, a square sharing an edge with the one he currently stands in) and moves to that square. When Erick reaches a square with money on it, he takes it and quits. The expected value of Erick’s winnings in dollars is m / n, where m and n are relatively prime positive integers. Find m+n.