Well, since you can walk back and forth across rows, you'll have to compute all of the probabilities for a given row at once by solving the resulting system of

Well, since you can walk back and forth across rows, you'll have to compute all of the probabilities for a given row at once by solving the resulting system of equations. This is generally quite simple. For example, take a four-column, one-row version, with probability-of-falling like so: * 0 0 0 0 * 1 x y y x 1 We have: x = 0 / 4 + 1 / 4 + y / 4 + x / 4 y = 0 / 4 + x / 4 + y / 4 + y / 4 giving the solutions x = 2/5 and y = 1/5. It is easier, of course, if you exploit the symmetry of the situation, as here (by writing x y y x instead of x y z w).