fij : the probability that the first (and last) visit to absorbing state j is in n turns.Fn : the ×(+) matrix of these "first transition" probabilitiesThe probability that the system goes from transient state i to absorbing state j is just the sum : The ×(+) matrix of probabilities for all of these + absorbing states can be obtained fromThe probability that the attacker wins is just the sum of the entries in the last (or (A,D)row of the submatrix of the last A columns of F :