Gambler's ruin with pushes

Each bet wins one unit with probability $p$, loses one unit with probability $q$, and is a push (no change) with probability $s = 1 - p - q$. (a) Show that the ruin probability is (3.16) with $\rho = q/p$, and that the expected duration is (3.17), computed with $p' = p/(p+q)$, divided by $p + q$. (b) Evaluate for $p = 0.45$, $q = 0.40$, $a = 8$, $N = 20$.