In example (2.a) let x be the conditional probability that the winner of the nth trial wins the entire game given that the game does not terminate at the nth trial; let yn and z be the corresponding probabilities of victory for the losing and the pausing player, respectively, of the nth trial.

(a) Show that (*) x = + + Yn - +1 2n = 'n+1' = = x, yny, z = z

(b) Show by a direct simple argument that in reality xn are independent of n.

(c) Conclude that the probability that player a wins the game is (in agreement with problem 5 in I, 8).

(d) Show that x = , Yn = 4, n = is the only bounded solution of (*).