14. Consider the gambler's ruin problem where on each bet the gambler either wins 1 with probability p or loses 1 with probability Image. The gambler will continue to play until his winnings are eitherI mage or −i. (That is, starting with i the gambler will quit when his fortune reaches either N or 0.) Let T denote the number of bets made before the gambler stops. Use Wald's equation, along with the known probability that the gambler's final winnings are Image, to find .

Hint: LetI mage be the gambler's winnings on betI mage. What are the possible values ofI mage? What isI mage?