Expected number of gambles

Question

Consider a gambler who at each game is equally likely to either win or lose $1$ dollars.

Suppose the gambler will quit playing further when he (cumulatively) either wins $100$ dollars or loses $100$ dollars. Find the expected number of games the gambler plays.

Please can someone help me with this question.

Answer 1

Are you familiar with Markov chains? You're asking about expected hitting time of a Markov chain. You can show the answer is equal to 100^2 but the methodology is elementary and can be lifted straight out of a textbook if you know where to look.