Markov Chains & Long-Run Behavior · Superchallenge problem

Two players play a sequence of points; the game ends as soon as one player leads by $2$ points. You win the first point with probability $1/2$. After you win a point, you win the next one with probability $3/4$; after you lose a point, you win the next one with probability $1/2$. What is the probability that you win the game? Express your answer as a common fraction.