Markov Chains & Long-Run Behavior · Medium problem

A random walk on $\{0, 1, 2, 3\}$ moves up by $1$ with probability $2/3$ and down by $1$ with probability $1/3$, and stops as soon as it reaches $0$ or $3$. Starting at $1$, what is the expected number of steps until it stops? Express your answer as a common fraction.