Markov Chains & Long-Run Behavior · Challenge problem

A walker moves on $\{0, 1, 2, 3, 4\}$. From $1$, $2$ or $3$ it steps to either neighbour with probability $1/2$ each; from $4$ it always steps to $3$; state $0$ is absorbing. Starting at $2$, what is the expected number of steps until the walker reaches $0$?