Suppose I have a 1D random walk, initially starting at $n$. At each time step, I can either move 3 steps forward with probability $p = \frac{1}{3}$, or move 2 steps backward with probability $q = 1-p = \frac{2}{3}$. What is the expected number of steps for hitting 0 (reaching the origin)? Assume that there is no upper bound.
The problems I've seen so far consider the step size to be $\pm1$, so I'm not sure how to proceed here. Any leads will be appreciated!