Simple random walk on $\mathbb{Z}^d$ is defined as follows: at every step, a particle moves from its current position to a neighboring lattice point, with each neighbor being equally likely. In contrast, rotor walk on $\mathbb{Z}^d$ is a deterministic walk. Each lattice point has a rotor which points to one of its neighbors and a rotor mechanism which determines how the rotor rotates; at every step of rotor walk, the rotor at the particle's current position rotates according to the rotor mechanism, and the particle follows the rotor to its next position. Simple random walk is well-understood, but rotor walk is difficult to study because all randomness lies in the initial conditions. In this talk, we consider $p$-rotor walk, which bears similarities to rotor walk but introduces some randomness at each step. I will present new results which are the result of joint work with Swee Hong Chan and Boyao Li under Lionel Levine.