Cockroach shelter-seeking strategy may initially look like an undirected random search, but we show that they are attracted to darkened shelters. They arrive at a shelter in about half the time control cockroaches take to reach the same location with no shelter present. We were able to identify six statistically significant trends from the behavior of 134 cockroaches in 1-min naïve walking trials with four different shelter configurations. By combining these trends into a model, we built a stochastic algorithm that significantly biases a simulated agent toward a target location. We call this model RAMBLER (Randomized Algorithm Mimicking Biased Lone Exploration in Roaches). RAMBLER could be adapted for a mobile robot equipped with an onboard camera and antenna-like contact sensors.