Stochastic point location deals with the problem of finding a target point on a real line through a learning mechanism (LM) with the stochastic environment (SE) offering directional information. The SE can be further categorized into an informative or deceptive one, according to whether p is above 0.5 or not, where p is the probability of providing a correct suggestion of a direction to LM. Several attempts have been made for LM to work in both types of environments, but none of them considers a dynamically changing environment where p varies with time. A dynamic dual environment involves fierce changes that frequently cause its environment to switch from an informative one to a deceptive one, or vice versa. This article presents a novel weak estimator-based adaptive step search solution, to enable LM to track the target in a dynamic dual environment, with the help of a weak estimator. The experimental results show that the proposed solution is feasible and efficient.