In the design of control systems affected by uncertain parameters, a primary goal is to ensure that a controller designed based on nominal values of parameters will perform satisfactorily in the presence of uncertainties. Adaptive randomized algorithms have been proposed in literature for overcoming the issue of conservatism and computational complexity which exponentially grows with respect to the dimension of uncertainty. In this paper, we demonstrate that such adaptive randomized algorithms are inherently associated with stopped random walks. We develop a unified theory of stopped random walks which has potential to make better decision and control strategies for uncertain systems.