The article discusses the evolution of Marian Smoluchowski’s reasoning in his research on causality and understanding the essence of chance. Initially, Smoluchowski focused on the epistemic study of causality, looking for evidence supporting the kinetic-molecular theory. In proving the causes of Brownian motion, he used the concepts of physical causality. The fundamental change in Polish physicist's perception of causality was the understanding of the position of chance on the cause-effect line. Introducing mathematical relations into his considerations, he analyzed the aspect of the occurrence of the effect. The chance suitable for calculating probability was distinguished from the chance in a broader sense by the essential regularity of the frequent recurrence of the phenomenon, regardless of the knowledge of the cause. Smoluchowski's merit was the distinction between the philosophical and physical understanding of causality, chance and probability theory. Shifting the considerations on the nature of chance to the ontological plane moved the study of chance into the area of science, thus leading to the practical application of probability theory in physics.

The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ��1, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.