With recent relevant publications on stochastic motion robots in , , and other journals, research on such robots has gained increasing attention. However, theoretical and applied research on stochastic motion in the field of robotics and mechanisms face many challenges due to the uncertainty of stochastic motion. Currently, a large gap remains in the research of stochastic motion mechanism. In this study, a novel mechanism that can conduct probabilistic rolling is proposed to reach a designated position and achieve overlying movement over a particular area. The mechanism consists of a regular tetrahedron frame, a central node, and four connecting linear actuators. According to mobility and kinematic analyses, the mechanism can implement probabilistic rolling. Each rolling gait has three probable rolling directions, and the mechanism rolls in one of the three directions in probability. A kinematic simulation is conducted, and a control method is proposed on the basis of the moving path analysis. Furthermore, the mathematical principle of probabilistic rolling is revealed in terms of probability theory and statistics. Lastly, a prototype is fabricated. To achieve the rolling function, the design of the linear actuators is improved, and the extension ratio is increased from 0.58 to 1.13. Then, tests are conducted. In a 4 m test site, the mechanism makes 11 moves to reach the target position and covers 29.25% of the site.