In this thesis, we deal with two different types of problems related to nonlinear partial differential equations. We investigate regularity theory for oblique derivative problems and tug-of-war games. We study fully nonlinear elliptic and parabolic equations in nondivergnece form with oblique boundary conditions in the first part. Our boundary condition is a generalization of Neumann condition. We derive global Calder\`{o}n-Zygmund type estimates under $C^{3}$-boundary regularity assumption. In the second part, we study a stochastic two-player zero-sum game which is called tug-of-war. In particular, we consider here time-dependent games. We show global Lipschitz type estimates for value functions of such stochastic games. Furthermore, we also investigate their long-time asymptotics and PDE connections as applications.