  In this paper we show how to use a Tug-of-War game to obtain existence of a
viscosity solution to the infinity laplacian with non-homogeneous mixed
boundary conditions. For a Lipschitz and positive function $g$ there exists a
viscosity solution of the mixed boundary value problem, $$ \{\begin{array}{ll}
\displaystyle -\Delta_{\infty}u(x)=0\quad & \text{in} \Omega, \displaystyle
\frac{\partial u}{\partial n}(x)= g (x)\quad & \text{on} \Gamma_N,
\displaystyle u(x)= 0 \quad & \text{on} \Gamma_D. \end{array}. $$
