  We consider interior H\"{o}lder regularity of the spatial gradient of
viscosity solutions to the normalized $p(x,t)$-Laplace equation $$
u_t=\left(\delta_{ij}+(p(x,t)-2)\frac{u_i u_j}{|Du|^2}\right)u_{ij} $$ with
some suitable assumptions on $p(x,t)$, which arises naturally from a two-player
zero-sum stochastic differential game with probabilities depending on space and
time.
