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We prove local Lipschitz continuity and Harnack's inequality for valuefunctions of the stochastic game tug-of-war with noise and running payoff. As aconsequence, we obtain game-theoretic proofs for the same regularity propertiesfor viscosity solutions of the inhomogeneous $p$-Laplace equation when $p>2$.

Local regularity results for value functions of tug-of-war with noise and running payoff