A numerical scheme developed by Falcone, Finzi Vita, Giorgi and myself will be discussed for approximating the p-Laplacian based on a 2-player game called tug-of-war with noise. Consequential numerical results will be shown which have inspired a sequence of theoretical results. I will discuss theoretical results obtained with my collaborators including a mean value property for p-harmonic functions, a concrete realization of Wolff's example used in the proof that p-harmonic measure is not additive and discuss the local behavior of the Poisson problem for the game p-Laplacian in a corner. Time permitting I will discuss some current work on the 4-Laplacian in 2 dimensions which appears to have a remarkably simple numerical scheme.