In the late 1980s, Sam Edwards proposed an equilibrium-like statistical mechanical framework to describe the properties of disordered granular materials. The key assumption underlying this theory was that all jammed packings are equally probable. A “granular entropy” was then defined as the logarithm of the number of such mechanically stable packings. Until recently it was not possible to compute granular entropies for systems larger than a couple of dozen particles, nor it was possible to test whether for a given protocol jammed packings are equiprobable as conjectured by Edwards. In this talk I will describe how granular entropies for much larger systems can now be computed using a novel algorithm. Then, I will discuss how both the extensivity of granular entropy and Edwards’ equiprobability hypothesis were tested by this method, in two and three dimensions. Finally, I will argue that by the same approach we may obtain unprecedented insight into the nature of the yielding transition.