A sandpile on a graph is an integer-valued function on the vertices. It evolves according to certain local moves called topplings. Some sandpiles stabilize after a finite number of topplings, while others topple forever. If we start with a sandpile $s_0$ and successively add a sand grain at a random vertex and then stabilize if possible, then we eventually reach a sandpile $s_\tau$ that topples forever. Statistical physicists Poghosyan, Poghosyan, Priezzhev and Ruelle conjectured a precise value for the amount of sand in this threshold state $s_\tau$ in the limit as $s_0$ goes to negative infinity. I will discuss a recent proof of this conjecture and some consequences.