A sandpile on a graph is an integer-valued function on the vertices. It evolves according to local moves called "topplings". Some sandpiles stabilize after a finite number of topplings, while others topple forever. For any sandpile $s_0$ if we repeatedly add a grain of sand at an independent random vertex, we eventually reach a sandpile $s_\tau$ that topples forever. Statistical physicists Poghosyan, Poghosyan, Priezzhev and Ruelle conjectured a precise value for the expected amount of sand in this "threshold state" $s_\tau$ in the limit as $s_0$ goes to negative infinity. I will outline the proof of this conjecture in http://arxiv.org/abs/1402.3283 and mention some algorithmic open questions.