  We introduce a new model of a stochastic sandpile on a graph $G$ containing a
sink. When unstable, a site sends one grain to each of its neighbours
independently with probability $p \in (0,1]$. For $p=1$, this coincides with
the standard Abelian sandpile model. In general, for $p\in(0,1)$, the set of
recurrent configurations of this sandpile model is different from that of the
Abelian sandpile model. We give a characterisation of this set in terms of
orientations of the graph $G$. We also define the lacking polynomial $L_G$ as
the generating function counting this set according to the number of grains,
and show that this polynomial satisfies a recurrence which resembles that of
the Tutte polynomial.
