  The stochastic sandpile model (SSM) is a generalisation of the standard
Abelian sandpile model (ASM), in which topplings of unstable vertices are made
random. When unstable, a vertex sends one grain to each of its neighbours
independently with probability $p \in (0,1)$. We study the SSM on complete
graphs. We provide a stochastic version of Dhar's burning algorithm to check if
a given (stable) state is recurrent or not. We show that the recurrent states
for the SSM are given by convex sums of recurrent states for the ASM. This
allows us to recover a well-known result: that the number of integer lattice
points in the $n$-dimensional permutation polytope is the number of labeled
spanning forests on $n$ vertices. Finally, we study a family of so-called
"partial" SSMs, in which some vertices topple randomly, while others topple
deterministically (as in the ASM, sending one grain to all neighbours). We show
that this distinction is meaningful, yielding sets of recurrent states that are
in general different from those of both the ASM and SSM. We also show that to
get all recurrent states of the SSM, we can allow up to two vertices to topple
deterministically.
