  A new bound (Theorem \ref{thm:main}) for the duration of the chip-firing game
with $N$ chips on a $n$-vertex graph is obtained, by a careful analysis of the
pseudo-inverse of the discrete Laplacian matrix of the graph. This new bound is
expressed in terms of the entries of the pseudo-inverse.
  It is shown (Section 5) to be always better than the classic bound due to
Bj{\"o}rner, Lov\'{a}sz and Shor. In some cases the improvement is dramatic.
  For instance: for strongly regular graphs the classic and the new bounds
reduce to $O(nN)$ and $O(n+N)$, respectively. For dense regular graphs -
$d=(\frac{1}{2}+\epsilon)n$ - the classic and the new bounds reduce to $O(N)$
and $O(n)$, respectively.
  This is a snapshot of a work in progress, so further results in this vein are
in the works.
