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A new bound (Theorem \ref{thm:main}) for the duration of the chip-firing gamewith $N$ chips on a $n$-vertex graph is obtained, by a careful analysis of thepseudo-inverse of the discrete Laplacian matrix of the graph. This new bound isexpressed in terms of the entries of the pseudo-inverse.  It is shown (Section 5) to be always better than the classic bound due toBj{\"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 boundsreduce 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 arein the works.

Chip-firing may be much faster than you think