\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
\begin{thebibliography}{10}

\bibitem{Althoen-King-Schilling}
S.~Althoen, L.~King, and K.~Schilling, \emph{How long is a game of snakes and
  ladders?}, Mathematical Gazette \textbf{77} (1993), no.~478, 71--76.

\bibitem{Biggs}
N.~L. Biggs, \emph{Chip-firing and the critical group of a graph}, Journal of
  Algebraic Combinatorics \textbf{9} (1999), 25--45.

\bibitem{Bitar-Goles}
Javier Bitar and Eric Goles, \emph{Parallel chip firing game graphs},
  Theoretical Computer Science \textbf{92} (1992), 291--300.

\bibitem{Bjorner-Lovasz}
Anders Bj{\"{o}}rner and L{\'{a}}szl{\'{o}} Lov{\'{a}}sz, \emph{Chip-firing
  games on directed graphs}, J. Algebraic Combin. \textbf{1} (1992), no.~4,
  305--328.

\bibitem{Bjorner-Lovasz-Shor}
Anders Bj{\"{o}}rner, L{\'{a}}szl{\'{o}} Lov{\'{a}}sz, and Peter~W. Shor,
  \emph{Chip-firing games on graphs}, European J. Combin. \textbf{12} (1991),
  no.~4, 283--291.

\bibitem{Dirks}
R.~Dirks, \emph{{H}i {H}o! {C}herry-{O}!, {M}arkov chains, and {M}athematica},
  Stats (Spring 1999), no.~25, 23--27.

\bibitem{Engel1}
Arthur Engel, \emph{The probabilistic abacus}, Educational Studies in
  Mathematics \textbf{6} (1975), 1--22.

\bibitem{AEngel}
\bysame, \emph{Why does the probabilistic abacus work?}, Educational Studies in
  Mathematics \textbf{7} (1976), 59--69.

\bibitem{Gadbois}
S.~Gadbois, \emph{Mr. {M}arkov plays {C}hutes and {L}adders}, The UMAP Journal
  \textbf{14} (1993), no.~1, 31--38.

\bibitem{Goles-Kiwi}
Eric Goles and Marcos~A. Kiwi, \emph{Games on line graphs and sand piles},
  Theoretical Computer Science \textbf{115} (1993), 321--349.

\bibitem{Johnson1}
R.~Johnson, \emph{The dice game ``{D}rop {D}ead''}, Teaching Mathematics \& Its
  Applications \textbf{15} (1996), no.~3, 97--98.

\bibitem{RJohnson}
\bysame, \emph{Using games to teach {M}arkov chains}, PRIMUS \textbf{13}
  (2003), no.~4, 337--348.

\bibitem{Kemeny-Snell}
J.~Kemeny and J.~Snell, \emph{Finite {M}arkov chains}, D. Van Nostrand,
  Princeton, NJ, 1960.

\bibitem{Roberts}
Fred~S. Roberts, \emph{Discrete mathematical models, with applications to
  social, biological, and environmental problems}, Prentice-Hall, Englewood
  Cliffs, NJ, 1976.

\bibitem{Tardos}
G{\'{a}}bor Tardos, \emph{Polynomial bound for a chip firing game on graphs},
  SIAM Journal of Discrete Mathematics \textbf{1} (1988), no.~3, 397--398.

\bibitem{van-den-Heuvel}
Jan van~den Heuvel, \emph{Algorithmic aspects of a chip-firing game},
  Combinatorics, Probability \& Computing \textbf{10} (2001), no.~6, 505--529.

\end{thebibliography}
