  A gambler moves between the vertices $1, \ldots, n$ of a graph using the
probability distribution $p_{1}, \ldots, p_{n}$. Multiple cops pursue the
gambler on the graph, only being able to move between adjacent vertices. We
investigate the expected capture time for the gambler against $k$ cops as a
function of $n$ and $k$ for three versions of the game: (1) known gambler: the
cops know the gambler's distribution (2) unknown gambler: the cops do not know
the gambler's distribution (3) known changing gambler: the gambler's
distribution can change every turn, but the cops know all of the gambler's
distributions from the beginning. We show for $n > k$ that if the cops are
allowed to choose their initial positions before the game starts and before
they know the gambler's distribution(s), and if both the gambler and the cops
play optimally, then the expected capture time is $\Theta(n/k)$ for the known
gambler, the unknown gambler, and the known changing gambler.
