  A gambler moves on the vertices $1, \ldots, n$ of a graph using the
probability distribution $p_{1}, \ldots, p_{n}$. A cop pursues the gambler on
the graph, only being able to move between adjacent vertices. What is the
expected number of moves that the gambler can make until the cop catches them?
  Komarov and Winkler proved an upper bound of approximately $1.97n$ for the
expected capture time on any connected $n$-vertex graph when the cop does not
know the gambler's distribution. We improve this upper bound to approximately
$1.95n$ by modifying the cop's pursuit algorithm.
