  We bound expected capture time and throttling number for the cop versus
gambler game on a connected graph with $n$ vertices, a variant of the cop
versus robber game that is played in darkness, where the adversary hops between
vertices using a fixed probability distribution. The paper that originally
defined the cop versus gambler game focused on two versions, a known gambler
whose distribution the cop knows, and an unknown gambler whose distribution is
secret. We define a new version of the gambler where the cop makes a fixed
number of observations before the lights go out and the game begins. We show
that the strategy that gives the best possible expected capture time of $n$ for
the known gambler can also be used to achieve nearly the same expected capture
time against the observed gambler when the cop makes a sufficiently large
number of observations. We also show that even with only a single observation,
the cop is able to achieve an expected capture time of approximately $1.5n$,
which is much lower than the expected capture time of the best known strategy
against the unknown gambler (approximately $1.95n$).
