  We consider the open stadium billiard, consisting of two semicircles joined
by parallel straight sides with one hole situated somewhere on one of the
sides. Due to the hyperbolic nature of the stadium billiard, the initial decay
of trajectories, due to loss through the hole, appears exponential. However,
some trajectories (bouncing ball orbits) persist and survive for long times and
therefore form the main contribution to the survival probability function at
long times. Using both numerical and analytical methods, we concur with
previous studies that the long-time survival probability for a reasonably small
hole drops like Constant/time; here we obtain an explicit expression for the
Constant.
