  A natural question of how the survival probability depends upon a position of
a hole was seemingly never addressed in the theory of open dynamical systems.
We found that this dependency could be very essential. The main results are
related to the holes with equal sizes (measure) in the phase space of strongly
chaotic maps. Take in each hole a periodic point of minimal period. Then the
faster escape occurs through the hole where this minimal period assumes its
maximal value. The results are valid for all finite times (starting with the
minimal period) which is unusual in dynamical systems theory where typically
statements are asymptotic when time tends to infinity. It seems obvious that
the bigger the hole is the bigger is the escape through that hole. Our results
demonstrate that generally it is not true, and that specific features of the
dynamics may play a role comparable to the size of the hole.
