Сomputer experiments with elliptic billiard

The main optical property of an ellipse implies that a point particle moving inside of an elliptic billiard, having left a focus of the ellipse will, after a collision, certainly pass through the other focus. The same will happen also in the subsequent collisions. It is geometrically obvious that the trajectory of the particle will get closer and closer to the main axis of the ellipse after each collision. However, computer experiments give in a sense the opposite indications.