Nine collisions limit
Billiard players usually have an idea how to make a hit so that the balls move in the right direction. With more or less accuracy, they estimate the position of the balls, impact force, and other parameters to determine the trajectory.
Practice makes these calculations more accurate, but still, it seems rather easy to predict what would happen at the first hit. The second impact becomes more complicated. After a couple of collisions, the player is less able to determine where the balls go.
In 1978, a physicist Michael Berry calculated the number of collisions a billiard ball can make before a player has no way of knowing its eventual trajectory. It turned out that such calculations require taking into account not just mechanical forces but the gravity of Earth and the gravitational pull of objects close to the table. Berry estimated that if that object, for instance, is a person who weighs 50 kilos, the determinacy would be lost after 9 collisions (or even before if not considering the gravity impact).
Bottom line:
Dealing with a tightly coupled system is a difficult exercise of planning, as the complexity quickly arises even if the conditions were simple and clear at first glance.
Source: Regular And Irregular Motion by M.V. Berry (page 81)