Assuming that the boy is more energetic and agile than the old man, you might think at first that the conflict would end with all of the apples on the old man's side (Phases I and II).

It is true that with equal numbers of crabapples on either side, the boy will throw apples across the fence faster than the old man can return them. But this only means that apples will become more plentiful on the old man's side, and easier to reach.

They will become scarcer on the boy's side, and require more running around to locate. Eventually a standoff, or equilibrium, will be reached, in which the number of apples crossing the fence is the same in both directions.

The old man will throw less quickly but will have less trouble finding apples (Phase III); the boy will throw more rapidly but will waste time scurrying around hunting for the relatively few crabapples on his side (Phase IV). The ratio of apples on the two sides of the fence ultimately will be determined by the relative agility of the two combatants, but all of the apples will not end up on one side (Phase V).