If the boy had cleaned up his yard completely before the old man came out, then as the battle began, would be greater than , and there would be a net flow of apples to the boy's side. His agility would do him no good if there were no apples on his side to pick up.

Conversely, if the battle had begun with equal concentrations of apples on each side, then would have been greater than because the agility constant is greater than .

With the same number of apples at their disposal, the boy always can do better than the old man because he gets around faster.

In either case, a neutral observer would have found to his surprise that the battle eventually settled down into a stalemate, or equilibrium in which = , at a point where the extra apples on the old man's side just compensated for the extra agility of the boy.