The tennis ball problem

Natasha often says we should open more cans of tennis balls.  Last night we were playing with eight balls and she wanted to play with twelve.  Of course once all eight have been plowed into the net, you have to go collect at least some of them.

How many tennis balls should you play with?

Let’s say you had many, many balls and you could open the cans for free and never run out.  Opening a new can every four points (four balls fit in a can) would lead to a massive clean-up and carry problem at the end.  Furthermore how much help is it having more balls?  Once they hit the net you still have to deal with getting another ball into play.  In other words, the real trick is to manage your stock well (read: aim for good volleys), not to just to speed up the flow of balls into the court.

Just one ball is not efficient, because when it falls out of play it is probably far from you.  The greater the number of balls, the more likely at least one will be close.

Many problems in life, including those of dating, the number of children you should have, and optimal inventory management, resemble the tennis ball problem. 

I do not know how to solve the tennis ball problem, but I feel that twelve balls is too many.

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