Knuth's Toilet Paper Problem

Interesting problem that we face everyday. Knuth assumes that people are either big or little choosers. I don't think this is the case, e.g. my strategy is dependent on the size of the rolls.

When the roll is really big (i.e almost brand new), the low quality toilet paper (that my company thinks we're worth, if you're working in a better place this is a moot point) tends to tear, so that I can't get a piece of adequate length. This is because the tension on the paper is proportional to the moment of inertia of the roll and larger rolls have higher inertia. So, given a choice, I avoid these rolls.

On the other hand, really small rolls are annoying, too, since it's hard to estimate if the amount left is enough, i.e. while pulling a piece of paper they may finish unexpectedly, which is annoying.

So, my strategy is: avoid the very big and very small rolls. Around medium size, go for the smaller roll. I wonder how Knuth's analysis could accommodate such dynamic strategies based on roll size.

Wait - what kind of person would draw from the big roll?

The goal isn't to use them both up simultaneously. You use all of one and then the stall still has the other one during the period it takes the janitorial staff to notice and replace the empty.

Randall Munroe must be a fork of Knuth:

http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerabilit...

From the article:

"When both rolls are empty, everybody has a problem."

Indeed.

Is there some deep analogy that I'm missing, or is he just giving an example of how to analyze things?