How Many Times Did You Wash That Dish?

Updated to compare the put clean dishes on bottom option!

I put dishes away a lot – every day, it seems. From time to time I wonder – should I put the clean dishes on the bottom, in order to make sure I use them evenly? Or does it really matter – I do use all of them from time to time, so maybe that mixes them up enough?

Since my math is far too poor to do this analytically, I built a simulation. And since my primary “language” appears to be web pages, I built it in javascript on a web page.

This simulation models what happens when you use a random number of plates from the cupboard, wash them in your dishwasher, and put the clean ones back in the cupboard in random order. Do you end up using some more than others?

You can choose how many plates are in the stack, and determine whether the number of plates used each day is drawn from a uniform distribution (default), or from a normal distribution.

dishes in stack Use normal distribution, with parameters:
standard deviation

The stack of dishes below represents the current stack in your cupboard, top to bottom, and the number represents the times the dish in that current position has been washed.

Times washed:
Stdev is normalized

It appears from running a few variations of the parameters that you can end up with some relatively unused plates even after several years worth of wash cycles, especially if you model the dish usage on a normal distribution. Uniform distributions recycle things pretty efficiently after 100 days or so. As one would suspect, putting the clean ones on the bottom gives you almost perfect uniformity!

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