Bob,
It makes sense to clean them up and prepare them for the next round. So when the yeast is harvested, what is the method used to calculate/estimate how many you actually have so you can have the correct size pitch?
The easiest way is to to go to
http://www.mrmalty.com/calc/calc.html and use the calculator.
Click the "Repitching from Slurry" tab and dig in.
If you want to actually dig into brewing science, do your own calculations.
JZ on Mr Malty specifies 0.75 million cells per milliliter of wort per degree Plato for ales and 1.5 million for lagers. These are good numbers, and they're the numbers the Calculator uses.
I prefer simpler numbers, for several reasons.* I use a number in the middle.
I want one million
active cells per milliliter of wort. The arithmetic is pretty easy when one number is 1, too. Let's assume a 5-gallon batch of wort.
(1 million cells) x (ml of wort) x (°Plato)
or
1,000,000 x 20,000 x (1°P) = 20,000,000,000 cells
If you use "1 million" you can reduce the formula to:
20,000,000,000 x (°Plato)
For every °P you need 20 billion cells.**
Now, how much viable yeast is in the slurry in the bottom of your fermenter? Without a yeast laboratory, there's no way to know for certain, but we can make some well-educated estimates. There's between 4 and 5 billion cells in a milliliter of pure yeast, but a slurry (cake) isn't pure yeast; you can expect 1.2 billion cells in a fresh slurry.
So if you need, say, 240 billion cells (to pitch a wort of 12°P or 1.048 OG), you need:
240/1.2 = 200 ml of slurry
It's really easy once you do it a couple of times.
It's the formula I was taught to use in my professional-brewing apprenticeship, and it's served me extremely well over the years. It's slightly overpitching ales and slightly underpitching lagers, theoretically, but not so much as I've ever noticed a difference.
Cheers!
Bob
* Homebrewers who can actually count active cells are vanishingly rare. A middling number gets you close enough for success without going overboard, investing in a yeast laboratory.
**
http://www.fermsoft.com/gravbrix.php - SG to °P conversion table.