> It is psychologically useful to have a
> playing bankroll, although it is
> theoretically redundant.

This is more or less what I do although I understand that your definition is more precise: I play "full" kelly of my playing bankroll (PBR, say it is $10,000). If the PBR goes down I don't resize. If I happen to double it then I double my unit size.
Of course, my theoretically kelly number is 1/n being "n" the quotient between my "Net Worth" and my "PBR". If my NW is $100,000 then my kelly number is 1/10.

Sincerely,
Cacarulo