[BillC]

I am making some assumptions to invoke Kelly of course. Some fool might want to bet his whole BR on a coin flip, but Kelly is optimal in well-known senses, which one can read about.

Bankrolls can't be replenished by definition. The replenishment would be included in the initial BR. If I am going to inherit a million dollars in 30 years, I would include the present value in my BR.
The 1% rule is in line with the usual 300-500 big bet bankroll often recommended for limit holdem for a "skilled player".

You are incorrect--I am the same BillC