I think your logic is correct.
Although I wouldn't necessarily interrupt everything the same way.
- You have no idea what your ROI is at the $500 level, because you haven't had a significant sample size at that level. So you won't know what your "ideal" bankroll should be.
- Technically, since your bankroll changes as you play (either + or -), you should be changing levels as you go. So if you're on a downswing, you technically should be going to a lower level.
- Also this method is volatile. If you keep the same bet size: your bankroll will halve before doubling 1/3 of the time. That may not be a very good thing if you tilt.
Also your statement -
"By doing so, there is a 1/3 chance that you will halve your roll to $500 before doubling it to $2000 (implying that there is twice as good a chance of you doubling your roll before cutting it in half)."
Isn't quite true. According to KC, you should never bust your roll....because your Bankroll changes, thus your bet size changes. (Not really practical in poker because your ROI isn't constant, and players may not be willing to grind microlimits if it came down to that). That statement says, 1/3 of the time you're going to halve your bankroll before you eventually double it. It doesn't mean you will double 2/3 of the time before halving your bankroll.
I think it means that your bankroll will always eventually double - assuming the following to be true:
- ROI is constant
- Your bet size is = to the KC all the time
- And that your bet size can be small enough where you can continue to place the bet.
***I don't know if everything I wrote is necessarily correct.
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