common-ap: Daily replenishable trip BR with a twist

[common-ap]

Having lost my trip bankroll, I?m planning to remain on the same trip for another 60 days. I have the ability to replenish or supplement my BR daily by an amount equivalent to 3 max bets. I?m trying to figure out what reduction of my betting ramp should I implement if my only goal is to maximize the EV I get out of this trip.
I am not concerned about playing for a small hourly EV and I?m prepared to play until I run out of money or 8 hours every day (whichever comes first.)

One way to go about it would be to keep the same max bet and then promptly lose the day?s BR in 30 minutes. That would be exactly the way to do it if I valued my time and wanted to keep my usual hourly rate. But I don?t, my goal is to maximize the EV I get out of the trip and I realize that method won?t do it.
Another way would be to look up trip bankroll tables and figure out what my max bet should be for that day in order to not lose my day?s BR within an arbitrary certainty that I choose (e.g. 95%)

I believe that given a certain BJ game (EV and speed) and assuming a well proportioned betting ramp (e.g. 1/2000th Kelly of the original BR) there is one and only one such ramp at any moment that would produce the max EV for the trip. I?m just not sure I can come up with it at the moment.
Another question that may need to be answered first is whether a daily fixed Kelly betting ramp that maximizes the EV of the next 8 hours also maximizes the EV of the next 480 hours. In other words even if I find the ramp that maximizes my EV for the next 8 hours is that THE ONE? Or do I need to reduce it even further (or maybe even increase it?) to be consistent with maximizing the total EV for the 60 days?

[Don Schlesinger]

Your question, and ones like it, have been kicking around for quite a while. I don't have the exact answer for you, but I'm quite sure that there is no one, fixed, ramp. Rather, there would be a whole slew of them, based not only on your current bankroll, but how many days remain in the trip.

The latter is important, as well, because, it is clear that how you play to try to be reasonably sure that you'll last 60 days is very, very different from how you'd play to make sure you lasted one or two days.

We began a similar discussion a while ago, and we asked Karel Janecek for a little guidance. He provided a few references of works on similar topics, but I must admit that I didn't get around to reading them. As you might suspect, this is a question whose answer is not easy to pin down.

Don

[common-ap]

Thanks Don

I found Karel?s take on this issue that you?re referring to. His thread starts with this post:
http://www.advantageplayer.com/black...s.cgi?read=698

I need to get this problem figured out so I might give the Monte-Carlo sims a try unless someone who sees this has already done that.
I?m guessing excel will probably not cut it. If anyone has knowledge on selecting the right software for this kind of problem I?d be grateful. Especially if someone has used any of the following:
@RISK
CRYSTAL BALL
or matLab

common-ap