Terry: One & Two deck games in Nevada

[Parker]

> If you were doing the latter, couldn't you just
> determine the duration between bankroll additions, the
> risk you are willing to take on for any given
> duration, and adjust your bet ramp according to that
> info? So, if you start with BR, and every month will
> add X, in month 1 you have a trip bankroll BR, then
> let BR = BR + NET + X and proceed accordingly? How is
> a replenishable bankroll different from constantly
> readjusted one? Set ROR to a constant and bet
> accordingly.

That's one possibility.

Suppose we had a player who had $2K and could come up with another $2K every two months to a total of $24K, but he wants to start playing immediately. One extreme would be to only count the money actually in hand, which means he would be starting off betting low red if he wished to keep ROR to what is generally considered an acceptable level.

The other extreme would be to size his bets as if he already had the $24K in hand, knowing that he would stand a high risk of tapping out in early sessions, even though the overall ROR would still be acceptable.

The best answer is probably some sort of middle ground, but so far nobody has come up with a trick formula to quantify it, although as I mentioned earlier, there have been a couple of threads on Don's Domain.

[Trapper]

But I think the assumption is that you are starting out betting to a theoretical bankroll higher than the bankroll you currently have. That bankroll is based on the amount you start with as well as taking in to consideration the amount you will be adding over time.

When you are continually readjusting your bankroll based on a fraction of Kelly for instance, you are always betting optimally to your actual bankroll (or Kelly bank). In the first case, you would be overbetting your actual bankroll (cash on hand) but if you sized your bets based only on your cash on hand wouldn't you be underbetting based on your total annual bankroll?

[Parker]

> But I think the assumption is that you are starting
> out betting to a theoretical bankroll higher than the
> bankroll you currently have. That bankroll is based on
> the amount you start with as well as taking in to
> consideration the amount you will be adding over time.

> When you are continually readjusting your bankroll
> based on a fraction of Kelly for instance, you are
> always betting optimally to your actual bankroll (or
> Kelly bank). In the first case, you would be
> overbetting your actual bankroll (cash on hand) but if
> you sized your bets based only on your cash on hand
> wouldn't you be underbetting based on your total
> annual bankroll?

Exactly - and therein lies the dilemma: How to come up with a formula for calculating bet ramp, ROR, etc., that is somewhere between the two. As I've previously mentioned, this is not a simple problem.

[AutomaticMonkey]

> Exactly - and therein lies the dilemma: How to come up
> with a formula for calculating bet ramp, ROR, etc.,
> that is somewhere between the two. As I've previously
> mentioned, this is not a simple problem.

It's always an issue, which is why I do all my bet sizing in terms of trip ruin now. I tolerate a trip ROR between 2% and 5%, depending on my state of mind, length of trip, and other personal considerations. I've a decent income, such that losing my BR only means I'll be spending less time at the casino and more time at the gym for a few weeks. But going out on a dedicated BJ trip for a few days is a time when you really don't want to run out of funds. Just imagine tapping out on the UP of Michigan with a few days to go!