Bankroll Management: Static, Stepwise, or Continuous?

[DavidC]

Hey guys, I confess, I don't know how to manage my roll. [img]/images/graemlins/frown.gif[/img]

You're given bb/100 of 2bb, and std dev of 15 bb. Generally I like to have ROR = 0.1% = 0.001, therefore my BR at ROR = 0.1% is 440.36 BB... FYI, ROR = exp(-2*BR*EV/VAR).

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How do I manage my roll within that threshold? Here's a few options:

A) I start playing 2/4 LHE with 440 bb, until I lose a bb, then drop to 1/2.

B) I start playing 2/4 LHE with 440 bb, until I drop to 220bb, then drop to 1/2 at 440bb at that level.

C) Play 2/4 until I bust.

For option C, although I originally had taken a 1/1000 ROR shot, when I get to 30bb in my stack, there's about a 60% chance of busting.

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Option A represents what I will call a "Continuous" risk threshold. This means that you're constantly looking at your BR to determine what you should be doing. This is going into super-conservative territory, but it may be the correct approach. I'm just not sure yet if I should be using this approach or not. I suspect that this approach makes your actualized ROR much much lower than 1/1000, since you'll be reducing bet sizes in a downswing.

Option C represents what I'll call a "Static" risk threshold. This is actually pretty funky: if you had something like a million dollar roll, but for some reason you could only accept swings of a maximum of $1760, you'd go ahead and set this threshold, and there's only a 1/1000 chance that you'd ever see an absolute downswing (not relative to EV) this violent. On the other hand, if you play your bankroll like a "system", accepting one shot at risk, in a sense, this is it. You take your 1/1000 chance, no matter what happens, you'll never exceed that chance.

FWIW, the reason that a 300bb roll is acceptable is because of people's willingness to drop down in limits if they hit a bad swing. Otherwise, you may be best to keep a 440 roll just to protect you from the really bad swings. They DO happen.

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Option B, which is what most people take, is what I'll call the "step-wise" approach to bankroll management. Here's how it might work in practice:

You have a roll of X. You decide to bet at threshold ROR=0.1% until your new roll, Y, is either 1.5X or 0.5X, at which point, you will re-evaluate your bet size (stakes) to be consistent with ROR = 0.1% at new bankroll X.

Alternatively, you might play until Y = 0 or 2X, before you re-evaluate.

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I've shown some different bankroll management practices, and I've shown you guys why Miller says what he says (in the 2p2 mag) about bankroll management, but I can't tell you guys what is best. On one hand, it's subjective, and I can't tell you what an acceptable level of risk is for YOU, and on the other, I don't have a clue which of these three approaches is the most suited to an advantage gambler in general.

Any input on this would be appreciated.

[DavidC]

[ QUOTE ]
ROR = exp(-4*BR/225)

[/ QUOTE ]

Correction, my ROR = 0.01% at 388.56 bets (at one point during the ROR discussion I moved to 255 instead of 225, which threw off the results.

[DavidC]

Also, a kinda dumb question as long as I'm on the subject of ror.

When calc'ing the ror, should I be using ev and std dev for 100 hands, or for one hand?

if it's for one hand, then what should I be doing?

ev = 0.02, of course.

now is std dev 0.15, or is it 1.5? (i.e. should I be using the sqrt of 100 or just dividing it?)

[BillC]

Your option B is esseentially using a smaller bankroll requirment, with higher instantaneous ror. Maybe you are just saying in this case that your risk tolerance is somewhere between two endpoints. You can use any unit of 'time' since the ratio var/ev does not depend on the no. of hands.
See my July magazine article.

[DavidC]

[ QUOTE ]
Your option B is esseentially using a smaller bankroll requirment, with higher instantaneous ror.

[/ QUOTE ]

Firstly, I didn't get your article, sorry. [img]/images/graemlins/frown.gif[/img]

Secondly, if we started at 1% ror, then we can never achieve greater than 1% ror on our bankroll unless we increase stakes, right?

If that's true, then option B gives necessarily a lower ROR than option C.

OOC, do you have another link to the article?

If it was the Kelly Betting article, I wasn't really able to understand those types of articles in July. [img]/images/graemlins/smile.gif[/img]

--Dave.

[DavidC]

[ QUOTE ]
Firstly, I didn't get your article, sorry.

[/ QUOTE ]

By this I meant that I didn't remember your article.

Is option A the same as option B except for a factor of 2?

Anyways, I prefer option B. From a theoreticall point of view, the only things that should matter are your EV and variance at the relevent levels, and how big your roll is. What limits you have been playing in the past may have an indirect effect on your EV at various levels (maybe even a bit on the variance, probably negligable though) but it should have no direct effect on your decision to play whatever stakes

In option C, there is a huge dependence on what limits you have been playing in the past, which doesn't make a lot of sense theoretically

[DavidC]

[ QUOTE ]
Is option A the same as option B except for a factor of 2?


[/ QUOTE ]

Here's what I was thinking on my walk home tonight (from a coffee shop):

To evaluate Option B, where you're going to take a 0.1% ror at BR B, where BR B is half BR A, and you will not further decrease bet size as your roll drops:

ROR 0.1% at BR A gives a certain bet size.

Then you take your roll, cut it by the bet size, divide it by half, then figure out your ROR of losing that amount.

Then you multiply that risk by 0.001, and you've got your new ROR for your bankroll.

--Dave.

Of course, this doesn't tell you what's BEST, it just tells you what IS.

--Dave.

So to answer your question, No (at least, I don't think so, but run some numbers and see what you get).

Edit: --Dave [img]/images/graemlins/cool.gif[/img] .... it's saturday night man, and I'm half-drunk, give me a break.