An Aggressive Approach to Bankroll Management Article

[pzhon]

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I would almost never invest anything close to 10% of my BR on one SNG, even with a fairly large perceived edge. This is because I gamble for over 90%+ of my living, and I place such negative value on losing all my assets that I'm willing to go pretty far to ensure that doesn't happen.

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Non sequitur. Your reason is part of the assumptions of the bankroll management models. Kelly's work assumes that going broke is infinitely bad. So, you need to have another reason to justify not ever buying in for

Let's suppose you normally toss coins for $10 with an edge of 1%. Let's suppose you feel adequately bankrolled with $5000, but you wouldn't with only $1000. How much of that $5000 would you be willing to bet as a 3:2 favorite? How much would you be happy to get in with AA against a random hand, let's say as a 6:1 favorite?

I don't see how to answer these consistently without using math, and the math says that the edge you have matters a lot.

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Anytime you base decisions that involve putting risk aversion into a number based purely on plugging numbers into an equation, you're not gonna get a prefect answer.


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That looks like an irrational distrust of mathematics. It's good to understand something so well that you can model it mathematically. Why would you trust the answer more if you fail to quantify something? I hope you are trying to say something else.

[Jetto2]

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Anytime you base decisions that involve putting risk aversion into a number based purely on plugging numbers into an equation, you're not gonna get a prefect answer.


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That looks like an irrational distrust of mathematics. It's good to understand something so well that you can model it mathematically. Why would you trust the answer more if you fail to quantify something? I hope you are trying to say something else.

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I agree but most of the time and this the case in this article a formula come from no where with very few explanation so this is quite the same to assume that result is right than assuming the formula is right. In most case authors silently does hypothesis that are obvious in his personal case but may be false for others. The most common hypothesis is the normal distribution of results.

I don't understand how to manage a BR without speaking of RoR. Without this BR management is only gambling.

Whatever, if our RoR formula a right, if values we use in formula are right, if we perfectly manage our BR to have less than 1% of RoR, we still have 1% to run out of money [img]/images/graemlins/tongue.gif[/img]

[k-rag]

hi all,

it's pretty cool to see this topic in the magazine.

here is a post i made a while back on the topic, with some discussion that went on. the first post i made in the thread below was a little off, scroll down to the revision i made a few posts down. there is also some good discussion there from some folks overseas on using exact finish distributions to better understand the variance involved.

http://forumserver.twoplustwo.com/sh...umber=10403633

it's good to see in the article the author used finish distributions, as this gives a little bit more info than using just ROI & ITM. anyway, in SnG practice, i ran into the a lot of limitations in using this. for one, it essentially forces you to play in sets rather than continuously. if you are 8-tabling or so you will often be playing across 2 buy-in levels, which sometimes makes it hard to adapt. this problem gets worse the more tables you add. also you need to set a floor for the BR (and buy-in level) so that you don't get stuck playing micro-limit sng's during a bad run.

of course the other catch 22 is not knowing your ROI for the levels in which you are taking a shot. with a large sample size at multiple limits, however, this is the best way to ramp up a small BR or to rebuild a BR up to a level after cashing out or sitting out for awhile.

[Lucky Nick]

The article seems to recommend some bankroll fraction (f*=5% or 1/2 f* =~ 2%) for a 30% win rate in a 9 men SNG? But I'd think that a 30% win rate (ITM percentage) for a 9 man SNG is actually a losing proposition, with a ROI that cannot be higher than -15% to -20%?! So , bankroll recommendation for losing propositions?!? what am i missing here?

[pzhon]

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I'd think that a 30% win rate (ITM percentage) for a 9 man SNG is actually a losing proposition, with a ROI that cannot be higher than -15% to -20%?!

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No, the discussion is about a player with a 30% ROI. The ITM rate assumed in the article was 40%, above the 33% average.

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For example, the person cashing 40% of the time over 1,500 games will cash in 600 games. Let's say they won 210, second place 238, and third place 152 times.[/list]

[pzhon]

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here is a post i made a while back on the topic, with some discussion that went on.

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Would you care to summarize what you think that discussion accomplished? I don't think it made the progress you think it made.

You mentioned,
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this is nowhere close to the suggested 100 buy-ins: definitely RoR has plenty to do with that.

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No, it doesn't. Risk of ruin is not a separate consideration. It's easy to translate a proportional guideline to a ROR value if you stay at a fixed level, e.g., Kelly corresponds to a ROR of about e^-2 ~ 14%, and half-Kelly is about e^-4 ~ 2%. You can't blame the the tremendous discrepancy on a rational consideration of ROR.

100 buy-ins is a figure used out of context. Similarly, it is grotesquely inaccurate for the SSNL FAQ to suggest that you should have $100 to play NL $0.01-$0.02 on PokerStars just because there is a $5 buy-in. This ignores the fact that it is much harder to lose a 250 BB buy-in than a 100 BB buy-in, and that most penny-ante players hate money so serious players' win rates are ridiculously high compared with other stake levels. When people apply the 20 buy-ins rule out of context, they sit out until grossly overbankrolled for soft games, and but play while dangerously underbankrolled for tough games.

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scroll down to the revision i made a few posts down.

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Was the revision particularly concise and accurate? How does it compare with c * SD^2/ROI?

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there is also some good discussion there from some folks overseas on using exact finish distributions to better understand the variance involved.

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Do you mean the comment that the exact finish distribution has a very small effect? Paxinor wrote, "the difference is really really small so it won't matter." So, why bring it up?

With very skewed distributions, like +EV video poker with a large jackpot, the normal approximation is not good. You need a slightly smaller bankroll when the positive tail is thick, such as when you can win a jackpot. You need a slightly larger bankroll when the negative tail is thick, such as when you may have to pay out a jackpot. This isn't particularly relevant to SNGs.

To worry you that the recommended bankroll level might be too high by a few percent, you should have astoundingly accurate estimates elsewhere, particularly of your ROI (which should be known more accurately than 1%) and know exactly which Kelly fraction you are using (within a few percent). Others are worrying about getting the right bankroll within a factor of 2.

You also wrote,
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yes of course, roi is not constant. you don't need a more complex formula.

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You need to think about that more. Of course you need a more complicated formula when the ROI is level-dependent. In general, this says that you should play at levels where the fractional Kelly system you prefer would say that you are overbankrolled.

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it's good to see in the article the author used finish distributions, as this gives a little bit more info than using just ROI &amp; ITM.

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The article failed to use the finish distribution properly, as mentioned in the note at the bottom. So, what was the point?

You get very little from using the finish distribution, ROI, and ITM that you don't get from the far simpler ROI + a simple estimate of 1.7 buy-ins for the standard deviation. The latter gives you a simple, applicable formula. The former is an invitation to make many types of errors.

Some people find complicated formulas and page-filling tables of values aesthetically pleasing. As a mathematician and theoretician, I don't, and I maintain that you aren't getting an increase in accuracy from the additional factors you want to include that can justify a huge increase in complexity over Kelly's c * SD^2/WR.

[Mr. Now]

Optimal f maximizes theoretical return without regard to theoretical downstring magnitude (drawdown).

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Risk of ruin depends on what you will do when you hti a down swing. When will you move down, and what would that do to your win rate?


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That is not exactly how I think about it. If you can handle huge swings, go 100% Optimal f and optimize for max theoretical return without regard to theoretical downswing magnitude. Otherwise scale back to 1/2 Kelly etc. There is the emotional impact of drawdown to consider per individual.

RoR is a impossible to get rid of and must be managed. For Mr. Now, what he is likely to do during a downswing has EVERYTHING to do with defining an acceptable RoR and nothing to do with RoR itself per se.

'Acceptable RoR' is a great concept and easy (and essential) to put into practice.

That excellent discussion on the “Acceptable Risk of Ruin” concept appears here:
http://www.traderscalm.com/rorhandiwork2.html

[pzhon]

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That excellent discussion on the “Acceptable Risk of Ruin” concept appears here:


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Actually, that's horrible. Are you in any way associated with that site?

First, "The Calm Trader" is introduced as someone who never has substantial downswings, even 10%, and has been more than tripling his money each year. Are we supposed to believe this? It sounds like they are slowly unveiling a get-rich-quick scheme, preying on people who want to believe they can get ridiculous rates of return.

Then they discuss downswings as if the only way you can have a downswing is to lose continuously. Most 100 BB downswings do not come from losing a few hundred hands in a row. They come from losing more than expected (and winning less than expected) over stretches of thousands of hands which include many wins. No real, useful calculations are included, but there are some misleading tables.

Then they introduce the idea of hedging as "mindblowing." Come on. In a 15 minute introduction to the theory of investing, I get to hedging. It shouldn't be new to anyone who is serious... but maybe some get-rich-quick victims would be impressed by it. Is this site's goal to collect potential scam victims?

Finally, the guy who is supposed to be making 11% per month thanks the interviewer for his insights. I think something got mixed up. What better indication is there of high quality, unbiased journalism?

The article was garbage. It had almost nothing to do with having an "Acceptable Risk of Ruin," and I have to wonder why you recommended it.

[Mr. Now]

I'm sorry to hear you get nothing from the article, assume Mr. Now is somehow associated with the site, and otherwise find the article less than useless.

Apparently the article does not validate your beliefs about downswings.

Go in peace.







Go in peace.

[pzhon]

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I'm sorry to hear you get nothing from the article, assume Mr. Now is somehow associated with the site, and otherwise find the article less than useless.

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Well, I'm sorry you linked the article twice, and wasted my time. I hope my summary saved other people from taking that article seriously.

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Apparently the article does not validate your beliefs about downswings.

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Excuse me? The article says things that are flat wrong, and you suggest I am rejecting it only because I have some questionable beliefs about downwings? I have no idea which beliefs you are talking about. Do you not understand that the article is wrong, misleading, and unrelated to what you claimed it was? Did you even read it?

The article mentions coinflips which pay off more than the fair value. That's a standard toy problem. Then it claims the risk of ruin depends only on the amount you can lose and the probability that you lose, and that the only way to go broke is to lose every single time. That is wrong and ridiculous. I'm not making this up or taking it out of context. Here is a direct quote:

<ul type="square">That means that if you bet $10 a time, that would give you ten bets before you lost all your $100. And the risk of ruin (that is losing all your money), betting $10 a time would be about 1 in a thousand.[/list]Obviously, the risk of ruin if you are getting paid 2:1 is different from if you are paid 3:1, and if you lose 9 bets out of 10, you aren't home free.

Don't you think you should apologize for recommending that load of garbage twice?