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#1
11-12-2007, 02:56 AM
 kerpowski Member Join Date: Feb 2004 Location: Worcester, MA Posts: 84
Kurtosis risk

It seems to me that the standard poker bankroll requirement calcs run on the assumption that pot sizes are normally distributed. In NL games this is certainly not the case. As an example a set of high stakes shortstacking NL hands of mine (10k hands) has the following characteristics:

Mean: 1.5ptbb/100
SD: 22ptbb/100
Kurtosis: 160ptbb/100

The kurtosis value is off the charts compared to a normal distribution. To what degree would this impact bankroll requirement calculations and is there any RoR forumlas that take kurtosis into account?

Regards,

Kerpowski
#2
11-12-2007, 04:47 AM
 Siegmund Senior Member Join Date: Feb 2005 Posts: 1,850
Re: Kurtosis risk

Wellll...

For a start, kurtosis is a dimensionless quantity. If you calculated something that came out with units of BB/100, then you probably have the wrong number.

Still, it is true that high kurtosis means a lot of observations very near and very far from the mean, and not very many numbers on the order of 1 standard deviation away from the mean. You DO expect poker results to be like that since you have a lot of breakeven (early fold) hands and a few big-loss and big-win hands.

There isn't a simple one-size-fits-all adjustment for you to make based on the kurtosis (and kurtosis takes a lot longer to converge to a stable value than means and standard deviations do.)

If you are paranoid and want a completely worst-case situation (which you can think of as kurtosis approaching infinity), for simple confindence intervals you can resort to using Chebyshev's theorem, which says that at least 1-(1/k)^2 of your observations are within k standard deviations of your mean -- that is, 75% within 2 SDs, ~89% within 3, ~95% within 4. But there won't be a tidy risk of ruin formula for you.
#3
11-12-2007, 06:10 AM
 curious123 Senior Member Join Date: Dec 2005 Location: not impressed by your perforaments Posts: 585
Re: Kurtosis risk

[ QUOTE ]
To what degree would this impact bankroll requirement calculations...?

[/ QUOTE ]

It doesn't seem to matter much. See MOP, p. 293.

Also, post more.
#4
11-12-2007, 10:52 PM
 Troll_Inc Senior Member Join Date: Mar 2006 Location: FGHIJKLM STUVWXYZ Posts: 2,566
Re: Kurtosis risk

[ QUOTE ]

The kurtosis value is off the charts compared to a normal distribution. To what degree would this impact bankroll requirement calculations and is there any RoR forumlas that take kurtosis into account?

[/ QUOTE ]

No there aren't any RoR formulas that take kurtosis into account.

Current RoR formulas are a joke.

This section of MoP is a joke.

I think it's pretty clear that the "experts" that post on this Probability Forum and Chen/Ankenman (whoever wrote that section) do not really have a clue about Probability Theory.

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