Re: Question about analyzing stats




On Jan 18 2006 12:02 AM, Chris Bellomy wrote:

> Gary Carson wrote:
>
> : If you have a standard deviation of about 30 big blinds, and you don't have
> : decent estimates after about 5,000 hands, then you probably should be
> looking
> : for some other explanations rather than sample size.
>
> I'm trying to figure out what you're measuring the 30 big blinds
> across. 100 hands?

I'm not measuring it across anything.



 IOW, if in your first 100 hands you win 20 BB;
> and in your second 100 you lose 10 BB; and the bulk of your other
> 100-hand clusters fall in between those two; then your standard
> deviation is likely 30 (or less)?

Observed and actual aren't the same thing at all.  Observed is the data you're
collecting, actual is some unknown constant that you're making the observations
so that you can estimate it;


>
> Sorry if I'm being obtuse, I did take the trouble to read up
> on standard deviation before composing this followup (I know
> very little of statistics). I just can't figure out exactly
> how we should be looking at the data to figure out the standard
> deviation.

I think you need to start your statitics studies at the beginning.  There's a
*** load of websites that explain basic ideas about using random samples to
estimate unknown parameters of a large population.

The population of note here is the outcome of a random process -- the process is
playing a hand of poker.  It's random because the inputs to each hand are random
(cards, etc). 

The assumption is that the process of playing cards will generate a series of
outcomes that over all possible outcomes will have some mean and variance. 
These are generally assumed to be fixed, constant, although we might not know
their value.

If we're going to use samples of play to estimate the mean, and want to know how
large the sample needs to be to get an estimate within a specified accuracy, you
just need to know what the variance is.  If you have to estimate them both from
the sample then no one can tell you in advance how big of a sample you need.

But, probably most people have about the same vairance, even though they won't
have the same mean.  After years of listening to people report their sample
variance, I'm guessing that 30 big blinds is about typical for a standard
deviation.  So, that's the number I used.

If that sample is too small for you then it might be that you have a much larger
varaince, and it might be that your mean is not a constant but a function of
time (if you or your opponents are learning) or a function of game selection, or
some other thing.  The trick then becomes identification of the correct
functional form for your mean (it it's not a constant) and that requires a lot
of looking into details of you and your opponents.

If you have no background in statistics at all, after a couple of months of an
hour or two a day study you should be able to clearly understand everything
above.


>
> If I'm reading you correctly, though, that bodes well for my
> smallish sample of stats.
>
> One externality, though: would EV in the hands one gets dealt
> tend to produce a standard deviation small enough to make a
> 5000-hand data sample meaningful?

EV doesn't produce a standard deviation.  They're pretty much independent.  If
they aren't independent then you have a much deeper statistical problem than
you're going to be able to address.


>
> Thanks, Gary.
>
> cb
Gary Carson
http://www.garycarson.com



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