I think JBQ has the answer about right, but let's no forget the
forest from the trees here....
the tree part first!
The Central Limit Theorem can be simply state as follows: when
sampling from a population that is not normally distributed, as the
sample size grows the sample distribution will approximate a normal
distribution, which then allows us to apply the well defined mean and
variance terms. Remember the normal distribution is completely
defined by its first two moments: mean and variance. The further the
parent population is from normal the less well the approximation to
normal is. In the video poker case the approximation is so-so at
best. Just think how skewed the results of individual hands are.
The forest part...
What video poker players really want to know is their chance of
ending up big losers over a single session; a weekend; or a lifetime!
For lifetime only expected returns matter, variance is irrelelvant.
For a single session or a weekend variance matters. But, the system I
use to guage this doesn't use variance. It's a system very similar to
what Harry Porter posted several days ago. Pull out the less likely
events for the given number of hands played and calculate expected
loss based on the new ev. This is a system that is actually usuable
by everyone on here. Perhaps the wrong people are writing all the
video poker books and articles...Harry do you have a book deal?
One final poke at the normal curve analysis, as one of the Army
Corps. of Engineers stated today," we designed the levees to a
tolerance of withstanding 99.5% of all natural disasters for a 200-
300 year time frame...we just experienced a 0.5% event"...small
comfort to the people of New Orleans!
--- In vpFREE@yahoogroups.com, Jean-Baptiste Queru <jbqueru@g...>
wrote:
The variance of the sum of unrelated events is the sum of the
variances, and the mean is the sum of the means.The standard deviation is the square root of the variance.
Since the mean grow linearly but the standard deviation grows as the
square root, the standard deviation is negligible compared to the
mean
when the number of samples tends to infinity.
After you normalize (by dividing by the mean), the normalized
standard
deviation tends to zero, and the variance (which is the square of
the
standard deviation) does the same.
That's the "law of large numbers": the deviation becomes negligible
compared to the mean when the number of samples grows toward
infinity
···
(and when the mean isn't zero, obviously).
JBQ
On 9/2/05, cdfsrule <groups.yahoo@v...> wrote:
> (BTW, how do you explain that the variance isn't geting smaller?)
