dunbar_dra wrote:
This is an important point that is not widely appreciated. It is a
clear case where a much bigger variance leads to a smaller risk.
One thing to recognize, however, is that when one speaks of "risk" in
regard to a progressive the focus is keenly on the downside when you
don't hit a royal. In that case, between royals the variance focus is
principally on those hands that exlude the the royal -- in this
context, a standard 9/6 paytable and a RF progressive 9/6 paytable
evaluate to the same ex-RF variance.
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The broader point I've repeatedly emphasized with statements such as
"variance is a fuzzy concept" and "variance is a poor descriptor of
expected video poker results" is that it's little more than a
convenient first pass indication of play volatility and downside risk.
I've discouraged any extended focus on the statistic. Short of a very
close examination of the components of game variance it's a leaky concept.
It's often discussed that one reason variance is a faulty indicator
when it comes to video poker is that vp results aren't normally
distributed (i.e. don't adhere to a bell-shaped curve, but instead are
skewed to the left of the mean, with a long tail to the right).
I think that's an unfortunate statement since it suggests that vp in
some manner defies that manner of natural phenomena, where deviations
from the "norm" tend to distribute themselves evenly about the mean.
(A ping pong ball drop demonstration is among the strongest
illustration of the mechanics at work.)
In truth, vp results adhere to a strictly normal distribution; it's
just that the variance statistic generally cited represents a
composite of the probability of several mostly discrete events - e.g.
hitting a RF, hitting a quad, etc. (clearly there are certain
interrelationships).
If you examine the distribution with which any given hand is hit, it's
a strictly normal one and variance is a strong descrptor of that
distribution. However, when you aggregate the expected return of
several events with differing probabilities and payouts, they have a
disproportionate contribution to total game variance and you end up
with a skewed composite result.
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Variance is truthfully a very strong and reliable descriptor of vp
results, but only when you scrutinize it at a detailed level --
something that for almost all applications of the concept is
impractical when looking for an insight into play.
Set aside that close scrutiny and it's little more than a rule of
thumb (e.g. "large variance/large risk") to be interpreted with a
sizable grain of salt, weighing the context of the game situation
under consideration.
Look to more apropos statistics (e.g. "risk of ruin") if you want a
true risk assessment.
- Harry