In a message dated 7/26/2003 4:32:55 PM Eastern Daylight Time,
harry.porter@verizon.net writes:
Steve Jacobs wrote:
> I fail to see how either can be "more pertinent" than the other.
> They each encompass the same information. Taking sqrt(V) to get
> S.D. just "stretches" the axes a bit, but in terms of accuracy they
> must inherently each be just as accurate as the other.Steve, I appreciate the input. It may be that "pertinent" was a poor
choice of wording. What I'm saying is the in the case of ROR, sd is a
more direct indication of the relative ROR's between to games inasmuch
as there's a direction proportion between the two. Ditto between
bankroll requirement and variance.Obviously there's a well-defined relationship between variance and
standard deviation; the former is the square of the latter.However, let me pose an analogy that should clarify the reason for the
distinction I make. If I define a 2-D object to have a specific
dimension and I ask how many of these objects can fit in a square of a
given size, I can define that square both in terms of length of one
size in fixed units, or the area of that square in terms of area.
Now, obviously given one measurement you can determine the other, and
therefore you can find the answer to this problem using either
definition of the square. However, it's the case that the solution
will be directly proportional to the area of the square, not the
length of one size.The problem players are faced with when presented with the variance
statistic of a game by any one of the popular video poker programs is
interpreting the statistic in some practical manner. Let's say we
take the hypothetical choice between play of 9/6 JB in one casino with
1% in cb and/or other cash incentives, and 10/7 DB with .37% cb.
(Clearly I've chosen these values to place total ER on par at 100.54%.)In this circumstance, I'm saying that the relative bankroll
requirements of these two games is directly proportional to the
relative variance of the two games. Also that play of the two games
with the same bankroll availability will pose a ROR that's
proportional to the relative standard deviations of the two games.That to me poses a more valuable statement than simply suggesting that
the relative variance of two games presents an ideal of the risk of a
game which is the general grasp under which most players play.(And I want to take a moment to say that while I have demonstrated
these conclusions for myself with a reasonable degree of satisfaction,
I would be much more comfortable in making these assertions publicly
had I tested them thoroughly under a number of alternate scenarios.
Of course, it's the fortunate nature of some members of this group
that they'll question my statements where appropriate.)> Don's formula is also an approximation based on EV and variance.
> This is essentially equivalent to using a normal approximation in
> place of the games true probability distribution. I seriously
> question the accuracy of such approximations in the short term.I've discussed the fact that I've used the Dunbar formula published in
1997 in lieu of the update in 1999, which I understand to take into
account the short to medium term skewed distribution of vp. In that
discussion I've noted that there's a basic argument which would cause
one to anticipate the alternate relationships between s.d. and
variance which should hold up under either formula. The 1997 formula
was used as a matter of expedience.> I disagree. I'd say that variance gives a "good approximation" but
> is not a "direct measure". The true, exact ROR value (I'll call it
> XROR to distinguish it from the other forms of ROR such as Don's
> approximate formula,) computed from the characteristic equation, is
> a direct measure. Anything else is not direct except perhaps for
> special cases.Again I'll have to own up to using a general description (direct
measure) when it's not entirely accurate. For example, in my own
review I found that there were modest variations in the ratio of
standard deviation and ROR. However, plotted on an X-Y axis the
resulting regression line would likely show a very high linear
correlation between the two variable -- strong enough to suggest that
one would give you a strong basis on which to form an expected
relationship between two games.> You can compares games on one basis or the other, but it is
> important to understand that these are like apples and oranges. An
> analogy is height and weight. They measure different things, and
> greater height doesn't necessarily imply greater weight, even though
> they often track closely.In this case the varables I've correlated (e.g. s.d. and ROR) reflect
a very strong direct linear relationship. That would not be the case
beween the height and weight of various people, given a number of
other significant variables. However, even in that case, if you're
able to define the other variables well enough and look at cases in
which they're held constant that a strong direct relationship will
likely reveal itself.Now, that limitation may appear to weaken the value of the
relationships I've drawn. However, the key alternative variable is
the ER at which each game is played. That's obviously apparent when
examing the variance of two games. However, an understanding of how
the variance effects the bankroll requirements of a game clearly is
beneficial. In addition, presumably using a two-step approach would
be of use in determining the absolute relationship between two games.
One would first make the assumption that variance were a constant and
determine effect on return and then adjust that effect by the relative
actual variance of two games.Now, I'm simplifying that suggested means tremendously. Understand
that it's by way of demonstrating the mechanics at play here. The
point I really am attempting to drive home is a means by which the
player can apply to values of variance and standard deviation to
develop a reasonably concrete grasp of their impact on bankroll
requirements and ROR. In absence of that, these statistics are of
little use to the typical player. Interpreted with a understanding of
the limitations, these relative aspects of two games are revealed to a
modestly useful extent. The alternative is to say to the player that
they're totally meaningless without a complete grasp of the
relationships involved.> The problem with this is that ROR isn't a function of return. It is
> easy to construct biased-coin games where game A has 10X EV of game
> B, but game B has much lower risk of ruin.Clearly, and as noted both variance and return on critical components
of the ROR of a game. The intent of my exercise has been noted above.> To throw another curve in here, consider the fact that for most VP
> games, the playing strategy which is optimal from an XROR
> perspective is significantly (read "measureably") different than the
> playing strategy which maximizes EV. The goals "minimize ROR" and
> "maximize EV" are simply different, and require different tactics.Again, I'll concede this point. However, in seeking a general
practical use of game statistics the relationships lend considerable
insight, even if not precise.> Since variance/std_dev are approximate, I prefer working directly
> with XROR.There's no argument if one has access to the XROR of a game. The
purpose of my review was to find a means by which the recreational
player might find a valuable interpretation of s.d. and variance in
their play without simply shrugging their shoulders. It's clearly
inadequate for anyone seeking to strongly/precisely quantify aspects
of a game.Ultimately, I expect from your observations that you'll express the
opinion that my observations aren't sufficiently solid to serve as
such guidance to even the recreational player. That would leave them
without any means by which to generally apply these statistics, which
would be unfortunate.> This is an area that I've been spending a lot of time thinking about
> in recent months. I'd be very interested in discussing/exploring
> this further. I think this area is poorly understood, even by
> experts, and there are some surprising conclusions that pop out of
> the math.As noted, my purpose has been to serve the recreational player. I
clearly have an interest in the more precise quantitative aspects of
vp, but I admit to being inadequately prepared to explore them at any
length and willing sit on the sidelines.My principal concern with this discussion is that in absence of any
clear consensus, the average player is left without any clear
indication of the reliability of what I've put forth.Again, Steve, I appreciate the earnest manner in which you've explored
what I've posted. I'll admit to some disappointment that you've found
what I've posted largely wanting, but certainly I anticipated that
might well be the reception I received.- Harry
So Harry, in plain English, what you're trying to say is.......(If I
understand correctly) 
Interestingly enough, initiation of basic
charismatic subculture development does not
readily tolerate the philosophy of commonality
and standardization. It is further assumed
that the natural general principle that will
subsume this case is functionally equivalent
and parallel to any discrete configuration
modality. Thus, any associated supporting
element cannot be arbitrary in a parasitic gap
construction. Thus a further and associated
contradictory element necessitates that
coagulative measures be applied to Krapp's Last
Tape. To approach true user-friendliness, this
selectionally introduced contextual feature is
a notational variant of a stipulation to place
the constructions into these various
categories. It appears that a descriptively
adequate grammar can be defined in such a way
as to impose the strong generative capacity of
the theory. Analogously, the interrelation of
system and/or subsystem technologies maximizes
the probability of project success, yet
minimizes cost and time required for a general
convention regarding the forms of the grammar.
As a resultant implication, our fully
integrated field program presents a valuable
challenge showing the necessity for the total
system rationale. Interestingly enough, this
selectionally introduced contextual feature
delimits an abstract underlying order.
CF
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