vpFREE2 Forums

"There are no stupid questions, only stupid people."

#1

This is something I've been wondering for a while and have been unable to
find a plain-English explanation that does the trick.

When we refer to the variance of a game, what specifically does that number
refer to?

I mean, I know what it MEANS. I know how it's used. I know that
mathematically, it's the square of the standard deviation. And I realize,
in this context, that variance refers to the volatility of a game. I get how
it's used to extrapolate the bankroll requirements and so on and so forth...

But when we talk about FPDW having a variance of 25.84, what does that
number itself mean? 25.84 what? Does it refer to coins bet? Fully loaded
units bet?

Inquiring minds (or those in need of something more productive to do) want
to know.

[Non-text portions of this message have been removed]

#2

While the standard deviation possess a more or less straight forward
interpertation through the empirical rule (68% for the outcomes lie
within one standard deviation if the mean, 95% lie within two ....) the
variance has no such interpertation. Typically, from the underlying
probability distribution the mean and variance are computed. The
standard deviation is then found, as you say by taking the square root
of the variance.

#3

Lot of not so correct responses here... (sorry so long)

1) Standard deviation is in units of your bet. If you bet in dollars, the sdev is in dollars. If
you bet in "units", its in "units"

2) Variance is in units of bets squared, so its in dollars squared or "units" squared

3) There is NO empirical rule for estimating the range of expected outcomes (given a
variance or standard deviation). If there was, it would be equally applicable to both sdev
and var, given their relationship to each other (except when complex/imaginary numbers
are allowed, lol). BUT, If you know the distribution (PDF or CDF) you can derive a rule.
And in the case of a normal distribution, that 68% percent figure does show up.

4) The sdev and the var, the mean (EV), mode (most likely), median (50%) are all just
"statistics" -- single numbers that partially describe a more complex situation. Each
alone, in general represents a partial, incomplete description of the game or of the set of
number you have (see #9)

5) For a game that is described by a "normal" or bell curve, all you need is the mean and
the sdev, and you know everything. In other words, for such a game, I could tell you
exactly what any value of sdev "means" in pretty simple terms.

6) But for vp-- which doesn't have a normal distribution-- I'd have to muddle up the
proper explanation with a bunch of simplifications or approximations to explain what
"sdev" means, other than saying...

"the standard deviation is a numerical measure of the variation of the expected results in
units of your bet; the bigger the number the more the expected variation of expected
return."

7) Anything that affects the PDF potentially affects ev, sdev, etc. In other words, play
"errors" that affect EV, likely affect SDEV to. For example, going for the RF when a high
pair is present not only reduces EV, but also increase sdev. In other words, your play
affects the variance/sdev of your results.

9) you can compute the ev and sdev for the game and for your actual results.
In the case of the game, those number describe what you expect to see if you play the
game. In the case of your results, those numbers describe your actual results. Sounds
obvious, and it is. But what this means, is that given a set of numbers, like the results of
n-hands of video poker, you can compute the EV (whether you've won or lost) and the
sdev (a measure of the range of your actual results). Do that a few times, and you rapidly
gain an appreciation of the meaning of the "sdev" or "variance". Now, if you do this, you
should quickly realize that you are taking a large set of numbers and reducing it to two
numbers, the EV and SDEV. That reduction represents a loss of information; clearly the EV
and SDEV does not describe the original set of numbers, and you could not generate the original numbers from the EV and SDEV. You can, however, compare the EV and SDEV
from two sets of numbers-- in a much easier manner than comparing all the individual
numbers-- and that is where the meaning and value of SDEV lies.

9) I can't say how "luck" plays into this if it does at all, because for me at least, the effect
of "luck" can only be evaluated after you've played, once your results are in. One could
argue that "luck" is some measure of the how your results differ from the expected results.
In this case, most people compare EV, and claim if their EV was way better than expected
they were lucky. In the language of sdev & variance, one "might" expect this kind of "luck"
more often when the variance is bigger than when it is smaller (though for VP this is NOT
generally true, dispute the fact that most people believe it to be true). In other words, one
uses variance to place significance on one's results: given a big enough variance, most
actual results (EV) are not that significant... however if the the variance is small, a weird EV
result is significant.

···

--- In vpFREE@yahoogroups.com, "rosspark100" <rosspark100@...> wrote:

While the standard deviation possess a more or less straight forward
interpertation through the empirical rule (68% for the outcomes lie
within one standard deviation if the mean, 95% lie within two ....) the
variance has no such interpertation.

--- In vpFREE@yahoogroups.com, b.glazer@... wrote:

Another way is to say EV is the contribution of skill, and variance is the
contribution of luck; again, most people can grasp that too.

#4

Will be coming to Vegas in about a month and have a lot of "old" station points to use. Looking to buy gifts, etc and was wondering which gift shop might be the best. Are these good at Red Rock or GVR for massages/services, ? Are there other--non-food uses for them ?

Thanks

[Non-text portions of this message have been removed]

#5

Jay Fenster wrote:

When we refer to the variance of a game, what specifically does that
number refer to?

I mean, I know what it MEANS. I know how it's used. I know that
mathematically, it's the square of the standard deviation. And I
realize, in this context, that variance refers to the volatility of a
game. I get how it's used to extrapolate the bankroll requirements
and so on and so forth...

But when we talk about FPDW having a variance of 25.84, what does
that number itself mean? 25.84 what? Does it refer to coins bet?
Fully loaded units bet?

You've had several answers (cdfsrule obviously covers all the bases).
But I want to come back to your core question. It puzzles me in
light of your foregoing statements.

If you know what variance means, mathematically, then you know that
it's calculated by summing the squares of the differences between
values in a sample and the mean of a sample.

For video poker, that takes the form of summing, across all possible
hands, the difference between each hand's payout and the EV game
payout, after weighting that difference by the probability of the
hand's occurrence.

The squaring involved results in units of bets-squared (payouts for
this calculation are expressed in bets, not credits). And that's the
gist of it.

Now, while relative variance between one game and another gives us a
decent idea of relative magnitude with which losses might accumulate,
it doesn't offer up a whole lot in the way of other tangible meaning
short term, and it's best not to look to do much more than that with it.

···

------

Touching on standard deviation, as noted, it's merely the square root
of variance. That's helpful in that it brings the unit back to the
units of our original data. And if we're looking at a normally
distributed data set, it gives us a very handy shorthand reference to
describe the data distribution: 68% of the data lies +/- 1 SD from
the mean, 95% +/- 2 SD, 99.7% +/- 3 SD.

But as is frequently pointed out, vp results aren't normally
distributed and we get no such benefit ... or do we?

------

The flop and draw of cards in vp is no different that any other
natural phenomenon. Consequently the natural role of math that
produces normal distributions through the universe rule here as well.
Video poker is full of normal distributions. It's just that in
playing a hand, the payout isn't the consequence of a single normal
distribution ... it's the combination of several.

In truth, when you place a vp bet, you're making several discrete
wagers: That you'll hit a RF, you'll hit a SF, you'll hit a quad (or
subset of quads) ... you can divide your bet up between these wagers
any way you like -- because it's an all or nothing proposition (you
can't just bet on the quads), it's only the payouts that matter.

So, for each of these "sub"-wagers, the distribution of payouts is
decidedly normal ... they adhere strictly to a binomial distribution
which over a large number of wagers approaches a normal distribution.

However, because the hands underlying each wager appear with a
different frequency, each of the wagers approaches "normality" at a
different rate. This is the reason why when you look at the
distribution of vp results over a limited number of plays (say,
100,000), the result is decidedly skewed and very non-normally
distributed.

So don't be misled when someone states that vp doesn't adhere to a
normal distribution into thinking that there's something unnatural at
work.

------

Ultimately, for every vp game, the distributions of the various hand
results over time take on a strongly normal distribution. A rule of
thumb is that if you randomly take a sample of 30 observations out of
a large population, the results will be roughly normally distributed
about the mean.

The extension of this is that when you plot hands trials, measuring
payout from a given hand type, over a sufficient number of hands for
the expected number of that hand to be >= 30, then the distribution of
payout from those hands will approximate normality.

If you look at a game such a JB, where other than the RF, all other
hand cycles are well under 1000, then about the time you play out 30
RF cycles (1.2 mil hands), you look for overall play results to adhere
to a normal distribution. This is reasonably deemed the "long term"
of JB play, and you can begin to apply statistics normally reserved to
normal distributions with reasonable confidence. You can now talk
about x% of results falling within a certain range and calculate
bankroll requirements using the basic statistic of SD or VAR.

With other games, where there are hands in addition of the RF that
fall with relative improbability, the number of hands to reach the
long terms is decidedly longer.

- Harry

#6

Will be coming to Vegas in about a month and have a lot of "old"

station points to use. Looking to buy gifts, etc and was wondering
which gift shop might be the best. Are these good at Red Rock or GVR
for massages/services, ? Are there other--non-food uses for them ?

Thanks

I had old points at Station and when I went 2 weeks ago, I got cash to
play with. They may of made a mistake, but I got slot play for mine.

···

--- In vpFREE@yahoogroups.com, Kristine Hood <KcjHood@...> wrote:

#7

I've been shopping at Sunset Station gift shop for years, by far I
feel it's the best.

Yes, points can be used for spa services at GVR & RR.

However, you may want to inquire first, in June GVR let me cash in my
old points $879 for free play & I'm from out of state.

Best Regards,
Lolly

#8

Why doesn't the 30 rf cycle apply in other games also for an
approximation of the long term?

Next question, so if I get 30 or more of each type of hand they are
normally distributed. I can accept that. However, how do their
distributions when taken together make one giant normal distribution?

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

If you look at a game such a JB, where other than the RF, all other
hand cycles are well under 1000, then about the time you play out 30
RF cycles (1.2 mil hands), you look for overall play results to adhere
to a normal distribution. This is reasonably deemed the "long term"
of JB play, and you can begin to apply statistics normally reserved to
normal distributions with reasonable confidence. You can now talk
about x% of results falling within a certain range and calculate
bankroll requirements using the basic statistic of SD or VAR.

With other games, where there are hands in addition of the RF that
fall with relative improbability, the number of hands to reach the
long terms is decidedly longer.

- Harry

#9

deuceswild1000 wrote:

Why doesn't the 30 rf cycle apply in other games also for an
approximation of the long term?

Next question, so if I get 30 or more of each type of hand they are
normally distributed. I can accept that. However, how do their
distributions when taken together make one giant normal distribution?

First clarification: In playing through 30 cycles or more of a hand
type, the distribution of results approaches a normal distribution to
the extent that you can begin using statistical methods applicable to
normal distributions with some reliability. However, the distribution
isn't, nor ever will be, "normal" (i.e. a perfectly continuous
bell-shaped distribution).

Jumping to your last question, when distributions that are normally
distributed (or approximate a normal distributions) are summed, the
result is normally distributed. If you visualize a couple of
examples, this should become apparent.

So re your first question:

···

------

If plotting the return from a given hand type over play of 30 cycles,
you arrive at something that has a decent degree of smoothness. You
need to visualize what you're plotting. For a given length of play,
you're plotting how many credits have been won on those hands.

If you plot RF hits over sessions of only 5,000 hands, then you're
going to see a large spike at 0 credits, a fairly small spike at 4000
credits, and very small spikes at multiple of 4K starting at 8K. When
plotting RF hits over 1.2 mil hands (30 cycles), you're still looking
at very discrete spikes being plotted, but the overall distribution
takes on a fairly smooth curve that peaks at roughly 30x4000 credits
and tapers out to each side.

But compared to a normal distribution superimposed over this same
plot, it's a very rough match.

------

So the question as to when overall game results approach a normal
distribution (vs. when a specific hand's payout distribution
approaches normality) relates back to the individual hand pays within
the game's paytable.

For a game such as Jacks or Better, where after the RF, the frequency
of the next hand that has a significant contribution to game return
(Quad) is approx 100x the RF frequency. This means that at the point
that the distribution of RF payout begins approximating a normal
distribution, the overall game payout also does so ... all other hand
payout distributions have long since smoothed to a very strong
approximation of a normal distribution.

However, when you talk about a game such as DDB, where the quad Aces
and the bonus hands represent a strong portion of game return yet
those hands occur fairly infrequently, at 30 RF cycles the return
distributions from those hands still is in the realm of a "rough"
normal approximation. Taken together with the RF distribution, things
are still a little too rough and the overall picture needs further
play before things smooth out sufficiently where statistics applicable
to a normal distribution can be applied.

- Harry

#10

To you maybe. For me how about some illustrations or examples.

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

Jumping to your last question, when distributions that are normally
distributed (or approximate a normal distributions) are summed, the
result is normally distributed. If you visualize a couple of
examples, this should become apparent.

#11

?? Please put this in differnt words. If I plot all the hands that I
play while I accumulate 30 rfs, I am plotting what?

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

If plotting the return from a given hand type over play of 30 cycles,
you arrive at something that has a decent degree of smoothness. You
need to visualize what you're plotting. For a given length of play,
you're plotting how many credits have been won on those hands.

#12

deuceswild1000 replied:

?? Please put this in differnt words. If I plot all the hands that
I play while I accumulate 30 rfs, I am plotting what?

I'm talking about plotting your payout from hits of these hands, where
the aggregate payout is along the x-axis, the frequency is the y-axis.
You're plotting the end result of numerous trials of 30 RF (or any
other paying hand) hand cycles. When you're looking at a trial of
something over 50 cycles of a given hand, it's most practical to plot
x-axis values that represent a range of payouts (e.g. 50001-100000
credits, 100001-150000, etc ... striving for no less than 30 bands).

Harry Porter wrote:

Jumping to your last question, when distributions that are normally
distributed (or approximate a normal distributions) are summed, the
result is normally distributed. If you visualize a couple of
examples, this should become apparent.

deuceswild1000 replied:
To you maybe. For me how about some illustrations or examples.

For the above plot, you might consider plotting the sum of the
cumulative payouts of quads and full houses over trials of a given
number of hands. If you run trials of 1000, 5000, and 20000 hands,
you should get a feel for how the payout distributions for each
individual hand smooth out to approach a normal distribution and why
they additively approach a normal distribution.

I might be a little hard pressed to suggest the best tool for this.
VP for Winners might excel at this, but in my copy I seem to be having
difficulty modifying a game paytable so that only the quad and FH
hands having paying values (or making any other paytable change). But
I suspect this is a corruption only to my copy.

···

------

I'll suggest (without any aspersion) that the nature of the subject
matter here is such that it can easily invite several rounds of "20
questions". I encourage you to struggle with this topic on a "big
picture" basis to get the general gist of what's at work here.

- Harry

#13

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...>
wrote:

deuceswild1000 replied:
> ?? Please put this in differnt words. If I plot all the hands

that

> I play while I accumulate 30 rfs, I am plotting what?

I'm talking about plotting your payout from hits of these hands,

where

the aggregate payout is along the x-axis, the frequency is the y-

axis.

You're plotting the end result of numerous trials of 30 RF (or any
other paying hand) hand cycles. When you're looking at a trial of
something over 50 cycles of a given hand, it's most practical to

plot

x-axis values that represent a range of payouts (e.g. 50001-100000
credits, 100001-150000, etc ... striving for no less than 30 bands).

Harry Porter wrote:
> Jumping to your last question, when distributions that are

normally

> distributed (or approximate a normal distributions) are summed,

the

> result is normally distributed. If you visualize a couple of
> examples, this should become apparent.

deuceswild1000 replied:
To you maybe. For me how about some illustrations or examples.

For the above plot, you might consider plotting the sum of the
cumulative payouts of quads and full houses over trials of a given
number of hands. If you run trials of 1000, 5000, and 20000 hands,
you should get a feel for how the payout distributions for each
individual hand smooth out to approach a normal distribution and why
they additively approach a normal distribution.

I might be a little hard pressed to suggest the best tool for this.
VP for Winners might excel at this, but in my copy I seem to be

having

difficulty modifying a game paytable so that only the quad and FH
hands having paying values (or making any other paytable change).

But

I suspect this is a corruption only to my copy.

------

I'll suggest (without any aspersion) that the nature of the subject
matter here is such that it can easily invite several rounds of "20
questions". I encourage you to struggle with this topic on a "big
picture" basis to get the general gist of what's at work here.

- Harry

I think one answer fits both, maybe? For 30 rf cycles are you
saying I would plot the out come of over a million hands. IOW, I do
not understand what you are saying to plot. I understand freq on y
axis and ??? on x axis and concept of groouped data, but I fail to
unerstand what you would have me plot.

Your expertise is appreciated, but I need explanation at a lower
level.

#14

deuceswild1000 wrote:

I think one answer fits both, maybe? For 30 rf cycles are you
saying I would plot the out come of over a million hands. IOW, I do
not understand what you are saying to plot. I understand freq on y
axis and ??? on x axis and concept of groouped data, but I fail to
unerstand what you would have me plot.

http://www.jazbo.com/videopoker/curves.html

But instead, plot just payout (for the specific hand payouts noted),
not net result.

- H.

#15

Harry's description (of the distribution of the RF hands, for example) and the procedure he
suggests for plotting it do not always match. You shouldn't sum anything (except for
counting occurrences of a single hand type). Doing so changes the statistics alot. And It's
not necessary to plot payouts (x) and occurrences (y) since you are dealing with only a
single hand at a time. Instead, heres, the prescription:

create an x-axis numbered from 0 to whatever. And for each x, plot a dot at the y
corresponding to the # of RF's (or whatever hand) you observed for a certain # of hands.
The result you see should be (more-or-less) the poisson distribution. This distribution
has the interesting feature that the value of the mean and the variance (ignoring units) are
the same. So if you play 30 cycle for the RF, you expect about 30 RF's with quite a spread.
You can see examples here

http://en.wikipedia.org/wiki/Poisson_distribution

or look in Dan Paymar's book

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

deuceswild1000 replied:
> ?? Please put this in differnt words. If I plot all the hands that
> I play while I accumulate 30 rfs, I am plotting what?

I'm talking about plotting your payout from hits of these hands, where
the aggregate payout is along the x-axis, the frequency is the y-axis.
You're plotting the end result of numerous trials of 30 RF (or any
other paying hand) hand cycles. When you're looking at a trial of
something over 50 cycles of a given hand, it's most practical to plot
x-axis values that represent a range of payouts (e.g. 50001-100000
credits, 100001-150000, etc ... striving for no less than 30 bands).

Harry Porter wrote:
> Jumping to your last question, when distributions that are normally
> distributed (or approximate a normal distributions) are summed, the
> result is normally distributed. If you visualize a couple of
> examples, this should become apparent.

deuceswild1000 replied:
To you maybe. For me how about some illustrations or examples.

For the above plot, you might consider plotting the sum of the
cumulative payouts of quads and full houses over trials of a given
number of hands. If you run trials of 1000, 5000, and 20000 hands,
you should get a feel for how the payout distributions for each
individual hand smooth out to approach a normal distribution and why
they additively approach a normal distribution.

------

#16

cdfsrule wrote:

Harry's description (of the distribution of the RF hands, for
example) and the procedure he suggests for plotting it do not always
match. You shouldn't sum anything (except for counting occurrences
of a single hand type). Doing so changes the statistics alot.

In the interest of addressing a basic concept without getting bogged
down in details that would take volumes to precisely outline (at least
for me) without much added value, I'm taking some pretty broad swipes.

When I speak of "summing" distributions, I would hope that anyone who
really is paying sufficient attention to care exactly what type of
summing might be at work would realize that I'm not really talking
about an arithmetic addition, and instead would interpret the word in
the context of the discussion. I'm referring, for example, to looking
at the distribution of RF and quad A w/ kicker payouts individually
vs. the distribution of the combined payouts over a given length of play.

The broader topic at hand is what influences when a game might be
deemed to reach the "long term" (i.e. the distribution of results
approaches a normal distribution sufficiently that you can apply
relatively simple forms of statistical equations) ... and what aspects
of vp innately drive this.

FWIW, I don't really care when anyone shoots down anything I write ...
it's just helpful if they erect something in its place that helps
others (and myself) better understand the subject at hand.

- Harry

#17
#18

Apparently not.

···

From: "jw776655" <jw776655@yahoo.com>
Subject: [vpFREE] "Do stupid people ask smart questions?"

#19

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...>
wrote:

cdfsrule wrote:
> Harry's description (of the distribution of the RF hands, for
> example) and the procedure he suggests for plotting it do not

always

> match. You shouldn't sum anything (except for counting

occurrences

> of a single hand type). Doing so changes the statistics alot.

In the interest of addressing a basic concept without getting bogged
down in details that would take volumes to precisely outline (at

least

for me) without much added value, I'm taking some pretty broad

swipes.

When I speak of "summing" distributions, I would hope that anyone

who

really is paying sufficient attention to care exactly what type of
summing might be at work would realize that I'm not really talking
about an arithmetic addition,

Seriously, I am trying, but the level is beyond me, and most often
when I ask for help on here it is beyond me. I do not mind admitting
that.

I also feel that there are a lot of people on here who could care
less due to the elavated level of discussion, but if they would dig
in and speak up about needing simpler explanations,we could all
benefit.

Instead, the subject get the "next" click

#20

--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...>
wrote:

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@>
wrote:
>
> cdfsrule wrote:
> > Harry's description (of the distribution of the RF hands, for
> > example) and the procedure he suggests for plotting it do not
always
> > match. You shouldn't sum anything (except for counting
occurrences

I also feel that there are a lot of people on here who could care
less due to the elavated level of discussion, but if they would dig
in and speak up about needing simpler explanations,we could all
benefit.

Instead, the subject get the "next" click

  Don't feel stoopid. I too wish these explanations were in plain
English. Maybe with real life examples.