vpFREE2 Forums

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

#21

vpbauer1 wrote:

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

Of course, part of the problem is that when the topic being discussed
is statistics is that it can require great pains to engage in the
discussion in terms where the jargon of statistics doesn't predominate.

To write in the clearest and most coherent fashion requires
considerable focus and effort. When jotting something off the cuff
for a post, the result will often be lacking in that regard.

And there's the fact that many, such as myself, might enter the
discussion without a consummate grasp of the subject. I have what
likely equates to something a little more comprehensive than a minor
in college math under my belt (my degree being in finance, but first
couple of years study were as a math major). So I'm going to be
stumbling awkwardly a bit in what I contribute ... hoping that someone
more conversant will set me straight.

Underlying the original post in this thread was the general question
of how statistics can be interpreted re/applied to video poker. The
answer is that only very poorly, where it comes to the short-term
(such as session to session results, or even over longer periods of
100,000 hands).

What's commonly offered up is that "video poker results aren't
normally distributed", thus you can't apply the basic statistical
relations that only apply to normally distributed (bell curve shaped)
data (e.g. 67% of data lies +/- 1 sd from the mean).

That's, of course, very true. But the statement, on it's face, should
leave one a little uneasy. What's not "natural" about the deal/draw
of a deck of cards, preventing a normal distribution? The answer is
that every aspect of how the cards fall adheres to a normal
distribution. It's that when you discuss video poker results, you're
talking about an accumulation of several normal distributions -- the
patterns with which pairs, flushes, straights, etc. fall -- the
payouts from which each are normally distributed, but because of
unequal frequencies, don't add to a cumulative normal distribution
(but instead, in the short to medium term, takes on a skewed,
long-tailed shape).

However, over a large number of hands, the skewness of that shape
diminishes and ultimately approaches (though never reaches) something
that approaches the bell shape of a normal distribution.

Now the phrase "long term" is tossed about pretty casually ... with
such a casualness that some will inaccurately say "no player achieves
the long term; only the machines does" ... as if to imply most of the
concepts underlying "optimal play" aren't really applicable to one's play.

But what "long term" is actually referring to is the point when play
results can be looked to adhere to expectation within certain desired
thresholds. That's hardly a precise definition ... those thresholds
are arbitrary. But when set in practical terms such as "how many
hands must be played for there to be a strong confidence of a positive
outcome" (a concept introduced here as "N0", by nightoftheiguanna),
the the "long term" becomes something very tangible and within the
scope of an active players play.

What I sought to address as an additional thought appended to a post
in this thread is the question of why the "long term" varies from one
game to the next. What is it about each game that drives that "long
term"? For that matter, what is it that ultimately converts the
short-term skewed distribution of a vp game into one that approaches a
normal distribution in the longer term.

Well, it's at this point that I begin to do a fair amount of less than
fully satisfactory hand waving. Intuitively I grasp what's going on.
But I haven't voiced that understanding sufficiently to to so
succinctly ... nor am I so conversant in statistics that I'm apt to do
so off the cuff.

But to start with it's helpful to visualize a short term vp
distribution (and at DW2K's prompting I offered up:
http://www.jazbo.com/videopoker/curves.html) and picture how the
individual normally distributed hand payouts (HP, 2P, S, F ...)
aggregate to form such a curve.

Now that, in itself, is a bit of a stretch. You have to picture
what's represented in the overall short term distribution ... every
combination of hits over the n hands charted (at one extremes, n hands
without any hits at all; at the other extreme, n successive RF hits --
both with minuscule probability, and therefore flat-lined as "0" on
the chart).

All of these possible hand combinations is directly related to the
underlying distributions of each potential hand type payout (i.e., for
a high pair, the frequency with which you hit 1 HP, 2 HP, ... over the
course of those n hands). But, the put it simply, the overall
distribution is a rather complex combination of those individual
normally distributed hand frequency charts.

But here's a key point: If all the hand types had the same frequency,
than the resultant overall chart of result frequency would also
reflect a normal distribution. It's the disparate frequencies that
give rise to the skewness (the differing payouts impact the shape of
that skewness, but aren't responsible for the skewness in itself).

But the crux of that skewness lies in a related concept: If you
sample a population for some measure and chart the sample, then it
generally takes about 20 more more measurements for that chart to
approximate a normal distribution. Until that point, you're apt to
sample only a portion of that overall distribution. Pull more than 20
measurements and the more measurements you pull, the more that chart
will approach a normal distribution.

So you can extend this concept to the charting of the distribution of
vp results for a length of n hands. If that sample isn't large enough
that you expect at least 20 occurrences of each hand (most notably,
doesn't extend at least 20 RF cycles), then the contribution of the
respective hands won't reflect a contribution that approaches
something normally distributed.

Having suggested that if your charted play length extends at least 20
cycles of each hand, the contribution of each hand's cumulative payout
will approach a normal distribution, it might seem that for any game
you would expect the "long term" to be reached within about 800,000
hands (20x40,000).

However, the key is that for each hand the payout distribution
"approaches" a normal distribution. When you look at a game such as
DDB, with more than one high paying hand with a frequency of less than
1 in 5000 hands, the cumulative disparity of those hands at 20 RF
cycles is sufficient to still skew the overall distribution
significantly. You need to chart a play length considerably beyond 20
RF cycles before you see a result that's bell shaped.

In the case of a low variance games such as Jacks or Better, even the
cumulative deviation for a truly normal distribution of the quad and
RF hands (the relatively low payout vs infrequency of the SF makes it
a much more negligible factor) means that something greater than 20 RF
cycles is necessary before the overall payout distribution looks
reasonably bell shaped (about 30 cycles, or 1.2 mil hands, does the
trick).

Trust me when I say I've played fast and loose with the facts in
spilling this out. Anyone knowledgable can find much to critique
(something I welcome, if they can shed greater light on the
discussion). But I'm fairly confident that this carries the essence
of what's going on here.

This may well not address what you were really after, or even
interested in ... but it's my best shot "off the cuff" :wink:

- Harry

#22

I wrote:

When you look at a game such as DDB ... the cumulative disparity of
those hands at 20 RF cycles is sufficient to still skew the overall
distribution significantly. You need to chart a play length
considerably beyond 20 RF cycles before you see a result that's bell
shaped.

In the case of a low variance games such as Jacks or Better ...
something greater than 20 RF cycles is necessary before the overall
payout distribution looks reasonably bell shaped (about 30 cycles, or
1.2 mil hands, does the trick).

An added thought here: While we're talking a million hands or
possibly much more of play before cumulative vp payouts begin to
closely adhere to a normal distribution, that not to give any credence
to what some assert ... <in my best Carl Sagan imitation> ... "It
takes MILLIONS and MILLIONS of hands to reach the long term -- no
player reaches the long term in their play".

In my post I alluded to nightoftheiguanna's introduction here of the
"N0" concept (I beleive that's "N" followed by the number "0", not
some takeoff on "Just Say ..."), which addresses how long is necessary
to be confident of a positive play result when playing a positive
expectation play.

The bottom line of "N0" is that when you play a decently strong play,
you can look for strong assurance of a profitable result within
surprisingly short time. That's probably the strongest testament to
the principals of optimal play.

Details and further discussion of the concept can be found at:
http://members.cox.net/vpfree/Bank_NO.htm

- H.

#23

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.

  So are you saying that if I choose 10,000 hand increments, and plot
ending bankroll after playing each 10000 hands and do this until I have
hit 30 royalflushes, that the distribution of ending bankroll will be
approximately normal. That is how I would interpret your reference to
Jazbo. I would guess that I will have played many many 10000 hand sets
before I accumulate 30 rfs and so my data will definately have quite a
smoothing effect.

That is how I interpret those curves. I play 10000 hands put the
ending bankroll on the x axis and if more than one occurence happens in
a cell unit then they will start to accumulate on the y axis.

Now if I am reading those curves wrong, ok. But if I am reading them
correctly, then I fail to see the application you are stating

···

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

#24

deuceswild1000 wrote:

So are you saying that if I choose 10,000 hand increments, and plot
ending bankroll after playing each 10000 hands and do this until I
have hit 30 royalflushes, that the distribution of ending bankroll
will be approximately normal. That is how I would interpret your
reference to Jazbo. I would guess that I will have played many many
10000 hand sets before I accumulate 30 rfs and so my data will
definately have quite a smoothing effect.

Refer again to the graphs on Jazbo's website:
http://www.jazbo.com/videopoker/curves.html

If you look at the chart labelled "Probability Distributions after
10,000 Hands", you'll see that the charts are decidedly non-symmetric
(i.e. not strongly bell-shaped). What's plotted is the bankroll
outcome for a very large number of individual 10,000 hand sequences.
These are plotted independently of each other; not as a cumulation of
such sequences, as you suggest.

The JB curve particularly stands out -- it consists of two jointed
peaks, both of which are individually moderately bell shaped ...
representing the distribution of those sessions in which RF's were hit
and weren't hit. For other games, it's the nature of the hit
frequency and payout of each component paytable hand that the chart
blends together more evenly (but with noticeable skew).

Again to clarify: the ending bankroll (in bet units) at the end of
"n" hands. (This differs slightly in that this equals total bet
payout - total wagers ... I've discussed plotting only total bet
payout. The two plots would be exactly the same; the one I suggest
would be offset to the right on the scale by "n" bets.)

For a session of 10000 hands you would anticipate only 1 royal hit.
However, each chart continues off the end of the scale to the right.
For the JB chart, this continuation represents sessions of 1 RF hit
that include an unusually large number of quad/FH/etc. hits. However,
ultimately there would be points on that chart representing 10000 hand
sequences in which multiple RF's were hit (with considerably low
frequency, of course ... i.e. of only nominal height on the chart).

You can see in the chart progression (which here are ordered 1000
hands, 10000 hands, 5000 hands), that there is a progression toward a
true bell-shaped curve. What I suggest is that if you plot sessions
of 30 RF's (1.2 mil hands), the JB curve will show a strong
approximation to a bell-shaped normal distribution. PE will be even
stronger, as should be evident -- despite 1.2 hands representing far
short of 30 PE RF cycles, because the PE RF has a smaller contribution
to return ... other PE hands having a strong contributing to return
occur with much greater frequency (thus the smaller game variance
value). However, the plots of DW and DB will require plots of much
greater hand "sessions" to achieve that strong normal approximation.
A game such as DDB (and other large variance games) will require even
more.

- Harry

#25

1) Those 10,000 hand curves of Jazbo's represent the results from an INFINITE number of
10,000 hand sessions. As such, you don't "anticipate only 1 royal hit". Instead, you have a
certain probability of 0 royal hits, of 1 royal hit (and its less then 100% at 10,000 hands),
of 2 hits, of 3 hits all the way up to 10,000 RF hits. Ok, those #'s get small fast. So small
that Jazbo cut off hit computation after a couple of royals. To get the the accurate probability of hitting any # of royals in a certain # of hands , use the poison distribution.

2) The basic "meaning" of variance is simple: the more variance, or the larger the
standard deviation, the variation in a set of numbers. To get more precise than that, you
need numbers and/or precise language. Sorry. Oh, using numbers (over language) will be
more efficient.

3) There is nothing particularly natural about the normal distribution. Nah I should say it
this way: distributions occurring in nature are decidedly non-normal. They all have long lopsided tails and are not symmetric. Take rainfall for example. Or floods. What about
that 100-year storm? Or 50-year flood? Humans don't like it that those bad things can
happen and we don't intuitively (so it seems) no how to handle the risk associated with
rare events. In other words, we just don't know what to do with the variance, what
meaning to give it. Now that 100-year storm, it's like the RF, but the RF is a good thing. Nonetheless, we just (as humans seemingly ) don't know how to deal with the variance associated with it. And if you give it some thought (really, do some research), you realize
people have trouble with understanding and managing variance and risk of all kinds, not
just of rare events with large impacts.

···

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

For a session of 10000 hands you would anticipate only 1 royal hit.
However, each chart continues off the end of the scale to the right.
For the JB chart, this continuation represents sessions of 1 RF hit
that include an unusually large number of quad/FH/etc. hits. However,
ultimately there would be points on that chart representing 10000 hand
sequences in which multiple RF's were hit (with considerably low
frequency, of course ... i.e. of only nominal height on the chart).

#26

Ok, right here is where I am having trouble. I think I understnd
Jazbos curves ok. He plays either 5000 or 10000 hands and plots the
ending bank roll. He then does this a large number of times until he
has a distribution of ending bankrolls. This distribution takes on a
near bell curv as the size of the increment increases. IOW the 10000
increment hands are more bell curved than the 5000 hands increments.

In your statement above, are your increments 1.2 million or what.
Still not clear. And where does the 30 come in?

Finally does this agree with CDF rules explanation?

···

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

true bell-shaped curve. What I suggest is that if you plot sessions
of 30 RF's (1.2 mil hands), the JB curve will show a strong
approximation to a bell-shaped normal distribution.

#27

Hats off to the master. This was one of the best explanations ever(notwithstanding the disclaimer)! REB

···

--- On Fri, 7/18/08, Harry Porter <harry.porter@verizon.net> wrote:

From: Harry Porter <harry.porter@verizon.net>
Subject: [vpFREE] Re: "There are no stupid questions, only stupid people."
To: vpFREE@yahoogroups.com
Date: Friday, July 18, 2008, 12:51 AM

vpbauer1 wrote:

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

Of course, part of the problem is that when the topic being discussed
is statistics is that it can require great pains to engage in the
discussion in terms where the jargon of statistics doesn't predominate.

To write in the clearest and most coherent fashion requires
considerable focus and effort. When jotting something off the cuff
for a post, the result will often be lacking in that regard.

And there's the fact that many, such as myself, might enter the
discussion without a consummate grasp of the subject. I have what
likely equates to something a little more comprehensive than a minor
in college math under my belt (my degree being in finance, but first
couple of years study were as a math major). So I'm going to be
stumbling awkwardly a bit in what I contribute ... hoping that someone
more conversant will set me straight.

Underlying the original post in this thread was the general question
of how statistics can be interpreted re/applied to video poker. The
answer is that only very poorly, where it comes to the short-term
(such as session to session results, or even over longer periods of
100,000 hands).

What's commonly offered up is that "video poker results aren't
normally distributed" , thus you can't apply the basic statistical
relations that only apply to normally distributed (bell curve shaped)
data (e.g. 67% of data lies +/- 1 sd from the mean).

That's, of course, very true. But the statement, on it's face, should
leave one a little uneasy. What's not "natural" about the deal/draw
of a deck of cards, preventing a normal distribution? The answer is
that every aspect of how the cards fall adheres to a normal
distribution. It's that when you discuss video poker results, you're
talking about an accumulation of several normal distributions -- the
patterns with which pairs, flushes, straights, etc. fall -- the
payouts from which each are normally distributed, but because of
unequal frequencies, don't add to a cumulative normal distribution
(but instead, in the short to medium term, takes on a skewed,
long-tailed shape).

However, over a large number of hands, the skewness of that shape
diminishes and ultimately approaches (though never reaches) something
that approaches the bell shape of a normal distribution.

Now the phrase "long term" is tossed about pretty casually ... with
such a casualness that some will inaccurately say "no player achieves
the long term; only the machines does" ... as if to imply most of the
concepts underlying "optimal play" aren't really applicable to one's play.

But what "long term" is actually referring to is the point when play
results can be looked to adhere to expectation within certain desired
thresholds. That's hardly a precise definition ... those thresholds
are arbitrary. But when set in practical terms such as "how many
hands must be played for there to be a strong confidence of a positive
outcome" (a concept introduced here as "N0", by nightoftheiguanna) ,
the the "long term" becomes something very tangible and within the
scope of an active players play.

What I sought to address as an additional thought appended to a post
in this thread is the question of why the "long term" varies from one
game to the next. What is it about each game that drives that "long
term"? For that matter, what is it that ultimately converts the
short-term skewed distribution of a vp game into one that approaches a
normal distribution in the longer term.

Well, it's at this point that I begin to do a fair amount of less than
fully satisfactory hand waving. Intuitively I grasp what's going on.
But I haven't voiced that understanding sufficiently to to so
succinctly ... nor am I so conversant in statistics that I'm apt to do
so off the cuff.

But to start with it's helpful to visualize a short term vp
distribution (and at DW2K's prompting I offered up:
http://www.jazbo. com/videopoker/ curves.html) and picture how the
individual normally distributed hand payouts (HP, 2P, S, F ...)
aggregate to form such a curve.

Now that, in itself, is a bit of a stretch. You have to picture
what's represented in the overall short term distribution ... every
combination of hits over the n hands charted (at one extremes, n hands
without any hits at all; at the other extreme, n successive RF hits --
both with minuscule probability, and therefore flat-lined as "0" on
the chart).

All of these possible hand combinations is directly related to the
underlying distributions of each potential hand type payout (i.e., for
a high pair, the frequency with which you hit 1 HP, 2 HP, ... over the
course of those n hands). But, the put it simply, the overall
distribution is a rather complex combination of those individual
normally distributed hand frequency charts.

But here's a key point: If all the hand types had the same frequency,
than the resultant overall chart of result frequency would also
reflect a normal distribution. It's the disparate frequencies that
give rise to the skewness (the differing payouts impact the shape of
that skewness, but aren't responsible for the skewness in itself).

But the crux of that skewness lies in a related concept: If you
sample a population for some measure and chart the sample, then it
generally takes about 20 more more measurements for that chart to
approximate a normal distribution. Until that point, you're apt to
sample only a portion of that overall distribution. Pull more than 20
measurements and the more measurements you pull, the more that chart
will approach a normal distribution.

So you can extend this concept to the charting of the distribution of
vp results for a length of n hands. If that sample isn't large enough
that you expect at least 20 occurrences of each hand (most notably,
doesn't extend at least 20 RF cycles), then the contribution of the
respective hands won't reflect a contribution that approaches
something normally distributed.

Having suggested that if your charted play length extends at least 20
cycles of each hand, the contribution of each hand's cumulative payout
will approach a normal distribution, it might seem that for any game
you would expect the "long term" to be reached within about 800,000
hands (20x40,000).

However, the key is that for each hand the payout distribution
"approaches" a normal distribution. When you look at a game such as
DDB, with more than one high paying hand with a frequency of less than
1 in 5000 hands, the cumulative disparity of those hands at 20 RF
cycles is sufficient to still skew the overall distribution
significantly. You need to chart a play length considerably beyond 20
RF cycles before you see a result that's bell shaped.

In the case of a low variance games such as Jacks or Better, even the
cumulative deviation for a truly normal distribution of the quad and
RF hands (the relatively low payout vs infrequency of the SF makes it
a much more negligible factor) means that something greater than 20 RF
cycles is necessary before the overall payout distribution looks
reasonably bell shaped (about 30 cycles, or 1.2 mil hands, does the
trick).

Trust me when I say I've played fast and loose with the facts in
spilling this out. Anyone knowledgable can find much to critique
(something I welcome, if they can shed greater light on the
discussion). But I'm fairly confident that this carries the essence
of what's going on here.

This may well not address what you were really after, or even
interested in ... but it's my best shot "off the cuff" :wink:

- Harry

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

#28

But when set in practical terms such as "how many
hands must be played for there to be a strong confidence of a positive
outcome" (a concept introduced here as "N0", by nightoftheiguanna) ,
the the "long term" becomes something very tangible and within the
scope of an active players play.

Another useful discussion of N0:

http://gamemasteronline.com/StrategyContent.shtml
"I have always preached that a counter must be able to realize a
long-term advantage of at least one percent in order to make the
effort worthwhile; otherwise, you might get stuck early on and spend
the rest of your life trying to dig out. And that 1% really is the
minimum, which leads us to a discussion of what's called N0 (the
letter N and the number 0). The logic here is that it's possible to
calculate how many hands you must play in order to overcome a one
Standard Deviation downswing, given a specific overall playing advantage."

#29

Richard Boozer wrote:

Hats off to the master. This was one of the best explanations
ever(notwithstanding the disclaimer)! REB

Well, thanks ... that's very gracious. (Particularly so since, in
doing a cold read of my post just now, I got lost in the convoluted
text a little over half way through :wink:

- H.

#30

> true bell-shaped curve. What I suggest is that if you plot
> sessions of 30 RF's (1.2 mil hands), the JB curve will show a
> strong approximation to a bell-shaped normal distribution.

deuceswild1000 wrote:

Ok, right here is where I am having trouble. I think I understnd
Jazbos curves ok. He plays either 5000 or 10000 hands and plots the
ending bank roll. He then does this a large number of times until
he has a distribution of ending bankrolls. This distribution takes
on a near bell curv as the size of the increment increases. IOW the
10000 increment hands are more bell curved than the 5000 hands
increments.

In your statement above, are your increments 1.2 million or what.
Still not clear. And where does the 30 come in?

Finally does this agree with CDF rules explanation?

I've stated that while a plot of payout from RF's alone will closely
approximate a normal distribution over the course of 20 cycles, the
plot of total game payout (all hands) will take longer. For a low
variance games such as JB, I've suggested that about 30 RF cycles is
sufficient, or 1.2 million hands. (For a game such as DDB, that
"normalization" of results will take much longer.)

(It goes without saying that the limited run 10,000-hand plots on
Jazbo's website have a loose bell-shape, but are a far cry from a
normal distribution.)

re cdfrules, you'd have to cite the specific text to which you're
asking correlation.

- Harry

···

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

#31

> For a session of 10000 hands you would anticipate only 1 royal hit.
> However, each chart continues off the end of the scale to the
> right.
> For the JB chart, this continuation represents sessions of 1 RF hit
> that include an unusually large number of quad/FH/etc. hits.
> However, ultimately there would be points on that chart
> representing 10000 hand
> sequences in which multiple RF's were hit (with considerably low
> frequency, of course ... i.e. of only nominal height on the chart).

cdfsrules comments on the above. I'm interspersing a few remarks.

cdfsrule replied:

1) Those 10,000 hand curves of Jazbo's represent the results from an
INFINITE number of 10,000 hand sessions. As such, you don't
"anticipate only 1 royal hit". Instead, you have a certain
probability of 0 royal hits, of 1 royal hit (and its less then 100%
at 10,000 hands), of 2 hits, of 3 hits all the way up to 10,000 RF
hits. Ok, those #'s get small fast. So small that Jazbo cut off hit
computation after a couple of royals. To get the the accurate
probability of hitting any # of royals in a certain # of hands , use
the poison distribution.

No argument. Just hope you intended to make the topic I address more
clear, but not suggest I might not grasp this info.

The "anticipate" statement (which would best have been ended with "at
most") was offered in the casual spirit of "you play 10,000 hands
through and you look to maybe hit a single royal" ... not to suggest
that you have a fixed expectation of 1 royal.

3) There is nothing particularly natural about the normal
distribution. Nah I should say it this way: distributions occurring
in nature are decidedly non-normal. They all have long lopsided
tails and are not symmetric. Take rainfall for example. Or floods.
What about that 100-year storm? Or 50-year flood? Humans don't like
it that those bad things can happen and we don't intuitively (so it
seems) no how to handle the risk associated with rare events. In
other words, we just don't know what to do with the variance, what
meaning to give it.

It could be that I simply have a spotty grasp of the subject, but this
strikes me as off.

When you talk about "decidedly non-normal", I gather that you're
talking about truncated distributions, i.e. "bounded" (using your
examples, we know we can't have negative rainfall, or a negative
number of storms), therefore any "bell curve" distribution won't be
perfectly symmetric. I'd still call these "normal" in all respects
... just not perfectly bell curved.

On the intuitive count, I agree: When it comes to experiences that
are so rare as to not be part of routine human experience, intuition
isn't going to be a factor.

But for experiences where we have a decent grasp of frequency, even if
quite variable (for example, a RF hit), then most reasonably witted
people have a rather strong intuition that's correlates decently with
true expectations.

I get the feeling that you suggest we don't innately know what to do
with "variance" ... I'd argue that its application is almost
instinctual, provided sufficient experience from which to assess it
(of course, that "instinct" can be markedly out-of-whack when skewed
by such things as a strong desire to win ... or, in my case, a
desperate fear of losing ;).

- Harry

···

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

#32

Yup-- that's exactly what I am saying: our reaction is (almost ?) instinctual and often at
odds with the "math" - we just don't know the right thing to do with variance or risk.
That's not to suggest that our behavior is or is not rational, but rather that we don't
instinctively understand variance (risk). From... http://www.conferenz.co.nz/why-do-
workers-make-the-decisions-they-do.html

" The fact that it is (in evolutionary terms) a recently developed abstraction means that
human beings are not hard-wired to process or understand risk."

risk and variance are very much related here...

"Finally, thinking analytically about risks is not easy or natural."

So I don't think we totally disagree: Just because we act instinctively, or from experience,
doesn't mean we understand.

···

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

I get the feeling that you suggest we don't innately know what to do
with "variance" ... I'd argue that its application is almost
instinctual, provided sufficient experience from which to assess it
(of course, that "instinct" can be markedly out-of-whack when skewed
by such things as a strong desire to win ... or, in my case, a
desperate fear of losing ;).

- Harry

#33

cdfsrule wrote:

Yup-- that's exactly what I am saying: our reaction is (almost ?)
instinctual and often at odds with the "math" - we just don't know
the right thing to do with variance or risk.
That's not to suggest that our behavior is or is not rational, but
rather that we don't instinctively understand variance (risk).
From... http://www.conferenz.co.nz/why-do-
workers-make-the-decisions-they-do.html

"The fact that it is (in evolutionary terms) a recently developed
abstraction means that human beings are not hard-wired to process or
understand risk."

risk and variance are very much related here...

"Finally, thinking analytically about risks is not easy or natural."

So I don't think we totally disagree: Just because we act
instinctively, or from experience, doesn't mean we understand.

When it comes to the core of what we're discussing, I think we're on
absolutely the same wavelength. But we do disagree on the finer points.

You see, I think most players do instinctively understand
risk/variance -- at least their instinct ultimately leads them to make
play choices that are rationally consistent with their priorities. In
fact, it's the only way they have to deal with play variance.

We're in agreement that most players have no concrete idea of play
risk ... no way to deal with to concept analytically. Ask them the
probability that they'll lose $x for any period over their attention
span of two hours (I'm being generous), and they'll be taking a
complete stab in the dark.

Nonetheless, via trial and error, they instinctively gravitate toward
those plays that most suit their desire for variance and their risk
tolerance. (Well, maybe instinct isn't the only thing at work here
... there could be a video poker equivalent to the plant auxins that
explain the phototropic nature of plants :wink:

Think of variance as being the wind in their instinctive sail. If you
take a Sunfish out for a spin, you don't need to know the directional
coordinates and speed of the wind if you wish to steer a course toward
a given landmark, provided you can instinctively guide the boat in
response to the wind.

Now, when it comes to that instinctual aspect of some player behavior,
it's absolutely true that it parallels the intelligence such as that
displayed by my cat (who, for example, claws at the wall when finished
eating, in a feeble attempt to cover the balance of the food from
predators ... at least I've assumed that this is akin to the player
behavior of leaving piles of ashes scattered across the machine).
<Oct 15 in AC will be the casino equivalent of Earth Day>

However, ultimately their instinct steers most players true when it
comes to finding those plays that are best (and most intelligently)
suited for them.

- Harry

#34

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

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

wrote:

> > true bell-shaped curve. What I suggest is that if you plot
> > sessions of 30 RF's (1.2 mil hands), the JB curve will show a
> > strong approximation to a bell-shaped normal distribution.

deuceswild1000 wrote:
> Ok, right here is where I am having trouble. I think I

understnd

> Jazbos curves ok. He plays either 5000 or 10000 hands and plots

the

> ending bank roll. He then does this a large number of times

until

> he has a distribution of ending bankrolls. This distribution

takes

> on a near bell curv as the size of the increment increases. IOW

the

> 10000 increment hands are more bell curved than the 5000 hands
> increments.
>
> In your statement above, are your increments 1.2 million or

what.

> Still not clear. And where does the 30 come in?
>
> Finally does this agree with CDF rules explanation?

I've stated that while a plot of payout from RF's alone will closely
approximate a normal distribution over the course of 20 cycles, the
plot of total game payout (all hands) will take longer. For a low
variance games such as JB, I've suggested that about 30 RF cycles is
sufficient, or 1.2 million hands. (For a game such as DDB, that
"normalization" of results will take much longer.)

I will try asking my question another way, as I have read and re-read
your answers, but I would like them in the context of the Jazbo
reference. Using Jazbo as the reference and using 10000 hands as a
reference, Jazbo get a curve that starts to look like a normal (yes
it is skewed and bimodal), when he plots ending bankroll. Yes, I
know that he really derived them using another technique, but I
understand that the technique described would do the same if a large
number of samples were taken.

So in your example are you saying 1.2 million hands for 20 cycles and
plotting the resultant 20 game payout will give an approximation to
the normal distribution for WHAT? There are reallly two questions
in that statement.

Please leave it in the example which I understand and be specific as
you can.

#35

deuceswild1000 wrote:

So in your example are you saying 1.2 million hands for 20 cycles and
plotting the resultant 20 game payout will give an approximation to
the normal distribution for WHAT? There are reallly two questions
in that statement.

No. 1.2 million hands IS 20 RF cycles. So I'm talking about plotting
1.2 million hands (vs. Jazbo's 10,000 hands).

The other difference is in this specific instance I'm referring to a
plot solely of the payout from RF hits during those trials ... not, as
in Jazbo's charts, a plot of the aggregate of all hand payouts during
the trial.

My statement was that the shape of the resultant distribution of RF
payouts over the course of 20 cycles will strongly adhere to a normal
distribution. I then went on to discuss what's at work such that it
requires longer trials for a plot of aggregate payout from all hands
to "normalize" (in other words, what it takes for the Jazbo charts to
smooth out).

- H.

#36

And then I went on to say that that distribution of just the results from the RF is the poisson
distribution, and that one can simply compute it, and there is NO need for simulation. In fact
this page has a plot for the distribution for up to 10 Royal's right on it. It's the black curve,
top right (lambda = 10). Yes it looks quite normal already at 10 RF's.
http://en.wikipedia.org/wiki/Poisson_distribution

···

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

My statement was that the shape of the resultant distribution of RF
payouts over the course of 20 cycles will strongly adhere to a normal
distribution. I then went on to discuss what's at work such that it
requires longer trials for a plot of aggregate payout from all hands
to "normalize" (in other words, what it takes for the Jazbo charts to
smooth out).

- H.

#37

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

No. 1.2 million hands IS 20 RF cycles. So I'm talking about

plotting

1.2 million hands (vs. Jazbo's 10,000 hands).

Harry, I assume this is so clear to you that it does not make sense
that I cannot follow your explanation. I ask again, are you talking
about 1.2 million times 20 trials. Jazbo woulld have been 10000
times infinite trials, yes?

The other difference is in this specific instance I'm referring to a
plot solely of the payout from RF hits during those trials ... not,

as

in Jazbo's charts, a plot of the aggregate of all hand payouts

during

the trial.

Again, your explanation is clear to you but not to me.
Wouldn't the payout for each royal be 4000 units? I need some more
help.

My statement was that the shape of the resultant distribution of RF
payouts over the course of 20 cycles will strongly adhere to a

normal

distribution. I then went on to discuss what's at work such that it
requires longer trials for a plot of aggregate payout from all hands
to "normalize" (in other words, what it takes for the Jazbo charts

to

···

smooth out).

- H.

#38

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

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@>
wrote:
> No. 1.2 million hands IS 20 RF cycles. So I'm talking about
plotting
> 1.2 million hands (vs. Jazbo's 10,000 hands).

Harry, I assume this is so clear to you that it does not make sense
that I cannot follow your explanation. I ask again, are you

talking

about 1.2 million times 20 trials. Jazbo woulld have been 10000
times infinite trials, yes?
>
> The other difference is in this specific instance I'm referring

to a

> plot solely of the payout from RF hits during those trials ...

not,

as
> in Jazbo's charts, a plot of the aggregate of all hand payouts
during
> the trial.

Again, your explanation is clear to you but not to me.
Wouldn't the payout for each royal be 4000 units? I need some

more

help.

>
> My statement was that the shape of the resultant distribution of

RF

> payouts over the course of 20 cycles will strongly adhere to a
normal
> distribution. I then went on to discuss what's at work such that

it

> requires longer trials for a plot of aggregate payout from all

hands

> to "normalize" (in other words, what it takes for the Jazbo

charts

to
> smooth out).
>
> - H.
>

Unfortunately, we cannot edit these posts, and we are advised not to
cancel any posts without just cause.

So I post a second time. I need a receipe for what you are saying.
IOW, do this, record that, plot this, sum that etc.

Words of concept are not getting through to me.

#39

Maybe this will help...

Jasbo's results DO NOT CONSIDER the contribution from 30 RF's or even 20 RF"s. A
computational issue requires him to limit contributions to the return to a few RF's. So his
curves really aren't an example of Harry's (otherwise correct) point.

So...

You are correct, the contribution from the RF (for 1.2 million hands about 30 cycles),
would be a normal-like curve centered on 4000 * 30 = 120,000 units. Yup, that number
is way off the graph. And if one did draw the plaot to way out there, the overall curve
would not look at all normal, even after 1.2M hands. You see it only looks normal in the
central region near the mean.

To understand how the contribution from the RF quickly becomes normal, all you need to
do is look at the poisson distribution. The wonderful thing about the poisson distribution
is that don't need to know the probability of the RF or its payout. All you do need to know
is ho w many cycles you have played. As I said before, the plot on the top right of http://en.wikipedia.org/wiki/Poisson_distribution shows the poisson distribution for 1,4
and 10 cycles -- of any (rare) video poker hand! I'd recommend you study that plot for a
while. You should see that if you play 1 cycle, you have an equal change of getting 0 or 1
RF's, and a small chance of getting more RF"s.

Now, once you understand that, think about this: If the RF is the most rare hand in a
game, its contribution to the overall PDF takes the LONGEST time (most hands) to become
normal. That is, the RF contribution approaches normality slowest (this might seem to be
at odds with what Harry has been saying; I'll leave that up to him). In other words, the
rarer the hand, the more hands are in a cycle. You know that already. So, if normality
depends only on the number of cycles (remember the poisson distribution?), then the RF,
as the rarest hand (in a game) approaches normality slowest.

OK-- please ask your followup questions.
Again-- I think your question was a good one. While the fact that Jaszbo's curves don't
extend out to 20 RF might be clear to many people, the fact that his results don't include
the contribution from large # of RF's at all is not obvious. And nor is the effects of that
approximation. Good catch.

Back to the main issue: None of the this really has much to do with the overall curve
looking normal nor understanding the variance. A distribution with finite variance always,
in a central region, converges towards normality. Not so in the tails. But as you play more
and more, that central region (of normality) gets bigger and bigger (so the affect of the
tails, that is, non-normality, is smaller).

···

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

Unfortunately, we cannot edit these posts, and we are advised not to
cancel any posts without just cause.

So I post a second time. I need a receipe for what you are saying.
IOW, do this, record that, plot this, sum that etc.

Words of concept are not getting through to me.

#40

deuceswild1000 wrote:

Unfortunately, we cannot edit these posts, and we are advised not to
cancel any posts without just cause.

So I post a second time. I need a receipe for what you are saying.
IOW, do this, record that, plot this, sum that etc.

Words of concept are not getting through to me.

Tell you what ... I imagine some day we'll manage to meet up in LV.
What do you say we sit down over a couple of drinks, grab 30 (or so)
cocktail napkins and give this a good run though. It'll be fun
(earnestly!) :wink:

With any luck, there'll actually be a good bar game to dabble at while
we hash this through (the TI bar is a distant memory).

- H.