vpFREE2 Forums

An illustrative example of variance and multi-line play

#1

Hi.

My "temporary" fixation, as some of you might see, from my recent postings, is
the variance within VP and how it changes with machine denomination and
number of lines, FOR A GIVEN GAME. I think that I might even understand
Shackleford's algorithm and have come up with the following illustration, the
results of which, I find interesting. It sort of speaks to a similar earlier question
as to how one might reach Diamond in a Day with several choices of
machines to play and seeking the "lowest risk" (whatever that means).

For my illustration, I want to put $30,000 through a 9/6 JOB machine and I
have the following choices: 1-line $.25, 1-line $1, 1 line $5, 3 line $1, and 10-
line $.25.

I get the final results, in terms of standard deviation:

1-line @ $0.25 $855.45 (24,000 plays @ $1.25)
10-line @ $0.25 $1,181.29 (2,400 plays @ $12.50)
1-line @ $1 $1,710.91 (6,000 plays @ $5.00)
3-line @ $1 $1,875.40 (2,000 plays @ $15.00)
1-line @ $5 $3,825.70 (1,200 plays @ $25.00)

Of course, one can get figures for any combination one desires. I was just
looking for some illustrative examples.

The computations depend upon the "Variance on the Deal" and the "Variance
on the Draw). Shackleford gives values of these for FPDW, 10/7 DB, and 9/6
JOB. Jazbo deals with Variance and Co-Variance and gives values for a
couple of other VP games.

Does anyone have values for NSUD?

Thanks.

.....bl

#2

bornloser1537 wrote:

I get the final results, in terms of standard deviation:

1-line @ $0.25 $855.45 (24,000 plays @ $1.25)
10-line @ $0.25 $1,181.29 (2,400 plays @ $12.50)
1-line @ $1 $1,710.91 (6,000 plays @ $5.00)
3-line @ $1 $1,875.40 (2,000 plays @ $15.00)
1-line @ $5 $3,825.70 (1,200 plays @ $25.00)

I'm taking a 2 second gander at messages from today and don't have the
opportunity to check this post out more fully. But, I've taken quite
a stumble over those comparative 1-line and 3-line $1 numbers.

I would have anticipated the 3-line number to be close to twice the
1-line. Has my practical experience at the machines misled me that much?

- Harry

#3

These results are generated using the Shackleford algorithm. I duplicated the
algorithm using a Microsoft Excel spreadsheet and checked it out by
successfully generating the 8 "answers" to Shackleford's 8 "problems" at his
web-site.

I certainly may have fat-fingered" something while in-puting the data to
generate the 5 results quoted below. I will give them another check.

.....bl

···

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

bornloser1537 wrote:
> I get the final results, in terms of standard deviation:
>
> 1-line @ $0.25 $855.45 (24,000 plays @ $1.25)
> 10-line @ $0.25 $1,181.29 (2,400 plays @ $12.50)
> 1-line @ $1 $1,710.91 (6,000 plays @ $5.00)
> 3-line @ $1 $1,875.40 (2,000 plays @ $15.00)
> 1-line @ $5 $3,825.70 (1,200 plays @ $25.00)

I'm taking a 2 second gander at messages from today and don't have the
opportunity to check this post out more fully. But, I've taken quite
a stumble over those comparative 1-line and 3-line $1 numbers.

I would have anticipated the 3-line number to be close to twice the
1-line. Has my practical experience at the machines misled me that much?

- Harry

#4

bornloser1537 wrote:

These results are generated using the Shackleford algorithm. I
duplicated the algorithm using a Microsoft Excel spreadsheet and
checked it out by successfully generating the 8 "answers" to
Shackleford's 8 "problems" at his web-site.

Ok, I've returned for a 30-second peak at this. No doubt the standard
deviation calcs are correct. But I find the approach entirely
inappropriate in assessing the risk you're looking for -- which
appears from your discussion to be assessing the downside of putting
through $x coin on a game under various play options.

For a limited number of hands, standard deviation isn't a reasonable
measurement of this. The outcome distribution is far from a "normal"
one. If you were looking for a more accurate determination, I'd use
ER and sd values for play excluding the RF -- but I don't believe
Shackleford provides the necessary data.

- Harry

#5

I think that the numbers are correct.

The covariance in JoB is pretty low, so playing 6000 total draws in
1-line or 3-line won't be very far in terms of standard deviation.

The standard deviation for 1 line of 1-line play is 4.42, and for 1
line of 3-line play it is 4.84.

JBQ

···

On 8/30/05, bornloser1537 <bornloser1537@yahoo.com> wrote:

I certainly may have fat-fingered" something while in-puting the data to
generate the 5 results quoted below. I will give them another check.

#6

Thanks. I fully appreciate the "sense" of your reply. However, my posting was
not trying to find a low risk way to push money through a VP machine.

I was trying to illustrate that the answer that had been given to the question,
"what has a lower variance, single line VP or multi-line VP?" was much too
simplistic. There are many things that have to be assumed and stated before
giving an answer.

.....bl

···

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

But I find the approach entirely
inappropriate in assessing the risk you're looking for -- which
appears from your discussion to be assessing the downside of putting
through $x coin on a game under various play options.

- Harry

#7

bornloser1537 wrote:

Thanks. I fully appreciate the "sense" of your reply. However, my
posting was not trying to find a low risk way to push money through
a VP machine.

I was trying to illustrate that the answer that had been given to
the question, "what has a lower variance, single line VP or
multi-line VP?" was much too simplistic. There are many things that
have to be assumed and stated before giving an answer.

Ok ... I have to own up to having a little difficulty reading that
into your post containing your calculations for $30K coin-in though.

In any case, I'll simply note that my concern is that the values you
report (the variance of playing $30K through in various manners) are
likely to be misleading if they were to be used as an expectation of
relative session results. (It's not apparent to me what other
practical use one might make of them.)

- Harry

#8

The purpose for the $30K was to establish a "constant" for the illustration of
the variation of variance (or standard deviation) as a function of denomination
and lines played. I could just as easily have used $1, or $0.01. It is probably
obvious to most that variance is a function of denomination and number of
lines played. I wanted to see how it varied. I then thought I would "share"
what I thought was interesting, as to just how it does vary. It appears that I
should not have assumed that.

bl

···

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

i have to own up to having a little difficulty reading that
into your post containing your calculations for $30K coin-in though.

- Harry

#9

Agreed on both points.

The standard deviation can be relevant if you decide to multiple the
coin-in by a million (and the SDs by a thousand). That would give you
a decent idea of how much money to expect after playing 30 billion
dollars through the machine. At that point your expected loss will be
over 100 million dollars, with a standard deviation in the few
millions. That's the "law of large numbers" in action.

Standard deviation is *not* a substitute for the risk of ruin.
Standard deviation tells you something about the spread of the final
result around the average value, but doesn't tell you anything about
how you got there. Risk of ruin is about not going below a pre-set
value on the way there, and nothing in SD tells you anything about it.

(Yes, for a large enough number of hands the distribution follows a
near-normal distribution, and the SD tells you how wide the
distribution is around the average value).

JBQ

···

On 8/30/05, Harry Porter <harry.porter@verizon.net> wrote:

For a limited number of hands, standard deviation isn't a reasonable
measurement of this.

But I find the approach entirely
inappropriate in assessing the risk you're looking for

#10

It is interesting, especially for long-term players. Harry justifiedly
doesn't like it when someone makes it sound like EV and SD are the
only relevant characteristics, when we know that the distribution of
VP results is strongly non-normal.

JBQ

···

On 8/30/05, bornloser1537 <bornloser1537@yahoo.com> wrote:

I then thought I would "share"
what I thought was interesting, as to just how it does vary. It appears that I
should not have assumed that.

#11

I agree with JBQ that application of the CLT in the short run is
problematic to estimation of vp variance.

I have had some fun backtracking through the recent archives on this
topic. I really appreciate Harry Porter's and JBQ's thoughtful posts. I
think Steve Jacobs and nightofiguana are well meaning in their posts,
but this topic is not really that complicated. Their replys seem a bit
like Rube Goldberg explaining how to fry an egg!

···

--- In vpFREE@yahoogroups.com, Jean-Baptiste Queru <jbqueru@g...> wrote:

when we know that the distribution of
VP results is strongly non-normal.

JBQ

#12

--- In vpFREE@yahoogroups.com, Jean-Baptiste Queru <jbqueru@g...>
wrote:

(Yes, for a large enough number of hands the distribution follows a
near-normal distribution, and the SD tells you how wide the
distribution is around the average value).

JBQ

These millin/billion hand statement get kicked around a lot. If I
played 100,000,000 hands I would have one outcome. One data point. I
would be either up, down, or even. That would not have a std dev.

Where is my thinking wrong?

#13

deuceswild1000 wrote:

These millin/billion hand statement get kicked around a lot. If I
played 100,000,000 hands I would have one outcome. One data point. I
would be either up, down, or even. That would not have a std dev.

Where is my thinking wrong?

Shame on your -- you're toying with us, right? :wink:

You know darn well these discussions deal with the expected
distribution of likely outcomes in ADVANCE of the play ... how the
heck could we <fill in your favorite descriptor for "self abuse"> over
a done deal.

(written affectionately and very tongue in cheek!)

- H.

#14

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

deuceswild1000 wrote:
> These millin/billion hand statement get kicked around a lot. If

I

> played 100,000,000 hands I would have one outcome. One data

point. I

> would be either up, down, or even. That would not have a std

dev.

>
> Where is my thinking wrong?

Shame on your -- you're toying with us, right? :wink:

You know darn well these discussions deal with the expected
distribution of likely outcomes in ADVANCE of the play ... how the
heck could we <fill in your favorite descriptor for "self abuse">

over

a done deal.

(written affectionately and very tongue in cheek!)

- H.

Well Harry, I was trying to make a point. I think that many on here
kick around the term "millions of hands", etc and full well know
what they mean, but leave it too open for the less
experienced/learned. I also think that there are many on here who
confuse a million hand session outcome with a million hands. At
least I did when I first joined. Extrapolating that, I think that
many take it to mean that if they play a million hands they can
expect an approximately normal distribution of their win/loss, and
use the variance calculation form a vp program improperly.

So I set my self up as the fall guy hoping to help someone, even if
it is only one person.

DWK

#15

deuceswild1000 wrote:

Well Harry, I was trying to make a point. I think that many on here
kick around the term "millions of hands", etc and full well know
what they mean, but leave it too open for the less
experienced/learned. I also think that there are many on here who
confuse a million hand session outcome with a million hands.

I'm not quite sure about the distinction in this last statement, but
am sure you have one in mind.

Extrapolating that, I think that many take it to mean that if they
play a million hands they can expect an approximately normal
distribution of their win/loss, and use the variance calculation
form a vp program improperly.

Yes, the expected results of a low variance game such as JB or PE will
approximate a normal distribution within 2 million hands and, within a
relatively modest tolerance, the actual outcome of play can be
reliably expected to be close to the game ER. Use of statistical
methods, including variance, are valid for long-term play expectations
(such as the < 2 million hand long-term of JB).

- H.

#16

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

deuceswild1000 wrote:
> Well Harry, I was trying to make a point. I think that many on

here

> kick around the term "millions of hands", etc and full well know
> what they mean, but leave it too open for the less
> experienced/learned. I also think that there are many on here

who

> confuse a million hand session outcome with a million hands.

I'm not quite sure about the distinction in this last statement,

but

am sure you have one in mind.

Let me reword it to say the outcomes of many many sessions of one
million each as opposed to one session of one million hands. I
think this distinction is not made in most posting. I think it is
supposed to be. I hope I am not wrong about the distiction.
Opinion as to the need for the distinction is subject to debate.

> Extrapolating that, I think that many take it to mean that if

they

> play a million hands they can expect an approximately normal
> distribution of their win/loss, and use the variance calculation
> form a vp program improperly.

Yes, the expected results of a low variance game such as JB or PE

will

approximate a normal distribution within 2 million hands and,

within a

relatively modest tolerance, the actual outcome of play can be
reliably expected to be close to the game ER. Use of statistical
methods, including variance, are valid for long-term play

expectations

···

(such as the < 2 million hand long-term of JB).

- H.

#17

I'll take the example of 25c single-line, with the numbers I have used earlier
in this thread.

I do assume that for 24 billion hands (close to 600000 RF cycles) the
distribution is close to normal, and that therefore the average and
standard deviation are enough to qualify the distribution.

The expected loss is 138 million dollars, the standard deviation is
less than 1 million dollars (I'm rounding to the nearest million).

If I understand correctly, you're fine saying that 99.75% of such
sessions will end up between 135 and 141 million in the red, but
you're not fine saying that an arbitrary session has a 99.75%
probability of ending up between 135 and 141 million, or something
along those lines. Is that correct?

Since the sessions are independent, those two statements say exactly
the same thing as far as I'm concerned, which is why I do not see the
need for any distinction.

It's exactly the same reasoning that we use to say that the
probability of getting a RF on any hand in 1 in 40390, therefore the
number of RFs that we expect to hit over a session is on average 1 for
every 40390 hands.

JBQ

···

On 8/31/05, deuceswild1000 <deuceswild1000@yahoo.com> wrote:

Let me reword it to say the outcomes of many many sessions of one
million each as opposed to one session of one million hands.