vpFREE2 Forums

Wynn Jacks (9/6/90 JoB)

> --- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <
>
> nightoftheiguana2000@y...> wrote:
> > Per bet variance, the one that counts, is reduced for multiplays:
> >
> > JOB per bet variance = 2 + 17.5/N (N= number of multiplays)
>
> So, this means that the following statements are true?
>
> Playing 5-line JOB nickels has a lower variance than 1-line JOB quarters,
> since both have a "bet" of $1.25.

Correct. The variance is reduced by a factor of sqrt(5).

Make that "standard deviation is reduced by a factor of sqrt(5)".

Variance (per dollar^2) is reduced by 5.

> Playing 4-line JOB quarters has a lower variance that 1-line JOB dollars,
> since both have a "bet" of $5.

Correct. The variance is reduced by a factor of two = sqrt(4).

Same here.

···

On Monday 29 August 2005 07:22 pm, Steve Jacobs wrote:

On Monday 29 August 2005 11:52 am, bornloser1537 wrote:

No, not that much. In 5-line play the results that you get on the 5
lines aren't independent, they are correlated.

···

On 8/29/05, Steve Jacobs <jacobs@xmission.com> wrote:

Make that "standard deviation is reduced by a factor of sqrt(5)".

Yes, they are true.

In addition, the following ones are also true:

Playing 5 games of 1-line JOB nickels has a lower variance than
playing 1 game of 5-line JOB nickels.

Playing 4 games of 1-line JOB quarters has a lower variance than
playing 1 game of 4-line JOB quarters.

JBQ

···

On 8/29/05, bornloser1537 <bornloser1537@yahoo.com> wrote:

So, this means that the following statements are true?

Playing 5-line JOB nickels has a lower variance than 1-line JOB quarters,
since both have a "bet" of $1.25.

Playing 4-line JOB quarters has a lower variance that 1-line JOB dollars,
since both have a "bet" of $5.

Yes.

Variance is confusing because it varies linearly with number of wagers of
the same size, but varies according to a square law if you change the
size of each wager.

If you have a game where a single unit wager gives a variance of
V (units squared), the variance follows the following two rules:

1) If you make a single wager of N units, the overall variance is V*N^2
(units squared).

2) If you make N independent wagers of the same size, then the overall
variance for the group of N wagers is N*V (units squared)

Combining these rules gives:

3) If you take a single unit and divide it into N wagers that are each 1/N
units, then each small wager has a variance of (V/N^2) to give an overall
variance of N*V/N^2 = V/N (units squared).

You can view an N-play machine as either increasing variance or
decreasing variance, depending on what kind of machine you compare
with the N-play machine. An N-play is more or less the same as playing
five independent machines at the same time. Some comparisons:

A) If you normally play a 1-unit denomination single play machine, and
you "step up" to a 5-unit denomination single play, rule 1 says this
increases your variance by a factor of 25.

B) If you normally play a 1-unit denomination single play machine, and
you "step up" to a 1-unit 5-play machine, rule 2 says this increases your
variance by a factor of 5.

C) If you normally play a 5-unit denomination single play machine, and
you "step down" to a 1-unit 5-play machine, rule 3 says this decreases
your variance by a factor of 5.

So, whether you view a 5-play as increasing or decreasing variance
depends on whether you view it as playing fives times as "fast" or
as busting up your normal bet into 5 independent pieces that get played
simultaneously.

···

On Monday 29 August 2005 11:32 am, bornloser1537 wrote:

--- In vpFREE@yahoogroups.com, "vpFREE" <vpFREE@C...> wrote:
> On 28 Aug 2005 at 22:23, bedioyscans2000 wrote:
> > What's the normal JOB variance for single play,
>
> 19.5
>
> > triple pay, five play etc.
>
> Higher than SL.
>
> See the "Jazbo's Analysis of N-Play VP" link on the above url.

This simplistic answer is not correct (I think).

My understanding is that if you look at it one way, the multi-line game has
a HIGHER vaiance; if you look at it another way it has LOWER variance.

Am I correct in my thinking this?

I often find it hard to "guess" what the question is when there is
not enough information given in the question. That is why I try to
cover as many bases as possible, to give as much information as
possible, when I ask a question. As most can see, I am seldom
knowledgeable enough to give "answers. LOL.

In my opinion, this (the variance of multi-line play) is one of
those "classic" cases where the answer really is:

"On the one hand ...., on the other hand ...."

I am not sure that the original questioner was aware of all of the
ramifications of the question that was being asked. The answer, as
you have phrased it below (IMHO), is much better.

I have found that most people are intrested on the effects of "when
I bet this amount". I like the Shackleford treatment in that one
can see all sides of the "story".

bl

···

The answer is correct "IF" we're talking about the variance of
SL @ X denomination versus MLs @ the same X
denomination, as I was, and as "I BELIEVE" the questioner
was, and as Jazbo does in his paragraph on variance in
the cited url where he says " ... if you play the same game
in a 4-play version, then the variance will be higher ..." -
which I used as a basis for my reply.

Of course, if we're talking about the per bet variance, which
we weren't, and it appears that you are, then variance is lower
for ML than for SL.

vpFREE Administrator

Thanks, Steve! I think that this says it all.

bl

Yes.

Variance is confusing because it varies linearly with number of

wagers of

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

the same size, but varies according to a square law if you change the
size of each wager.

You're right, I should have said "approximately" here. I believe
the amount of correlation is fairly small.

···

On Monday 29 August 2005 08:34 pm, Jean-Baptiste Queru wrote:

No, not that much. In 5-line play the results that you get on the 5
lines aren't independent, they are correlated.

On 8/29/05, Steve Jacobs <jacobs@xmission.com> wrote:
> Make that "standard deviation is reduced by a factor of sqrt(5)".

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Correct, the correlation is quite small, but not entirely negligible.
For small numbers of hands it is certainly a good approximation.

JBQ

···

On 8/30/05, Steve Jacobs <jacobs@xmission.com> wrote:

You're right, I should have said "approximately" here. I believe
the amount of correlation is fairly small.

On Monday 29 August 2005 08:34 pm, Jean-Baptiste Queru wrote:
> No, not that much. In 5-line play the results that you get on the 5
> lines aren't independent, they are correlated.
>
> On 8/29/05, Steve Jacobs <jacobs@xmission.com> wrote:
> > Make that "standard deviation is reduced by a factor of sqrt(5)".
>
>
> vpFREE Links: http://members.cox.net/vpfree/Links.htm
>
>
> Yahoo! Groups Links
>
>
>

vpFREE Links: http://members.cox.net/vpfree/Links.htm

Yahoo! Groups Links

I would not expect the covariance among hands to be small, plus
remember there are many more covariance term than variance terms in
the matrix. The exception would be where you throw away all dealt
cards, even here you would some correlation due to the original five
cards discarded. Has anyone actually generated a correlation matrix?

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

Correct, the correlation is quite small, but not entirely

negligible.

For small numbers of hands it is certainly a good approximation.

JBQ

> You're right, I should have said "approximately" here. I believe
> the amount of correlation is fairly small.
>
> > No, not that much. In 5-line play the results that you get on

the 5

> > lines aren't independent, they are correlated.
> >
> > > Make that "standard deviation is reduced by a factor of sqrt

(5)".

···

On 8/30/05, Steve Jacobs <jacobs@x...> wrote:
> On Monday 29 August 2005 08:34 pm, Jean-Baptiste Queru wrote:
> > On 8/29/05, Steve Jacobs <jacobs@x...> wrote:
> >
> >
> > vpFREE Links: http://members.cox.net/vpfree/Links.htm
> >
> >
> > Yahoo! Groups Links
> >
> >
> >
>
>
>
> vpFREE Links: http://members.cox.net/vpfree/Links.htm
>
>
> Yahoo! Groups Links
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