Thank you for the detailed math answer. I believe I understand.
Would it be correct to say increasing the number of hands to say 15,
20,25 or even 50 would reduce the number of hands further?
Yes, and you can figure it out yourself using jazbo's expression that
I alluded to. For 15-line...
1. Var(15-lines) = 19.5 + (15-1) * 1.966, where 1.966 is jazbo's
figure for the covariance of 9/6 JOB.
2. Then divide the resulting variance by 15 to get the unit variance.
3. Now divide the unit variance by the EV^2. For 0.8% cashback,
EV=0.34%.
Would I also be correct that each increase in the number of hands
would increase the necessary bankroll or that reducing the number of
hand to say 5 would reduce the bankroll necessary?
Yes, assuming you are playing the same denomination.
How much difference in dollars would those choices make? Of course 5
lines are higher could not be played at an 800 hand per hour rate
but the number of hands could be used to determine the time based on
possible speed.
You can use jazbo's variance expression to get a rough idea. For a
precise answer, Bob Dancer's Video Poker for Winners does multi-line
bankroll calcs. I'm not sure if any other currently available
software does.
Thanks for your excellent contribution to this group.
You betcha!
--Dunbar
From: dunbar_dra <h_dunbar@...>
Subject: [vpFREE] Re: Bob Dancer's CasinoGaming Column - 4 NOV 2008
To: vpFREE@yahoogroups.com
Date: Thursday, November 6, 2008, 6:09 PM
--- In vpFREE@yahoogroups. com, John Clark <jaycee5353@ ...> wrote:
>
> How would a multi line game with they same 9/6 JOB and .8 cash
back
effect this concept? Say you played 10 lines would the hours
necessary be reduced? How much?
Yes, the hours would be reduced. To get NO for multi-line, you use
the same formula. But you have to express variance and ev in terms
of a single unit.
The variance of a single play of 1-line JOB is 19.5. That's the
variance of a 1-unit total bet. (If you bet $5 on a 5-coin $1
machine, your variance per play is NOT 19.5. It's actually 487.9;
that's 19.5 x 5^2.)
To get the variance of 10-line, we can use jazbo's figure for
covariance (see http://jazbo. com/videopoker/ nplay.html )
Jazbo's figure lets us calculate 10-line variance as 19.5 + (10-1)
*1.966 = 37.2. But because it's for 10 lines, that "37.2" is the
variance of a 10-unit play. The variance of a single unit on the 10-
play is 37.2/10 = 3.72.
Therefore, "NO" for the 10-line game with 0.8% cashback is:
"NO" = 3.72/(0.34%) ^2 = 321,800 plays.
So it takes about 1/5 as long to reach "NO" playing 10-line as 1-
line
for the JOB game with 0.8% cashback (and no errors). A mere 400
hours if you can play 800 plays/hr with a 10-line game.
--Dunbar
>
>
> From: dunbar_dra <h_dunbar@ .>
> Subject: [vpFREE] Re: Bob Dancer's CasinoGaming Column - 4 NOV
2008
> To: vpFREE@yahoogroups. com
> Date: Wednesday, November 5, 2008, 2:28 PM
>
>
>
>
>
>
> I agree with NOTI that "NO" is a very useful concept.
>
> http://members. cox.net/vpfree/ Bank_NO1. htm
>
> Here's another example of "NO" that is sobering. Consider a 9/6
JOB
> game with 0.8% cashback. Many would be excited by the opportunity
to
> play such a low variance version of video poker with a +0.34%
edge.
> But even with perfect play, "NO" is 1,650,000 hands. That's about
> 2000 hours if you play 800 hands/hr. So, if you play 40 hrs/week
for
> 50 weeks of the year (taking 2 weeks off to try to unfry your
brain),
> you'd still have a 16% chance of being behind after the year's
play.
> And that's with perfect play.
>
> If you give up as little as 0.05% to errors for that game, "NO"
> climbs to 2,300,000 hands. Now you're looking at 2900 hours
(about
a
> year-and-a-half of 40-hour weeks) just to get to the point where
you
> have about a 5/6 chance of being ahead.
>
> --Dunbar
>
> --- In vpFREE@yahoogroups. com, "nightoftheiguana20 00"
> <nightoftheiguana20 00@> wrote:
> >
> > Bob wrote:
> > "This column reflects a recent change in my thinking. In the
past
I
> > argued that if you played more than a couple of hundred hours a
> year,
> > your results were pretty much what you deserved. While this
would
> > undoubtedly be true if you could look at all 1,000 imaginary
times
> you
> > experienced the same year, when you only experience a year once
you
> > cannot know for sure. "
> >
> > That's where "N0" comes in:
> >
> > http://members. cox.net/vpfree/ Bank_NO.htm
> >
> > N0 can be approximated as variance/advantage^ 2 hands. For FPDW
and
> > zero error rate (an unrealistic error rate for most players),
that
> > comes out to 26/.0076^2 = 450,000 hands. Assuming a .1% error
rate:
> > 26/.0066^2 = 600,000 hands. Play that many hands and your
chances
of
> > being ahead are 84% while chances of being behind are 16%. For a
> > negative expectation game, the situation is reversed: 84%
chance
of
> > losing, only 16% chance of winning. For a breakeven game, it's
a
50-
> 50
> > proposition, meaning eventually a 50% risk of ruin (someone will
> > eventually quit, the bankroll requirement is infinite, either
you
or
> > the house will hit their limit, assuming equal limits the
results
> are
> > 50-50), which many people would consider unacceptably high. The
> games
> > you play and how you play them determines which distribution
you
are
> > in, your actual results in your distribution is determined
> by "luck".
> >
> > --- In vpFREE@yahoogroups. com, "vpFae" <vpFae@> wrote:
> > >
> > > Randomness in Video Poker Results
> > >
> > > http://www.casinoga ming.com/ columnists/ dancer/2008/
1104.html
···
--- In vpFREE@yahoogroups.com, John Clark <jaycee5353@...> wrote:
--- On Thu, 11/6/08, dunbar_dra <h_dunbar@...> wrote:
> --- On Wed, 11/5/08, dunbar_dra <h_dunbar@ .> wrote:
> > >
> > > <a
> href="http://www.casinoga ming.com/ columnists/ dancer/2008/
1104.html">
> > > http://www.casinoga ming.com/ columnists/ dancer/2008/
1104.html</a>
> > >
> > >
> > > ************ ********* ********* ********* *********
> > >
> > > This link is posted for informational purposes and doesn't
> > > constitute an endorsement or approval of the linked article's
> > > content by vpFREE. Any discussion of the article must be done
> > > in accordance with vpFREE's rules and policies.
> > >
> > > ************ ********* ********* ********* *********
> > >
> >
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
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