bankroll required for 3 day trip to vegas

[rgmustain]

While it may be useful to ignore the SF and RF, it certainly can't be
said that 8000 hands "is not enough". In fact, there's a pretty good
chance one will see a SF in 8000 hands.

In any event, the numbers ARE useful and provide a more conservative
approach with is probably a good way to go.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:

8000 hands is not enough for a royal or straight flush, so subtract
them from the expected return and variance:
new er = 99.5% -2% -0.5% = 97% (3% average loss)
new variance = 19.5 - 15.8 - 0.3 = 3.4
average loss for 8000 hands of 5 coin quarter job = 8000 x $1.25 x

3%

= $300
standard deviation = $1.25 x sqrt(8000 x 3.4) = $206
5% ror = 1.64 standard deviations
5% ror = 1.64 x $206 = $338
total = $300 + $338 = $638
that's an estimate, you can get an exact number from:
http://www.lotspiech.com/GamblersRuin.html
for stake=$638, retire=$2000, 8000 hands of JOB, I get:
busted (-$640)=4.2%
-$640 to -$400=16%
-$400 to -$160=34%
-$160 to $80=21%
$80 to $320=4.6%
$320 to $560=1%
$560 to $800=4.2%
$800 to $1040=7.1%
$1040 to $1280=3.9%
$1280 to $1520=0.77%
$1520 to $1760=0.12%
$1760 to $2000=0.15%
retired ($2000)=1.6%

> > I am going to Vegas saturday and wonder if any of you math

wizzes

> out
> > there could help me figure out how much money I need to avoid
going
> > broke playing 8000 hands of quarter 9/6 JOB. A 5% ROR would be
> > tolerable. Thanks
>
> I play 9/6 JOB machines and actually like them, but until you nail
a
> RF it will drain your bankroll, in Las Vegas you don't need to

play

VP
> that is lower than 100%, I would suggest playing 10/7 double

bonus,

> even if you don't get a RF which is hard to do, the 4 of a kind
will
> usually keep you solvent, if the casino has both 9/6 JOB and 10/7
DB
> I think the better choice would be 10/7 DB! I would also buy some
> strategy cards (SH, BD or DP) and carry them with you and when

you

> find a 100% VP machine that you don't know the correct play, just
> whip it out and it will tell you what the best cards are to hold,
you
> can stop at the gamblers warehouse and pick up some strategy

cards.

> I always take more money than I need just in case, but a grand
should
> be enough if you just play single line two bit machines. The only
> reason I visit Las Vegas is because they have 100% VP machines,

if

···

--- In vpFREE@yahoogroups.com, "rehtuaxela" <jacks1eyed@n...> wrote:
> they didn't, I live closer to Atlantic City and would go
> there!I'm not a math wizz but have experience playing VP.
> Good luck in Las Vegas
>
> Al

[cdfsrule1]

The poor horse...

Lotspiech's gambler's ruin page is a trully excellent resource.

But while I beleive that his computation is accurate enough for VP
players, it is by NO MEANS EXACT. In order to speed things up,
he "bins" the PDF. This simplification creates a small, but non-
zero, error in the RoR.

As I wrote in message # 49003, the required bankroll for RoR(8000
hands) of 5% is (almost exactly) $625. Michael Peck came in with
$575 BEFORE ME, and Dan Paymer subsequently came in with a number for
14% RoR (which would yeild about the same results for 5% RoR). You
now offered about $638 using yet a different simpification.

BTW, If you run $625 in Lotspeich's page, you come up with 4.9% RoR
at 8000 hands. (If you check his results, you will find that he
systematically underestimates RoR a wee bit due to the binning).

Surely these small differences (from all these advanced methods)
don't really matter much, so let's just say the answer is somewhere
between (or including) $575 and $638. That said, we ought always to
be critical of all computaional simplifications unless we understand
their limitations.

···

you can get an exact number from:

> http://www.lotspiech.com/GamblersRuin.html
> for stake=$638, retire=$2000, 8000 hands of JOB, I get:
> busted (-$640)=4.2%
>

[nightoftheiguana2000]

"not enough" has to do with the central limit theorem
for hands < cycle, assuming a normal distribution has significant error
for hands > cycle, assuming a normal distribution has small error for
the left side of the curve

···

--- In vpFREE@yahoogroups.com, "mroejacks" <rgmustain@a...> wrote:

While it may be useful to ignore the SF and RF, it certainly can't be
said that 8000 hands "is not enough". In fact, there's a pretty good
chance one will see a SF in 8000 hands.

In any event, the numbers ARE useful and provide a more conservative
approach with is probably a good way to go.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
> 8000 hands is not enough for a royal or straight flush, so subtract
> them from the expected return and variance:
> new er = 99.5% -2% -0.5% = 97% (3% average loss)
> new variance = 19.5 - 15.8 - 0.3 = 3.4
> average loss for 8000 hands of 5 coin quarter job = 8000 x $1.25 x
3%
> = $300
> standard deviation = $1.25 x sqrt(8000 x 3.4) = $206
> 5% ror = 1.64 standard deviations
> 5% ror = 1.64 x $206 = $338
> total = $300 + $338 = $638
> that's an estimate, you can get an exact number from:
> http://www.lotspiech.com/GamblersRuin.html
> for stake=$638, retire=$2000, 8000 hands of JOB, I get:
> busted (-$640)=4.2%
> -$640 to -$400=16%
> -$400 to -$160=34%
> -$160 to $80=21%
> $80 to $320=4.6%
> $320 to $560=1%
> $560 to $800=4.2%
> $800 to $1040=7.1%
> $1040 to $1280=3.9%
> $1280 to $1520=0.77%
> $1520 to $1760=0.12%
> $1760 to $2000=0.15%
> retired ($2000)=1.6%
>
> --- In vpFREE@yahoogroups.com, "rehtuaxela" <jacks1eyed@n...> wrote:
> > > I am going to Vegas saturday and wonder if any of you math
wizzes
> > out
> > > there could help me figure out how much money I need to avoid
> going
> > > broke playing 8000 hands of quarter 9/6 JOB. A 5% ROR would be
> > > tolerable. Thanks
> >
> > I play 9/6 JOB machines and actually like them, but until you nail
> a
> > RF it will drain your bankroll, in Las Vegas you don't need to
play
> VP
> > that is lower than 100%, I would suggest playing 10/7 double
bonus,
> > even if you don't get a RF which is hard to do, the 4 of a kind
> will
> > usually keep you solvent, if the casino has both 9/6 JOB and 10/7
> DB
> > I think the better choice would be 10/7 DB! I would also buy some
> > strategy cards (SH, BD or DP) and carry them with you and when
you
> > find a 100% VP machine that you don't know the correct play, just
> > whip it out and it will tell you what the best cards are to hold,
> you
> > can stop at the gamblers warehouse and pick up some strategy
cards.
>
> > I always take more money than I need just in case, but a grand
> should
> > be enough if you just play single line two bit machines. The only
> > reason I visit Las Vegas is because they have 100% VP machines,
if
> > they didn't, I live closer to Atlantic City and would go
> > there!I'm not a math wizz but have experience playing VP.
> > Good luck in Las Vegas
> >
> > Al

[Michael_Peck]

The poor horse...

I'm changing the subject header to something more appropriate since
the original questioner's weekend should be just about over now and
hopefully he did better than worst case scenarios.

As I wrote in message # 49003, the required bankroll for RoR(8000
hands) of 5% is (almost exactly) $625. Michael Peck came in with
$575 BEFORE ME, and Dan Paymer subsequently came in with a number for
14% RoR (which would yeild about the same results for 5% RoR). You
now offered about $638 using yet a different simpification.

As I mentioned and you noticed I completely ignored RoR in my
calculation, so $575 would be a strict lower limit on bankroll
requirement. After doing the same kind of PDF calculation as I did
Jazbo (http://www.jazbo.com/videopoker/curves.html) guessed that an
estimate like this should be padded by about 10% -- I think Harry
Porter offered a similar guess. That would make the bankroll
requirement about $575+58=$633. Jazbo's guess looks pretty good to me
if your "exact" computation is correct.

This is changing the subject just slightly: I've uploaded some
examples comparing Monte Carlo calculations of PDFs to distributions
calculated using Mr. "cdfsrule's" very clever method of using the
convolution theorem of Fourier transforms.

First, here <http://wildlife-pix.com/vpoker/vp8000jb.png> is the case
that came up this weekend of 8,000 hands of 9/6 JOB. This shows the
distribution of total returns in units with a standard 5 bet unit per
hand. The histogram is from a Monte Carlo simulation with a sample
size of 100,000. For comparison the red line is the "exact"
calculation, and the blue line is a Gaussian (normal) distribution
with the same mean and variance. The long-dashed vertical line is the
median return from the Monte Carlo simulation, and the short-dashed
line is the average return.

Just for fun here's <http://wildlife-pix.com/vpoker/vpe6jb.png> the
distribution of returns per unit bet for 1,000,000 hands of Jacks.
This time the Monte Carlo calculation used a sample size of 1,000,000
which makes for a slightly prettier histogram. Notice that the "exact"
PDF almost, but not quite, sits on top of the Gaussian curve: a
million hands still does not quite qualify as the "long run".

If you've had a statistics class or three you've maybe seen
quantile-quantile plots like this one:
<http://wildlife-pix.com/vpoker/vpe6jbqq.png>. This particular one
plots quantiles of the distribution of returns for a million hands of
Jacks against theoretical returns for a Gaussian. This is a really
sensitive graphical method to test whether a sample comes from some
given distribution. In this case the upward curving tails indicate a
skewed distribution: you're less likely to do very much worse than
expected and more likely to do very much better than expected based on
a Normal distribution.

I was going to write more, but I'm in Bangkok right now and my wife
keeps dragging me out to shop for antique Buddhas of dubious
provenance. I've written more than any sensible person is interested
in anyway.

Mike

···

--- In vpFREE@yahoogroups.com, "cdfsrule" <groups.yahoo@v...> wrote:

[deuceswild1000]

Please do. This is one of the most complete and understandable posts;
that is supported with documentation that is easy to understand; ever
published here. Too often we are left with formulae to try to figure
out for ourselves or just opinion without any docuementation.

DWK

···

--- In vpFREE@yahoogroups.com, "Michael Peck" <mpeck1@i...> wrote:

I was going to write more, but I'm in Bangkok right now and my wife
keeps dragging me out to shop for antique Buddhas of dubious
provenance. I've written more than any sensible person is interested
in anyway.

Mike