Test of Randomness, ER, etc.

[blaw57]

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

> The conclusion I came to is simply that normalization takes

longer

> than we think.

define normalization

Good point, and that raises a whole host of other issues.

My definiton, and most people I think, would be achieving my
expected return in dollars, no more, no less. Since I play a variety
of games and denominations, this would require more than simply
achieveing the average expected hand distribution. If all my quad
2's and Aces come in JOB and the quad 6's and 7's pop up in Triple
Deuces and Super Aces bonus, I'm going to be in trouble even with an
average hand distiributio.

To further stir the pot, I'm provisionally working under the theory
that "cross-normalization" will tend to occur, both over denoms and
across different games. This is in contrast to several friends, who
seem to believe have to play the same game/denom a million hands
before you can expect to hit the averages pretty close.

···

--- In vpFREE@yahoogroups.com, "blaw57" <blaw57@y...> wrote:

[nightoftheiguana2000]

hmm, well, you will never hit the averages pretty close
(sorry to disappoint)
if you play an infinite number of hands, you will approach the
averages
but for less than an infinite number of hands, there will always be
odds, it's always a gamble, it's always possible to go 20 royal cycles
without a royal, or even more, it's just not very likely

i think the best way to look at this problem is the N0 number:
for fpdw +0.25% cashback:
N0=variance/(er+cb-1)^2=26/(.01)^2=260,000 hands
at N0 hands (260,000) your chances of being a net winner are 84%
at 4N0 hands (1,040,000) your chances of being a net winner are 98%
at 9N0 hands (2,340,000) your chances of being a net winner are 99.9%
if you play N0 hands per year for 9 years, your chances of being a net
winner are 99.9% even though your chances of having at least one
losing year out of 9 are 80% (1-.84^9)

also important is the R(1) number, in the case of fpdw+.25%cb this
number is: 0.999102 so your losing streak probabilities are:
R(1)^(loss in bets)
1 royal (-800 bets): 49%
2 royals (-1600 bets): 24%
3 royals (-2400 bets): 12%
4 royals (-3200 bets): 6%
5 royals (-4000 bets): 3%
10 royals (-8000 bets): 0.08%
20 royals (-16000 bets): 0.00006%

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
>
> > The conclusion I came to is simply that normalization takes
longer
> > than we think.
>
> define normalization

Good point, and that raises a whole host of other issues.

My definiton, and most people I think, would be achieving my
expected return in dollars, no more, no less. Since I play a

variety

of games and denominations, this would require more than simply
achieveing the average expected hand distribution. If all my quad
2's and Aces come in JOB and the quad 6's and 7's pop up in Triple
Deuces and Super Aces bonus, I'm going to be in trouble even with

an

···

--- In vpFREE@yahoogroups.com, "blaw57" <blaw57@y...> wrote:

> --- In vpFREE@yahoogroups.com, "blaw57" <blaw57@y...> wrote:
average hand distiributio.

To further stir the pot, I'm provisionally working under the theory
that "cross-normalization" will tend to occur, both over denoms and
across different games. This is in contrast to several friends, who
seem to believe have to play the same game/denom a million hands
before you can expect to hit the averages pretty close.

[deuceswild1000]

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

N0=variance/(er+cb-1)^2=26/(.01)^2=260,000 hands
at N0 hands (260,000) your chances of being a net winner are 84%
at 4N0 hands (1,040,000) your chances of being a net winner are 98%
at 9N0 hands (2,340,000) your chances of being a net winner are

99.9%

if you play N0 hands per year for 9 years, your chances of being a

net

winner are 99.9% even though your chances of having at least one
losing year out of 9 are 80% (1-.84^9)

Iggy, you are starting to put words to your equations for us
dummies. So what is a NO hand

[kcace1024]

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

hmm, well, you will never hit the averages pretty close
(sorry to disappoint)
if you play an infinite number of hands, you will approach the
averages
but for less than an infinite number of hands, there will always be
odds, it's always a gamble, it's always possible to go 20 royal

cycles

without a royal, or even more, it's just not very likely

i think the best way to look at this problem is the N0 number:
for fpdw +0.25% cashback:
N0=variance/(er+cb-1)^2=26/(.01)^2=260,000 hands
at N0 hands (260,000) your chances of being a net winner are 84%
at 4N0 hands (1,040,000) your chances of being a net winner are 98%
at 9N0 hands (2,340,000) your chances of being a net winner are

99.9%

if you play N0 hands per year for 9 years, your chances of being a

net

winner are 99.9% even though your chances of having at least one
losing year out of 9 are 80% (1-.84^9)

also important is the R(1) number, in the case of fpdw+.25%cb this
number is: 0.999102 so your losing streak probabilities are:
R(1)^(loss in bets)
1 royal (-800 bets): 49%
2 royals (-1600 bets): 24%
3 royals (-2400 bets): 12%
4 royals (-3200 bets): 6%
5 royals (-4000 bets): 3%
10 royals (-8000 bets): 0.08%
20 royals (-16000 bets): 0.00006%

Iguana,

Another request for your help.

I will review my old college statistics books so I can discuss this
topic more accurately. However, I do remember that you cannot prove
much with statistics, but you can achieve 95% or 98% or more
confidence levels with sufficient trials. Can you determine how
many hands/trials it takes to be 95% confident that the ER without
the Royal is generating within the expected range.

I am hoping that removing the Royal from the equation will drop the
variance to the point where we can test the randomness of the lower
hands rather easily. If machines were rigged to take an extra 1%, I
believe it would be taken from the lower hands. Seeing a royal and
hitting one yourself is what keeps a lot of players playing beyond
their bankroll, using incorrect strategy to go for the royal, etc.
Taking 1% from the royal would be too noticeable to regular
players. Even if you are in a royal drought you still notice when
others in the casino hit a royal.

Chris

[nightoftheiguana2000]

wrote:

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

> N0=variance/(er+cb-1)^2=26/(.01)^2=260,000 hands
> at N0 hands (260,000) your chances of being a net winner are 84%
> at 4N0 hands (1,040,000) your chances of being a net winner are

98%

> at 9N0 hands (2,340,000) your chances of being a net winner are
99.9%
> if you play N0 hands per year for 9 years, your chances of being

a

net
> winner are 99.9% even though your chances of having at least one
> losing year out of 9 are 80% (1-.84^9)

Iggy, you are starting to put words to your equations for us
dummies. So what is a NO hand

N0 is the number of hands that must be played to gain an 84% chance of
being a net winner (for a positive gamble), in the case of fpdw+.25%cb
above, N0 is 260,000 hands or 260 hours at 1000 hands/hour

it varies by game, because its formula is variance/(er+cashback-1)^2

technically, it is the number of hands at which the average return
[(er+cashback-1)x hands] equals one standard deviation [sqrt(variance
x hands)], at 4xN0 the average return equals two standard deviations,
at 9xN0 the average return equals three standard deviations, you can
see that the more hands you play the greater are your odds of being a
net winner

···

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

[nightoftheiguana2000]

for deuces you should exclude the royal and deuces:
new er=1.007619624-0.017667091-0.04074064=0.949211893 (~5% loss)
new var=25.83461818-14.09809215-8.066232694=3.670293334

next winning hand is wild royal with a cycle time of ~557 hands

so, at around 2000 hands and above, excluding royals and deuces, you
should get with 95% confidence (2 standard deviations):
(er-1)x hands +/- 2x sqrt(variance x hands)
(0.95-1)x hands +/- 2x sqrt(3.67 x hands)
at 2000 hands:
(0.95-1)x 2000 +/- 2x sqrt(3.67 x 2000)=
-100 +/- 171 bets
at 5 coin quarters=
-$125 +/- $214

another approach is to play 25 cycles, at that point 95% confidence
would be +/- 2x sqrt(25)= +/- 10, for example, the cycles for deuces
are:
rf 45282
4d 4909
wrf 557
5k 312
sf 243
4k 15.4
fh 47.1
fl 60.3
st 17.7
3k 3.51
zip 1.83

so after 25x1.83=46 hands, you would expect 15 to 35 zip results
after 25x3.51=88 hands, you would expect 15 to 35 3k's and 48 +/- 14
zips
after 25x17.7=443 hands, you would expect 15 to 35 straights, 126 +/-
22 3k's, 242 +/- 31 zips
...
the average result is hands/cycle, two standard deviations is 2x
sqrt(hands/cycle)

I will review my old college statistics books so I can discuss this
topic more accurately. However, I do remember that you cannot

prove

much with statistics, but you can achieve 95% or 98% or more
confidence levels with sufficient trials. Can you determine how
many hands/trials it takes to be 95% confident that the ER without
the Royal is generating within the expected range.

I am hoping that removing the Royal from the equation will drop the
variance to the point where we can test the randomness of the lower
hands rather easily. If machines were rigged to take an extra 1%,

I

···

believe it would be taken from the lower hands. Seeing a royal and
hitting one yourself is what keeps a lot of players playing beyond
their bankroll, using incorrect strategy to go for the royal, etc.
Taking 1% from the royal would be too noticeable to regular
players. Even if you are in a royal drought you still notice when
others in the casino hit a royal.

Chris

[jackessiebabe]

--- In vpFREE@yahoogroups.com, "jackessiebabe"

<jackessiebabe@y...> wrote:

>
> >
> > >
> > When I'm playing with friends and I get dealt 4 to a royal, I
> > frequently take out my watch and watch it closely for 20-30
> seconds
> > before hitting the draw button. When asked why, I'll reply I'm
> > waiting for the random number seed to come around into the

Queen

> of
> > hearts (or whatever card is needed) range.
> >
> >
> >>>>>>>>>>>>>>>>>>>>> Bless you for your patience, if you can
> actually wait 20-30 seconds (an ETERNITY) to hit that draw

button! I

> can't wait an extra second to if that elusive Royal is there.

I am more like you Babe, I hit it pretty fast, but that reminds me

of

a couple I played next to earlier this year. They were dealt 4 to

the

royal, and they got so excited and went on and on almost like they

had

already won, then they had to get out thier lucky penny and each

one

rub on it and then set it on the machine and finally hit the draw
button. Well they got the royal and if you ask them it was all
because of the penny. It was pretty funny, although I believe I

was

having a bad session and it didnt make me feel any better, but they
were typical players and I am sure the money has long gone back in

the

machines. Sometimes randomness even looks kindly on the

uneducated,

···

--- In vpFREE@yahoogroups.com, "jimnkelli" <jbecker11@c...> wrote:

> --- In vpFREE@yahoogroups.com, "blaw57" <blaw57@y...> wrote:
and thank goodness because it keeps them coming back.

Happy royals
Jim

++++++++++++++++++++++

Hi Jim,

Happy Royals to you too! (With apologies to Roy & Dale, if you're
old enough to remember their old song).
I don't especially relate to people who play "can you top this
games", but I must share with you the story of the elderly couple
who were sitting together, sharing one seat, and playing JoB. She
would play (feed coins, hold cards & draw) as long as she was won
each hand (refunds counted). With each refund/win, they dumped the
coins. As soon as a hand was lost, the other partner took over and
the routine was repeated. Finally 4RF in hearts appeared, and the
dance began. Each was wearing a BB cap, bill forward. Each took off
a cap and planted it on the other's head, bill backward. Then. they
both rose from the shared seat, and hand-in-hand, walked around the
chair a few times. She then placed a monitor sized piece of paper
on the screen so that the cards were not visible, and humming some
(presumed) incantation to the God of VP, she put her hand on top of
his hand, and together, they drew the last card.....the 4 of clubs!
They were really deflated! I wasn't having a good session, and was
happy for the watching time, which cut down on my losses, but I felt
unhappy for them, and told them so. They said that this was their
normal routine when they came in with RF4, and that sometimes, it
even worked. Bless the Wonderful Side of Randomness!
Best to you, Babe

[kcace1024]

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

for deuces you should exclude the royal and deuces:
new er=1.007619624-0.017667091-0.04074064=0.949211893 (~5% loss)
new var=25.83461818-14.09809215-8.066232694=3.670293334

next winning hand is wild royal with a cycle time of ~557 hands

so, at around 2000 hands and above, excluding royals and deuces,

you

should get with 95% confidence (2 standard deviations):
(er-1)x hands +/- 2x sqrt(variance x hands)
(0.95-1)x hands +/- 2x sqrt(3.67 x hands)
at 2000 hands:
(0.95-1)x 2000 +/- 2x sqrt(3.67 x 2000)=
-100 +/- 171 bets
at 5 coin quarters=
-$125 +/- $214

another approach is to play 25 cycles, at that point 95% confidence
would be +/- 2x sqrt(25)= +/- 10, for example, the cycles for

deuces

are:
rf 45282
4d 4909
wrf 557
5k 312
sf 243
4k 15.4
fh 47.1
fl 60.3
st 17.7
3k 3.51
zip 1.83

so after 25x1.83=46 hands, you would expect 15 to 35 zip results
after 25x3.51=88 hands, you would expect 15 to 35 3k's and 48 +/-

14

zips
after 25x17.7=443 hands, you would expect 15 to 35 straights, 126

+/-

22 3k's, 242 +/- 31 zips
...
the average result is hands/cycle, two standard deviations is 2x
sqrt(hands/cycle)

Thanks Iguana,

Therefore, with only 2000 hands it is possible to be 95% confident
that a FPDW machine is generating all payoffs below the royal and
quad deuces as expected. This is much quicker than I thought
possible.

I would like to track the results of my All American play. How do
you calculate the variance contribution for each type of payoff.
The cycle for the straight flush in AA is quite a bit higher than
quad deuces so I expect the variance for AA without the royal and
the straight flush to be even lower than FPDW. Thanks again!

Chris

[Harry_Porter]

nightoftheiguana2000 wrote:

> so, at around 2000 hands and above, excluding royals and deuces,
> you should get with 95% confidence (2 standard deviations):
> (er-1)x hands +/- 2x sqrt(variance x hands)
> (0.95-1)x hands +/- 2x sqrt(3.67 x hands)
> at 2000 hands:
> (0.95-1)x 2000 +/- 2x sqrt(3.67 x 2000)=
> -100 +/- 171 bets
> at 5 coin quarters=
> -$125 +/- $214

Chris replied:

Thanks Iguana,

Therefore, with only 2000 hands it is possible to be 95% confident
that a FPDW machine is generating all payoffs below the royal and
quad deuces as expected. This is much quicker than I thought
possible.

Quicker, perhaps, Chris. But if you look at the numbers for 2000
hands, I'm not sure that it's going to be very helpful to you. Or,
perhaps it will simply put things into proper perspective before you
begin some extensive record-keeping.

Having run through $2500 through the machine, iggy is saying that 95%
of the time your result should run between a loss of $339 and a profit
of $94. If we were to assume a normal distribution, then about 2.5%
of the time (one in 40 trials) you'd expect a loss greater than $339.

Now, I don't know about you, but I'm the kind of guy that any time my
$.25 FPDW loss on about 3 hours play runs $300, even I get a little
nervous about the machine Yet, iggy tells us that this type of
result isn't out of bounds at all.

···

------

I do have a couple of questions for iggy here, though. You'll note
that I use the phrase "assume a normal distribution" above. My stat
knowledge in this area is weak relative to yours iggy, but it seems to
me that on this limited number of hands the cycle of the lesser
occurring hands (e.g. WRF) isn't sufficient to "normalize" and thus
the area of the result distribution lying out of the 95% confidence
interval may not divide nicely in half, as I've assumed above.

Bottom line, iggy, I expect Chris is going to want to compare his
adverse sessions against the lower bound you've calculated. What
percentage of sessions should he expect to fall below that?

Finally, if I understand the methodology to be employed, a single
session that falls outside of the 95% interval will suggest that the
machine is biased (negatively or positively, depending on result).
But, no one is likely to be satisfied with the result of one session.

So, are we talking about a methodology that would involve multiple
trials? If so, how many to achieve a given degree of confidence that
the machine is biased?

Steer me straight, iggy, if I've gone far astray here.

- Harry

[nightoftheiguana2000]

variance is probability x (win-er)^2 summed for each hand type:

hand_win_probability_er__________variance
rf___800_2.30149E-05 0.018411887_14.6924432
sf___200_0.000141786 0.028357274__5.614474563
4k____40_0.002251744 0.090069766__3.423634758
fh_____8_0.010981327 0.087850616__0.536975485
fl_____8_0.015722264 0.125778109__0.768802366
str____8_0.018423994 0.147391954__0.900914189
3k_____3_0.068834825 0.206504475__0.273354732
2p_____1_0.119598260 0.11959826___6.23577E-06
pJ+____1_0.183258412 0.183258412__9.55496E-06
zip____0_0.580764373 0____________0.589181766
totals___1___________1.007220753_26.79979685

(probability=1/cycle)

···

--- In vpFREE@yahoogroups.com, "kcace1024" <cy4873@h...> wrote:

I would like to track the results of my All American play. How do
you calculate the variance contribution for each type of payoff.
The cycle for the straight flush in AA is quite a bit higher than
quad deuces so I expect the variance for AA without the royal and
the straight flush to be even lower than FPDW. Thanks again!

[nightoftheiguana2000]

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

I do have a couple of questions for iggy here, though. You'll note
that I use the phrase "assume a normal distribution" above. My stat
knowledge in this area is weak relative to yours iggy, but it seems

to

me that on this limited number of hands the cycle of the lesser
occurring hands (e.g. WRF) isn't sufficient to "normalize" and thus
the area of the result distribution lying out of the 95% confidence
interval may not divide nicely in half, as I've assumed above.

Bottom line, iggy, I expect Chris is going to want to compare his
adverse sessions against the lower bound you've calculated. What
percentage of sessions should he expect to fall below that?

well, i think 2.5% is a pretty good estimate
if you wanted a more precise answer, the easy way would be to run
lotspiech's simulator:
http://www.lotspiech.com/GamblersRuin.html
select deuces, stake=$339, retire=$94, run for 2000 hands
result is busted (less than $340) 1.8%
retired (more than $95) 40%

i think those results are inline with the calculations, the
calculations assumed you didn't hit deuces or royal, the 40% above
includes the chances of hitting those hands, and instead of 2.5% below
$339 it says 1.8%

a more complicated method would be to derive the er and variance
without the wrf, then figure your odds of how many wrf and apply that
to the result

Finally, if I understand the methodology to be employed, a single
session that falls outside of the 95% interval will suggest that the
machine is biased (negatively or positively, depending on result).
But, no one is likely to be satisfied with the result of one

session.

you would have 95% confidence that the machine is biased
let me correct that, assuming your results fell below the expected,
you would have 98.2% confidence (using lotspiech's number)
i'm assuming if you found a loose machine in your favor you wouldn't
complain (results above expected range)

So, are we talking about a methodology that would involve multiple
trials? If so, how many to achieve a given degree of confidence

that

the machine is biased?

well, if one session falls below expected range, in this case $339,
you have 1.8% confidence that the machine is not biased

let's assume you play another 2000 hand session
if you fell below $339 again, you would have (1.8%)^2 = .03%
confidence that the machine is not biased (99.97% confidence that it
is)

it's just probabilities
not below range= 98.2% confidence in machine, 1.8% confidence against
machine
below range= 1.8% confidence in machine, 98.2% confidence against

probability of machine not being below range twice: .982^2=96.4%
probability of machine being below range twice: .018^2=0.03%
probability of one session above, one session below:
100-96.4-.03=3.57%

[Harry_Porter]

nightoftheiguana2000 wrote:

well, if one session falls below expected range, in this case $339,
you have 1.8% confidence that the machine is not biased

let's assume you play another 2000 hand session
if you fell below $339 again, you would have (1.8%)^2 = .03%
confidence that the machine is not biased (99.97% confidence that it
is)

it's just probabilities
not below range= 98.2% confidence in machine, 1.8% confidence
against machine below range= 1.8% confidence in machine, 98.2%
confidence against

probability of machine not being below range twice: .982^2=96.4%
probability of machine being below range twice: .018^2=0.03%
probability of one session above, one session below:
100-96.4-.03=3.57%

Thanks for the info, iggy ... much appreciated.

I've quoted the text for which I'm being just a little slow on the
uptake. Humor me, ok

If I'm reading this right, you seem to suggest that on just one trial
of 2000 hands you'll have 98.2% confidence in your assessment of the
fairness of the machine.

Now, I suspect I'm interpreting something incorrectly here. I read
this to say that if the result of your session was a loss of $330,
then the interpretation that the machine is fair is made with 98.2%
confidence. On the other hand, if the loss were $350, you have 98.2%
confidence that the machine is negatively biased.

You see my problem here. That seems to be a very small difference in
loss to sway the call that much. This was the driver behind my
assumption that it would take multiple 2000 hand trials to arrive as
an assessment with a large degree of confidence.

Keep your hands on my shoulders, iggy, and steer me in the right
direction

- Harry

[nightoftheiguana2000]

hmm, yeah, i see the problem
ok, i'm still gonna hold to this though:
let's say you have a sample of 2000 hands, and your results are -$339,
and we have figured out that the probability of this occuring with a
legit fpdw is 1.8%
so, based on this sample size, we have 1.8% confidence that it comes
from a legit fpdw machine and 98.2% confidence that the machine is not
a legit fpdw?
if our results were -$300, it would shift to something like 5%/95%?
since our sample size is too small for deuces and royals we are
expecting a mean of -5% (2000x$1.25x-.05=-$125)
if our sample came in at -$125, would we have 100% confidence?
this is where harry takes over
good luck harry
(i still think if you get -$339 it's 98.2% likely you've got a bum
machine or are suffering some sort of pilot error)

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

nightoftheiguana2000 wrote:

> well, if one session falls below expected range, in this case

$339,

> you have 1.8% confidence that the machine is not biased
>
> let's assume you play another 2000 hand session
> if you fell below $339 again, you would have (1.8%)^2 = .03%
> confidence that the machine is not biased (99.97% confidence that

it

> is)
>
> it's just probabilities
> not below range= 98.2% confidence in machine, 1.8% confidence
> against machine below range= 1.8% confidence in machine, 98.2%
> confidence against
>
> probability of machine not being below range twice: .982^2=96.4%
> probability of machine being below range twice: .018^2=0.03%
> probability of one session above, one session below:
> 100-96.4-.03=3.57%

Thanks for the info, iggy ... much appreciated.

I've quoted the text for which I'm being just a little slow on the
uptake. Humor me, ok

If I'm reading this right, you seem to suggest that on just one

trial

of 2000 hands you'll have 98.2% confidence in your assessment of the
fairness of the machine.

Now, I suspect I'm interpreting something incorrectly here. I read
this to say that if the result of your session was a loss of $330,
then the interpretation that the machine is fair is made with 98.2%
confidence. On the other hand, if the loss were $350, you have

98.2%

confidence that the machine is negatively biased.

You see my problem here. That seems to be a very small difference

in

···

loss to sway the call that much. This was the driver behind my
assumption that it would take multiple 2000 hand trials to arrive as
an assessment with a large degree of confidence.

Keep your hands on my shoulders, iggy, and steer me in the right
direction

- Harry

[nightoftheiguana2000]

just to summarize the results from the lotspiech calculator:
fpdw, stake=$340, retire=$95, 2000 hands ($1.25/hand)
<-$340 1.8%
-$340to-$295 1.6%
-$295to-$250 4.2%
-$250to-$205 7.0%
-$205to-$160 9.4%
-$160to-$115 10%
-$115to-$70 9.6%
-$70to-$25 7.4%
-$25to+$20 4.8%
+$20to+$65 2.3%
+$65to+$95 0.40%

+$95 40%

so, if you get less than -$340 in actual play, you have 1.8%
confidence that the machine is honest, if you get -$125 in actual
play, you have 10% confidence that the machine is honest, if you get
over +$95 you have 40% confidence
if you are trying to prove that the machine is honest with greater
confidence, you will have to play more hands
however, if you are trying to prove that the machine is fixed, and you
get less than -$340, you have 98.2% confidence that it is fixed (or
you are playing incorrectly)
best option at that point would be to report your findings to the
local regulation board and here (make note of machine number) and find
a different machine
if you insist, you can continue playing and evaluating, the worse the
results and the more hands the greater your confidence will be
that you've found a loser

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

hmm, yeah, i see the problem
ok, i'm still gonna hold to this though:
let's say you have a sample of 2000 hands, and your results are

-$339,

and we have figured out that the probability of this occuring with a
legit fpdw is 1.8%
so, based on this sample size, we have 1.8% confidence that it comes
from a legit fpdw machine and 98.2% confidence that the machine is

not

a legit fpdw?
if our results were -$300, it would shift to something like 5%/95%?
since our sample size is too small for deuces and royals we are
expecting a mean of -5% (2000x$1.25x-.05=-$125)
if our sample came in at -$125, would we have 100% confidence?
this is where harry takes over
good luck harry
(i still think if you get -$339 it's 98.2% likely you've got a bum
machine or are suffering some sort of pilot error)

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
>
> nightoftheiguana2000 wrote:
>
> > well, if one session falls below expected range, in this case
$339,
> > you have 1.8% confidence that the machine is not biased
> >
> > let's assume you play another 2000 hand session
> > if you fell below $339 again, you would have (1.8%)^2 = .03%
> > confidence that the machine is not biased (99.97% confidence

that

it
> > is)
> >
> > it's just probabilities
> > not below range= 98.2% confidence in machine, 1.8% confidence
> > against machine below range= 1.8% confidence in machine, 98.2%
> > confidence against
> >
> > probability of machine not being below range twice: .982^2=96.4%
> > probability of machine being below range twice: .018^2=0.03%
> > probability of one session above, one session below:
> > 100-96.4-.03=3.57%
>
>
> Thanks for the info, iggy ... much appreciated.
>
> I've quoted the text for which I'm being just a little slow on the
> uptake. Humor me, ok
>
> If I'm reading this right, you seem to suggest that on just one
trial
> of 2000 hands you'll have 98.2% confidence in your assessment of

the

> fairness of the machine.
>
> Now, I suspect I'm interpreting something incorrectly here. I

read

> this to say that if the result of your session was a loss of $330,
> then the interpretation that the machine is fair is made with

98.2%

> confidence. On the other hand, if the loss were $350, you have
98.2%
> confidence that the machine is negatively biased.
>
> You see my problem here. That seems to be a very small difference
in
> loss to sway the call that much. This was the driver behind my
> assumption that it would take multiple 2000 hand trials to arrive

as

···

> an assessment with a large degree of confidence.
>
> Keep your hands on my shoulders, iggy, and steer me in the right
> direction
>
> - Harry

[nightoftheiguana2000]

one more comment, you can plot those numbers with a spreadsheet and
decide for yourself how normalized they look, here's my quick and
dirty plot:
XXXXXXX
XXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXX
XX

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

just to summarize the results from the lotspiech calculator:
fpdw, stake=$340, retire=$95, 2000 hands ($1.25/hand)
<-$340 1.8%
-$340to-$295 1.6%
-$295to-$250 4.2%
-$250to-$205 7.0%
-$205to-$160 9.4%
-$160to-$115 10%
-$115to-$70 9.6%
-$70to-$25 7.4%
-$25to+$20 4.8%
+$20to+$65 2.3%
+$65to+$95 0.40%
>+$95 40%

so, if you get less than -$340 in actual play, you have 1.8%
confidence that the machine is honest, if you get -$125 in actual
play, you have 10% confidence that the machine is honest, if you get
over +$95 you have 40% confidence
if you are trying to prove that the machine is honest with greater
confidence, you will have to play more hands
however, if you are trying to prove that the machine is fixed, and

you

get less than -$340, you have 98.2% confidence that it is fixed (or
you are playing incorrectly)
best option at that point would be to report your findings to the
local regulation board and here (make note of machine number) and

find

a different machine
if you insist, you can continue playing and evaluating, the worse

the

results and the more hands the greater your confidence will be
that you've found a loser

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
>
> hmm, yeah, i see the problem
> ok, i'm still gonna hold to this though:
> let's say you have a sample of 2000 hands, and your results are
-$339,
> and we have figured out that the probability of this occuring

with a

> legit fpdw is 1.8%
> so, based on this sample size, we have 1.8% confidence that it

comes

> from a legit fpdw machine and 98.2% confidence that the machine is
not
> a legit fpdw?
> if our results were -$300, it would shift to something like

5%/95%?

> since our sample size is too small for deuces and royals we are
> expecting a mean of -5% (2000x$1.25x-.05=-$125)
> if our sample came in at -$125, would we have 100% confidence?
> this is where harry takes over
> good luck harry
> (i still think if you get -$339 it's 98.2% likely you've got a bum
> machine or are suffering some sort of pilot error)
>
> --- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
> wrote:
> >
> > nightoftheiguana2000 wrote:
> >
> > > well, if one session falls below expected range, in this case
> $339,
> > > you have 1.8% confidence that the machine is not biased
> > >
> > > let's assume you play another 2000 hand session
> > > if you fell below $339 again, you would have (1.8%)^2 = .03%
> > > confidence that the machine is not biased (99.97% confidence
that
> it
> > > is)
> > >
> > > it's just probabilities
> > > not below range= 98.2% confidence in machine, 1.8% confidence
> > > against machine below range= 1.8% confidence in machine,

98.2%

> > > confidence against
> > >
> > > probability of machine not being below range twice:

.982^2=96.4%

> > > probability of machine being below range twice: .018^2=0.03%
> > > probability of one session above, one session below:
> > > 100-96.4-.03=3.57%
> >
> >
> > Thanks for the info, iggy ... much appreciated.
> >
> > I've quoted the text for which I'm being just a little slow on

the

> > uptake. Humor me, ok
> >
> > If I'm reading this right, you seem to suggest that on just one
> trial
> > of 2000 hands you'll have 98.2% confidence in your assessment of
the
> > fairness of the machine.
> >
> > Now, I suspect I'm interpreting something incorrectly here. I
read
> > this to say that if the result of your session was a loss of

$330,

> > then the interpretation that the machine is fair is made with
98.2%
> > confidence. On the other hand, if the loss were $350, you have
> 98.2%
> > confidence that the machine is negatively biased.
> >
> > You see my problem here. That seems to be a very small

difference

> in
> > loss to sway the call that much. This was the driver behind my
> > assumption that it would take multiple 2000 hand trials to

arrive

···

as
> > an assessment with a large degree of confidence.
> >
> > Keep your hands on my shoulders, iggy, and steer me in the right
> > direction
> >
> > - Harry

[jaydavidson118]

Sometimes a little knowledge is a dangerous thing.

Just because you stick numbers into a statistical package and it
generates reams of output doesn't mean you have understanding of the
situation, or that your results are meaningful. Do you have any idea
how to apply the Central Limit Theorem CLT, or even what the central
limit theorem is? One important characteristic that effects the
ability to apply CLT is how close the underlying distribution is to
the Normal distribution. The answer in our case is not very close.
The normal distribution is a symetric distribution.

In indidvidual trials of video poker hands the resutls are extremely
skewed. On one hand (5 coin bet) you could win 4000 coins, the most
you could lose is 5 coins. This would greatly increase the number of
trials you would need before CLT can be applied and you could
mindlessly enter the numbers into your stat package.

Any simple thought experiment would point out how silly your
hypotheseis testing results are.

As any stat prof. will tell you these days, the real danger in
reading statistical results today is having confidence in the person
running the software. Anyone can stick numbers into a stat package,
having a ral understanding of statistics is another thing. I'm glad
you know how to run your stat package and paste the results in eMail
messages, the next step is to learn statistical theory.

Trying to draw meaningful inferences from a sample of 2000 where the
period is 40,000 is silly.

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

just to summarize the results from the lotspiech calculator:
fpdw, stake=$340, retire=$95, 2000 hands ($1.25/hand)
<-$340 1.8%
-$340to-$295 1.6%
-$295to-$250 4.2%
-$250to-$205 7.0%
-$205to-$160 9.4%
-$160to-$115 10%
-$115to-$70 9.6%
-$70to-$25 7.4%
-$25to+$20 4.8%
+$20to+$65 2.3%
+$65to+$95 0.40%
>+$95 40%

so, if you get less than -$340 in actual play, you have 1.8%
confidence that the machine is honest, if you get -$125 in actual
play, you have 10% confidence that the machine is honest, if you get
over +$95 you have 40% confidence
if you are trying to prove that the machine is honest with greater
confidence, you will have to play more hands
however, if you are trying to prove that the machine is fixed, and

you

get less than -$340, you have 98.2% confidence that it is fixed (or
you are playing incorrectly)
best option at that point would be to report your findings to the
local regulation board and here (make note of machine number) and

find

a different machine
if you insist, you can continue playing and evaluating, the worse

the

results and the more hands the greater your confidence will be
that you've found a loser

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
>
> hmm, yeah, i see the problem
> ok, i'm still gonna hold to this though:
> let's say you have a sample of 2000 hands, and your results are
-$339,
> and we have figured out that the probability of this occuring

with a

> legit fpdw is 1.8%
> so, based on this sample size, we have 1.8% confidence that it

comes

> from a legit fpdw machine and 98.2% confidence that the machine is
not
> a legit fpdw?
> if our results were -$300, it would shift to something like

5%/95%?

> since our sample size is too small for deuces and royals we are
> expecting a mean of -5% (2000x$1.25x-.05=-$125)
> if our sample came in at -$125, would we have 100% confidence?
> this is where harry takes over
> good luck harry
> (i still think if you get -$339 it's 98.2% likely you've got a bum
> machine or are suffering some sort of pilot error)
>
> --- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
> wrote:
> >
> > nightoftheiguana2000 wrote:
> >
> > > well, if one session falls below expected range, in this case
> $339,
> > > you have 1.8% confidence that the machine is not biased
> > >
> > > let's assume you play another 2000 hand session
> > > if you fell below $339 again, you would have (1.8%)^2 = .03%
> > > confidence that the machine is not biased (99.97% confidence
that
> it
> > > is)
> > >
> > > it's just probabilities
> > > not below range= 98.2% confidence in machine, 1.8% confidence
> > > against machine below range= 1.8% confidence in machine,

98.2%

> > > confidence against
> > >
> > > probability of machine not being below range

twice: .982^2=96.4%

> > > probability of machine being below range twice: .018^2=0.03%
> > > probability of one session above, one session below:
> > > 100-96.4-.03=3.57%
> >
> >
> > Thanks for the info, iggy ... much appreciated.
> >
> > I've quoted the text for which I'm being just a little slow on

the

> > uptake. Humor me, ok
> >
> > If I'm reading this right, you seem to suggest that on just one
> trial
> > of 2000 hands you'll have 98.2% confidence in your assessment of
the
> > fairness of the machine.
> >
> > Now, I suspect I'm interpreting something incorrectly here. I
read
> > this to say that if the result of your session was a loss of

$330,

> > then the interpretation that the machine is fair is made with
98.2%
> > confidence. On the other hand, if the loss were $350, you have
> 98.2%
> > confidence that the machine is negatively biased.
> >
> > You see my problem here. That seems to be a very small

difference

> in
> > loss to sway the call that much. This was the driver behind my
> > assumption that it would take multiple 2000 hand trials to

arrive

···

as
> > an assessment with a large degree of confidence.
> >
> > Keep your hands on my shoulders, iggy, and steer me in the right
> > direction
> >
> > - Harry

[jaydavidson118]

Harry, I've enjoyed reading yours posts, have alway found well
thought out. I think "iggy" could use your hands on his shoulders not
the other way around. As a trained actuary I'm used to raeading reams
of statistical output, and making sense of it, which is the first
thing you do, "do these results make sense". Trying to do an
hypothesis test with 2000 trials, where the period is over 40,000
just doesn't make sense. Any statistical pakage will spit out
numbers, it doesn't mean the numbers are meaningful...garbage
in/garbage out. I think simple thought experiments are always more
usefule than reams of output. Which is why I've enjoyed your posts,
along with others in that vein.

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

nightoftheiguana2000 wrote:

of machine not being below range twice: .982^2=96.4%

> probability of machine being below range twice: .018^2=0.03%
> probability of one session above, one session below:
> 100-96.4-.03=3.57%

Thanks for the info, iggy ... much appreciated.

I've quoted the text for which I'm being just a little slow on the
uptake. Humor me, ok

If I'm reading this right, you seem to suggest that on just one

trial

of 2000 hands you'll have 98.2% confidence in your assessment of the
fairness of the machine.

Now, I suspect I'm interpreting something incorrectly here. I read
this to say that if the result of your session was a loss of $330,
then the interpretation that the machine is fair is made with 98.2%
confidence. On the other hand, if the loss were $350, you have

98.2%

confidence that the machine is negatively biased.

You see my problem here. That seems to be a very small difference

in

···

loss to sway the call that much. This was the driver behind my
assumption that it would take multiple 2000 hand trials to arrive as
an assessment with a large degree of confidence.

Keep your hands on my shoulders, iggy, and steer me in the right
direction

- Harry

[Harry_Porter]

jaydavidson118 wrote:

Sometimes a little knowledge is a dangerous thing.

Just because you stick numbers into a statistical package and it
generates reams of output doesn't mean you have understanding of the
situation, or that your results are meaningful ...

Trying to draw meaningful inferences from a sample of 2000 where the
period is 40,000 is silly.

Hey, jay, I'm with you on the better part of what you've said in your
post. However, you're coming across surprizingly forceful ... almost
as if someone's stepped on your toes.

FWIW, I give iggy credit for a little more than "a little knowledge".
And his application of the analysis to a trial of 2000 hands excluded
the expected results of both the royal and quad deuces -- the largest
period of the remaining hands was a little over 500 hands, not 40000.

- Harry

[Harry_Porter]

nightoftheiguana2000 wrote:

so, if you get less than -$340 in actual play, you have 1.8%
confidence that the machine is honest, if you get -$125 in actual
play, you have 10% confidence that the machine is honest, if you get
over +$95 you have 40% confidence
if you are trying to prove that the machine is honest with greater
confidence, you will have to play more hands
however, if you are trying to prove that the machine is fixed, and
you get less than -$340, you have 98.2% confidence that it is fixed
(or you are playing incorrectly)
best option at that point would be to report your findings to the
local regulation board and here (make note of machine number) and
find a different machine

You've surfaced some very interesting material to think over, iggy,
and for that I'm appreciative.

Because it was Chris, and not myself, that expressed interest in
reviewing play results to assess machine fairness, I don't personally
want to belabor the specifics further.

···

_

However, it occurs to me that there may be a problem with suggesting
that given an adverse outcome (the $340 loss, in your example) that
has less than a 2% likelihood, you'd have less than a 2% confidence in
the machine's fairness.

After all, throw just 60 people at a fair machine for a trial of 2000
hands each and it's expected that on average one of the people will
cry "the machine is fixed!" using the criteria you suggest (mind you,
I realize I'm taking a little liberty with your actual wording).
_

You've given Chris a decent practical test of fairness. But it's
hardly a sufficient one to take to the Casino Control Commission as
the basis of a complaint. Plus, in his shoes I'd find it difficult to
translate it directly into some type of acid test (what to play/where
to play), given the inherent limitations.

That said, if he or anyone else wishes to maintain the necessary
detailed records, your methodology permits a specific measurement of
how likely a given adverse result is and, in comparing results from
one casino to the next, may be a meaningful guide that suggests one or
more casinos that it wouldn't hurt to avoid.

- Harry

[jaydavidson118]

granted, my post might have been a bit "forceful", but, I find it
rather surprising that no one ever posts rebuttals to some of the
silly statistical claims posted...what was the recent one if you lose
more than $340 on 2000 hands played you have x% chance the machine is
rigged What! Anyone who has played any amount of video poker knows,
intuitively, that this situation is well within the realm of
possibility...I have had 4 aces dealt to me twice within 20 min. I
didn't think the machine was broken...I just had a lucky streak.

It takes a little knowledge to put numbers into a statistical package
and print them out, it takes considerably more knowledge to know how
to intrepret the results, and to know whether they are meaningful. I
don't see much indication of the latter. Is that too forceful?

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

Hey, jay, I'm with you on the better part of what you've said in

your

post. However, you're coming across surprizingly forceful ...

almost

as if someone's stepped on your toes.

FWIW, I give iggy credit for a little more than "a little

knowledge".

And his application of the analysis to a trial of 2000 hands

excluded

the expected results of both the royal and quad deuces -- the

largest

period of the remaining hands was a little over 500 hands, not

40000.

···

- Harry