vpFREE2 Forums

Frequency of Dealt Royals

#1

I've only received one Royal Flush "on the deal" in my life. It was about
3 or 4 years ago. Now, I am trying to figure out how soon I can expect to
receive my next Dealt Royal. I play mostly BP, DB, DDB, and TDB.

In a Casino Gaming column, I read that a Dealt Royal occurs once in every
649,640 hands (on average). And, in vpFREE messages, I think I've read
that any Royal Flush occurs once in approx. 40,000 hands. (I understand
that this number varies, depending on the game(s) being played.)

649,640 divided by 40,000 is 16.241. Does this mean that I can expect to
get one Dealt Royal for every 16 Royals that I receive?

If I've received more than 16 Royals since my last Dealt Royal, should I
start
playing the progressive Triple Play machines that offer a super progressive
for a Dealt Royal?

[Non-text portions of this message have been removed]

#2

Luke Fuller <kungalooosh@gmail.com> wrote: 649,640 divided by 40,000 is 16.241. Does this mean that I can expect to
get one Dealt Royal for every 16 Royals that I receive?

If I've received more than 16 Royals since my last Dealt Royal, should I
start
playing the progressive Triple Play machines that offer a super progressive
for a Dealt Royal?

···

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   
  Absolutely! What ever you do, DO NOT practice on your home software. Hate to waste that dealt royal, no? (-;
   
  Jigger
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the neighbor's dog run to the end of his chain
and gag himself."

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Little things like being spanked every day by a middle aged
woman: Stuff you pay good money for in later life."

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You don't need any special clothing, but you can get some
if you are really into it."

__________________________________________________
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[Non-text portions of this message have been removed]

#3

I've only received one Royal Flush "on the deal" in my life. It

was about

3 or 4 years ago. Now, I am trying to figure out how soon I can

expect to

receive my next Dealt Royal. I play mostly BP, DB, DDB, and TDB.

In a Casino Gaming column, I read that a Dealt Royal occurs once in

every

649,640 hands (on average). And, in vpFREE messages, I think I've

read

that any Royal Flush occurs once in approx. 40,000 hands. (I

understand

that this number varies, depending on the game(s) being played.)

649,640 divided by 40,000 is 16.241. Does this mean that I can

expect to

get one Dealt Royal for every 16 Royals that I receive?

If I've received more than 16 Royals since my last Dealt Royal,

should I

start
playing the progressive Triple Play machines that offer a super

progressive

for a Dealt Royal?

This year I've had 3 dealt RFs in a little over 600K dealt hands. Not
one of them was on a 3/5 play machine that I play about 10% of the
time. In fact, I've never had a multi-line dealt RF although I know a
person who hit two in one week. I've had maybe 12-15 dealt RFs in my
life. Even with these "extra" dealt RFs this year I'm down 6 RFs for
the year.

In other words, random is random and you will get whatever you get :wink:
OTOH, since I haven't gotten any multi-play dealt RFs they may be out
there just waiting for you to play.

Dick

···

--- In vpFREE@yahoogroups.com, "Luke Fuller" <kungalooosh@...> wrote:

#4

I've only had one dealt royal in my entire video poker playing
career... despite playing $1,000,000+ coin-in every year for the last
eight years. So I, for one, don't want to hear that every
deal "starts the clock over" even though intellectually I know it to
be true.

>
> I've only received one Royal Flush "on the deal" in my life. It
was about
> 3 or 4 years ago. Now, I am trying to figure out how soon I can
expect to
> receive my next Dealt Royal. I play mostly BP, DB, DDB, and TDB.
>
> In a Casino Gaming column, I read that a Dealt Royal occurs once

in

every
> 649,640 hands (on average). And, in vpFREE messages, I think

I've

read
> that any Royal Flush occurs once in approx. 40,000 hands. (I
understand
> that this number varies, depending on the game(s) being played.)
>
> 649,640 divided by 40,000 is 16.241. Does this mean that I can
expect to
> get one Dealt Royal for every 16 Royals that I receive?
>
> If I've received more than 16 Royals since my last Dealt Royal,
should I
> start
> playing the progressive Triple Play machines that offer a super
progressive
> for a Dealt Royal?

This year I've had 3 dealt RFs in a little over 600K dealt hands.

Not

one of them was on a 3/5 play machine that I play about 10% of the
time. In fact, I've never had a multi-line dealt RF although I know

a

person who hit two in one week. I've had maybe 12-15 dealt RFs in

my

life. Even with these "extra" dealt RFs this year I'm down 6 RFs

for

the year.

In other words, random is random and you will get whatever you

get :wink:

OTOH, since I haven't gotten any multi-play dealt RFs they may be

out

···

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

--- In vpFREE@yahoogroups.com, "Luke Fuller" <kungalooosh@> wrote:
there just waiting for you to play.

Dick

#5

I've only received one Royal Flush "on the deal" in my life. It was

about

3 or 4 years ago. Now, I am trying to figure out how soon I can

expect to

receive my next Dealt Royal. I play mostly BP, DB, DDB, and TDB.

I've only had 10 quarter royals, including 4 dealt and 1 on pick'em
which is as good as dealt, in 4 1/2 years of infrequent play. What are
the odds of that?

···

--- In vpFREE@yahoogroups.com, "Luke Fuller" <kungalooosh@...> wrote:

#6

mroejacks wrote:

This year I've had 3 dealt RFs in a little over 600K dealt hands ...
I've had maybe 12-15 dealt RFs in my life. Even with these "extra"
dealt RFs this year I'm down 6 RFs for the year.

In other words, random is random and you will get whatever you get :wink:

Truer words haven't been spoken (at least, between the two of us of
late ... sorry, couldn't resist -- big :slight_smile:

One can't help but suspect that underlying the origin of the "gaffe"
question is a failure to appreciate the underlying variance of vp.
For every gaffe suspicion that has borne out, there no doubt have been
thousands of dubious ones that were in earnest. I'm casting no
aspersion ... against my better judgment, I've fleetingly "been there,
done that".

The truth is that in general terms it isn't until you've witnessed 20
cycles of an event that you have an inkling as to whether you're truly
experiencing anomalous results. By "anomalous", I'm referring to
results that deviate no more than 10% from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration. if you want 95% confidence, you need to play
through 60 cycles.

···

------

The typical player tends to be royal obsessed (again, count me in).
So, let's say there's a particular casino in which there are just a
limited number of rather extraordinarily "juicy" machines (say no more
than 3, or perhaps just 1). It's the best play in town and you play
it heavily for a year or so and are heavily under-royaled. Now
feeling like you have a substantial equity interest in the machine,
you begin to suspect you may have been had ... more than suspect.

The truth is even if you've played through 10-15 cycles in that time
(400,000 to 600,000 hands) you haven't even come close to a basis for
a reasonable suspicion. If you've merely played through 6 cycles
royalless, you haven't a ghost of a clue. But you're unlikely to
convince some casual players of that. (You might gather that this
isn't an entirely "off the top of my head" example :wink:

------

The 20-cycle of play suggestion for a 68% confidence in play fairness
bears a non-coincidental relationship to the oft cited statistic that
you need to play through a million + hands of a low variance game,
such as Jacks or Better, before you achieve what's commonly referred
to as the "long term" in your play -- i.e. the point at which your
play results might reasonably be expected to parallel expectation.

When you factor in a probability of only 68%, one can question whether
a million really is sufficient. In $ terms, the potential variance
when you fall within that long-term expectation is pretty substantial.
Boost that to 95% and you're realistically talking 3+ million.

And that's for a mild game like Jacks. Move up the ladder to
something like DB or DW, and the numbers grow quickly. Advance to DDB
and you can truly consider yourself a gambler.

------

Now, all this might suggest that if you feel with all your gut that a
machine has been gaffed that you pretty much can throw the towsl in
where it comes to a practical demonstration that you have cause for
your suspicion. Surprisingly, nothing could be further from the truth.

I'll venture to say that with just 50,000 hands (and most likely less)
of solid play data you might make a call that would be statistically
reliable enough to warrant further investigation, if it was the case
that results proved anomalous (doubtful).

I'll save that argument; I've ranted sufficiently for now.

- Harry

#7

Harry wrote:

The truth is even if you've played through 10-15 cycles in that time
(400,000 to 600,000 hands) you haven't even come close to a basis for
a reasonable suspicion. If you've merely played through 6 cycles
royalless, you haven't a ghost of a clue.

Could you put that in numbers? Where do you draw the line at the
starting point of suspicion? If, after x cycles of anomalous results,
there's a "reasonable" suspicion that a machine is gaffed, at what
point does there start being any? Define "reasonable" with numbers.
At what point does the probability that a machine is gaffed cross,
say, 50%? I don't see how there can be a dividing line between there
being no chance that a machine is gaffed and there being some chance.
They're both on the same continuum, with no chance necessarily being
at the very beginning. Theoretically, ANY result (even 1 hand) is
SOME (completely strictly speaking) reason for suspicion. Isn't
knowledge of the "a priori" chance that a machine is gaffed necessary
in order to do such calculations? If you start out assuming that the
manufacturer of the game could never produce a rigged machine, then no
result, even 1000 cycles without a jackpot, could provide any evidence
of a rigged machine. But if you start out assuming there's an x
chance that each machine is gaffed or if you change your starting
assumption that the manufacturer of the game could never produce a
rigged machine, then results can be evidence that they're rigged.

#8

Harry wrote:

>The truth is even if you've played through 10-15 cycles in that time
>(400,000 to 600,000 hands) you haven't even come close to a basis
> for a reasonable suspicion. If you've merely played through 6
> cycles royalless, you haven't a ghost of a clue.

Tom Robertson wrote:

Could you put that in numbers? Where do you draw the line at the
starting point of suspicion? If, after x cycles of anomalous
results, there's a "reasonable" suspicion that a machine is gaffed,
at what point does there start being any? Define "reasonable" with
numbers.
At what point does the probability that a machine is gaffed cross,
say, 50%? I don't see how there can be a dividing line between there
being no chance that a machine is gaffed and there being some chance.
They're both on the same continuum, with no chance necessarily being
at the very beginning. Theoretically, ANY result (even 1 hand) is
SOME (completely strictly speaking) reason for suspicion. Isn't
knowledge of the "a priori" chance that a machine is gaffed necessary
in order to do such calculations? If you start out assuming that the
manufacturer of the game could never produce a rigged machine, then
no result, even 1000 cycles without a jackpot, could provide any
evidence of a rigged machine. But if you start out assuming there's
an x chance that each machine is gaffed or if you change your
starting assumption that the manufacturer of the game could never
produce a rigged machine, then results can be evidence that they're
rigged.

Well, I might have cited other text from my post that better addressed
your concerns. That notwithstanding, your points are dead on.

Any measure for suspicion of a gaffe is necessarily arbitrary. As you
might suggest, going 100 cycles without a hand isn't impossible,
merely improbable ... but so is 3 cycles without a royal -- but, of
course, the latter is just a bit more probable.

So it's a question of what point in growing suspicion is cause for
investigation (or simply cause to leave off play of the machine).
It's prudent to make some decision, even if arbitrary. This calls for
calculating the probability that the play history might occur, based
upon actual hand experience vs. expected, and responding accordingly.

But you raise an important caveat. Say I'm an active player and I
play through 60 quad cycles and only see 40 quads. I'm going to tell
you that this is strong reason to suspect that the machine is gaffed.
Do you run right out and report the casino operator to the
regulators? -- absolutely not ... they'll politely tell you'll they'll
look into the matter and then promptly laugh their asses off when
you're off the phone. I'm not suggesting this is because they haven't
earnestly considered your complaint. (If they haven't, that's another
matter - a more likely scenario, but set that aside :wink:

The fact that a particular event, in isolation, is improbable isn't
cause alone to believe that abnormal behavior underlies the event.
For example, it's improbable that you might flip a coin 10 times in
succession and it comes up heads each and every time (about 1 in
1000). However, the probability that their might be at least one such
sequence over the course of 5000 flips is near certainty.

Merely waiting for an improbable event to occur doesn't make for a
call of a likely abnormality (i.e. "gaffe"). But it does signal the
point at which one can reliably begin to measure for one. This
doesn't mean that you start with a presumption of a gaffe; simply that
unlike the first measure, this one was taken without "a priori"
knowledge that the event was anomalous to begin with. As I said,
you're right on the money.

···

------

So, an appropriate methodology would be to watch for suspect machine
behavior and select a start point for your test trial. Now, if your
suspect behavior occurred over the last two years, the prospect of
playing on for another two in order to assess whether a gaffe
hypothesis bears out (more statistically accurately, gives no reason
to reject the idea of a gaffe) isn't likely to be appealing.

That isn't reason to say that it's implausible one might demonstrate
that there is, indeed, good reason to suspect a gaffe. But it
suggests the desirability of enrolling other reliable players to
accurately record their own play observations in order to collectively
assess the gaffe hypothesis over something like 3 or 6 months.

But say that alternative doesn't suit you. At the very minimum your
quantitative assessment of past experience lays the foundation of bare
minimum doubt that warrants abandoning the machine or casino that
gives concern. This is a far stronger rationale than simply because
"things don't feel right". My point, though, is that there is a solid
means by which to make an assessment should you elect to that
addresses your concerns.

------

You ask about the specific point that represents reason to suspect a
gaffe. Again, any such point is arbitrary. Where you set it would be
based upon your personal comfort level. One person might be pleased
with 50% confidence that they could reasonably reject the notion a
machine was gaffed. Someone else might want 99% confidence.

What I offered up is that the probability that the number of actual
hand hits will be within 10% of expectation after 20 cycles of play
(substitute royals, quads, etc. for "hands") is 67%. After 80 cycles,
that probability is 95%.

One might approach this by watching for the 67% threshold to be
crossed, and then running the test under the 95% threshold.

(As a sidenote, this is merely meant to be illustrative. It might be
noted that these thresholds test both negative and positive gaffeness
-- i.e. all results outside of 10% of expectation. Since only a
negative gaffe is of concern, not to be imaginable, the percentages
increase accordingly ... 83%/97% and fewer cycles are required for the
lower confidence levels.)

------

I appreciate the feedback and hope you'll respond if this isn't
satisfactory in any respect.

- Harry

#9

Harry, there are a couple of things in your post that are not clear
to me. You wrote:

"The truth is that in general terms it isn't until you've witnessed
20 cycles of an event that you have an inkling as to whether you're
truly experiencing anomalous results. By "anomalous", I'm referring
to results that deviate no more than 10% from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration. if you want 95% confidence, you need to play
through 60 cycles."

I'm guessing that the cycles you give are for a deviation from
expectation of exactly 10% instead of "no more than 10%". Otherwise
there could not be a single number of cycles that would fit the
bill.

Later, you wrote:

"The truth is even if you've played through 10-15 cycles in that time
(400,000 to 600,000 hands) you haven't even come close to a basis for
a reasonable suspicion. If you've merely played through 6 cycles
royalless, you haven't a ghost of a clue. But you're unlikely to
convince some casual players of that. (You might gather that this
isn't an entirely "off the top of my head" example ;)"

You must be talking about the 10% deviation still, right? Because
if you are talking about 400,000 to 600,000 hands with no royal, I'd
have to disagree with you!

Even 6 cycles with no royal would be grounds for "reasonable
suspicion" under the right circumstances. An example of wrong
circumstances would be if the drought was counted from immediately
after an RF. (ie, it was really 1 RF in 240,001 hands instead of no
RF's in 240,000 hands). An example of what might be right
circumstances would be if I walked into an Indian casino and played
my first 240,000 hands of JOB without an RF. An example of what
(for me) would definitely be right circumstances would be if I
walked into an Indian casino and said (to myself), "I am going to
play 240,000 hands of JOB, and if I don't hit at least 1 RF in that
stretch, I am going to quit." With a "test" structured like that,
there's only 1 chance in 380 that I would get no RF's in 240,000
hands by chance alone. I'm willing to live with the 0.26% chance
that my suspicions are ill-founded! ;>)

--Dunbar

(my first version of this, which I deleted, had some inconsistencies
in the last paragraph between 240,000 hands (6 cycles) and 600,000
hands (15 cycles).

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

mroejacks wrote:
> This year I've had 3 dealt RFs in a little over 600K dealt

hands ...

> I've had maybe 12-15 dealt RFs in my life. Even with

these "extra"

> dealt RFs this year I'm down 6 RFs for the year.
>
> In other words, random is random and you will get whatever you

get :wink:

Truer words haven't been spoken (at least, between the two of us of
late ... sorry, couldn't resist -- big :slight_smile:

One can't help but suspect that underlying the origin of

the "gaffe"

question is a failure to appreciate the underlying variance of vp.
For every gaffe suspicion that has borne out, there no doubt have

been

thousands of dubious ones that were in earnest. I'm casting no
aspersion ... against my better judgment, I've fleetingly "been

there,

done that".

The truth is that in general terms it isn't until you've witnessed

20

cycles of an event that you have an inkling as to whether you're

truly

experiencing anomalous results. By "anomalous", I'm referring to
results that deviate no more than 10% from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration. if you want 95% confidence, you need to

play

through 60 cycles.

------

The typical player tends to be royal obsessed (again, count me

in).

So, let's say there's a particular casino in which there are just a
limited number of rather extraordinarily "juicy" machines (say no

more

than 3, or perhaps just 1). It's the best play in town and you

play

it heavily for a year or so and are heavily under-royaled. Now
feeling like you have a substantial equity interest in the machine,
you begin to suspect you may have been had ... more than suspect.

The truth is even if you've played through 10-15 cycles in that

time

(400,000 to 600,000 hands) you haven't even come close to a basis

for

a reasonable suspicion. If you've merely played through 6 cycles
royalless, you haven't a ghost of a clue. But you're unlikely to
convince some casual players of that. (You might gather that this
isn't an entirely "off the top of my head" example :wink:

------

The 20-cycle of play suggestion for a 68% confidence in play

fairness

bears a non-coincidental relationship to the oft cited statistic

that

you need to play through a million + hands of a low variance game,
such as Jacks or Better, before you achieve what's commonly

referred

to as the "long term" in your play -- i.e. the point at which your
play results might reasonably be expected to parallel

expectation.

When you factor in a probability of only 68%, one can question

whether

a million really is sufficient. In $ terms, the potential variance
when you fall within that long-term expectation is pretty

substantial.

Boost that to 95% and you're realistically talking 3+ million.

And that's for a mild game like Jacks. Move up the ladder to
something like DB or DW, and the numbers grow quickly. Advance to

DDB

and you can truly consider yourself a gambler.

------

Now, all this might suggest that if you feel with all your gut

that a

machine has been gaffed that you pretty much can throw the towsl in
where it comes to a practical demonstration that you have cause for
your suspicion. Surprisingly, nothing could be further from the

truth.

I'll venture to say that with just 50,000 hands (and most likely

less)

of solid play data you might make a call that would be

statistically

reliable enough to warrant further investigation, if it was the

case

···

that results proved anomalous (doubtful).

I'll save that argument; I've ranted sufficiently for now.

- Harry

#10

dunbar_dra wrote:

Harry, there are a couple of things in your post that are not clear
to me. You wrote:

"The truth is that in general terms it isn't until you've witnessed
20 cycles of an event that you have an inkling as to whether you're
truly experiencing anomalous results. By "anomalous", I'm referring
to results that deviate no more than 10% from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration. if you want 95% confidence, you need to play
through 60 cycles."

I'm guessing that the cycles you give are for a deviation from
expectation of exactly 10% instead of "no more than 10%". Otherwise
there could not be a single number of cycles that would fit the
bill.

Well, that statement is certainly cause for pause, coming from you.
However, I stand by my wording.

Well, let me qualify that ... I should have written "20%", not "10%".
(I've been very intently working on a project this week ... the 4am
posting reflected an obsessive stirring from my sleep after only a
couple of hours in bed. Allow me that one lapse, ok? :wink:

In any case, what I suggest is that having played 20 cycles of play,
68% of the time the number of time the related event will occur within
the bounds of +/- 20% of 20, i.e. between 16 and 24 times. (This can
be confirmed with a binomial distribution.)

The probability of a deviation of exactly +/- 20% (i.e., the event
being observed either 16 or 24 times) is 12%.

Later, you wrote:

"The truth is even if you've played through 10-15 cycles in that time
(400,000 to 600,000 hands) you haven't even come close to a basis for
a reasonable suspicion. If you've merely played through 6 cycles
royalless, you haven't a ghost of a clue. But you're unlikely to
convince some casual players of that. (You might gather that this
isn't an entirely "off the top of my head" example ;)"

You must be talking about the 10% deviation still, right? Because
if you are talking about 400,000 to 600,000 hands with no royal, I'd
have to disagree with you!

Absolutely (well ... make that 20% <sheepish grin>). This is a
continuation of a scenario in which the 20% deviation and 68%
confidence level are the selected thresholds for suspicion (which, as
I separately discuss, are chosen in direct relation to one's tolerance
for a deviation before suspicion).

Even 6 cycles with no royal would be grounds for "reasonable
suspicion" under the right circumstances. An example of wrong
circumstances would be if the drought was counted from immediately
after an RF. (ie, it was really 1 RF in 240,001 hands instead of no
RF's in 240,000 hands). An example of what might be right
circumstances would be if I walked into an Indian casino and played
my first 240,000 hands of JOB without an RF. An example of what
(for me) would definitely be right circumstances would be if I
walked into an Indian casino and said (to myself), "I am going to
play 240,000 hands of JOB, and if I don't hit at least 1 RF in that
stretch, I am going to quit." With a "test" structured like that,
there's only 1 chance in 380 that I would get no RF's in 240,000
hands by chance alone. I'm willing to live with the 0.26% chance
that my suspicions are ill-founded! ;>)

Agreed, with the caveat that I raise in another post (and first
admirably noted by Tom Robertson). The version of this test that most
players are likely to employ is, "If I don't hit at least 1 RF in a
stretch of any 240,000 hands, I'm going to quit". And, most often,
such a test is employed retroactively, after they become aware that
they've suffered a dry stretch.

You haven't suggested the test in that manner and I know that I don't
need to tell you that such a "test" isn't an adequate measure of
gaffeness. However, I have little doubt that the great majority of
players who cry "gaffe" have done exactly that. In such a case, it's
merely a flag that it may be reasonable to begin the clean test you
suggest starting with the next play.

- Harry

#11

I like the 6 cycle test (99.75% confidence). It doesn't have to be
just royals, it can be straight flushes or quads or full houses, etc.
If a machine fails the 6 cycle test, it's probably time to find a new
machine, assuming it's not pilot error. If it cost you enough money it
might be worth going to gaming, but you'd be tipping your hat as a
knowledgeable gambler.

9/6 JOB 6 cycles:
RF = 241,935 hands
SF = 54,895 hands
4K = 2,539 hands
FH = 521 hands
FL = 544 hands
ST = 534 hands
3K = 81 hands
2P = 46 hands
HP = 28 hands

···

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:

Even 6 cycles with no royal would be grounds for "reasonable
suspicion" under the right circumstances. An example of wrong
circumstances would be if the drought was counted from immediately
after an RF. (ie, it was really 1 RF in 240,001 hands instead of no
RF's in 240,000 hands). An example of what might be right
circumstances would be if I walked into an Indian casino and played
my first 240,000 hands of JOB without an RF. An example of what
(for me) would definitely be right circumstances would be if I
walked into an Indian casino and said (to myself), "I am going to
play 240,000 hands of JOB, and if I don't hit at least 1 RF in that
stretch, I am going to quit." With a "test" structured like that,
there's only 1 chance in 380 that I would get no RF's in 240,000
hands by chance alone. I'm willing to live with the 0.26% chance
that my suspicions are ill-founded! ;>)

#12

Another comment: On the smaller cycle events, like say full houses,
you can use the following trick. Say you have accumulated 100 cycles
of data, one sigma is the square root, so sqrt(100) = 10. You have one
sigma confidence that the data should be within +/- 10 of the mean (90
to 110), two sigma for +/- 20, etc. One sigma is 68%, two sigma is
95%, three sigma is 99.75%, four sigma is 99.99%. I think, among other
things, this is what Harry is talking about. It's an approximation but
as has been shown in previous posts it's not far off from actual
data. About the smallest data set you can go with is 9 cycles with 3
sigma (0 to 18). So, for example, using 9/6 JOB below, 9 cycles of
full houses would be 782 hands, at which point you would expect to see
0 to 18 full houses in your data with three sigma confidence (99.75%).
16 cycles would be more accurate with three sigma being 4 to 28. As
Harry has pointed out, you don't care if you get too many of
something, that means the machine may be gaffed in your favor
(positive), so 3 sigma is actually 99.88% confidence of a negative gaff.

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

···

I like the 6 cycle test (99.75% confidence). It doesn't have to be
just royals, it can be straight flushes or quads or full houses, etc.
If a machine fails the 6 cycle test, it's probably time to find a new
machine, assuming it's not pilot error. If it cost you enough money it
might be worth going to gaming, but you'd be tipping your hat as a
knowledgeable gambler.

9/6 JOB 6 cycles:
RF = 241,935 hands
SF = 54,895 hands
4K = 2,539 hands
FH = 521 hands
FL = 544 hands
ST = 534 hands
3K = 81 hands
2P = 46 hands
HP = 28 hands

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@> wrote:
> Even 6 cycles with no royal would be grounds for "reasonable
> suspicion" under the right circumstances. An example of wrong
> circumstances would be if the drought was counted from immediately
> after an RF. (ie, it was really 1 RF in 240,001 hands instead of no
> RF's in 240,000 hands). An example of what might be right
> circumstances would be if I walked into an Indian casino and played
> my first 240,000 hands of JOB without an RF. An example of what
> (for me) would definitely be right circumstances would be if I
> walked into an Indian casino and said (to myself), "I am going to
> play 240,000 hands of JOB, and if I don't hit at least 1 RF in that
> stretch, I am going to quit." With a "test" structured like that,
> there's only 1 chance in 380 that I would get no RF's in 240,000
> hands by chance alone. I'm willing to live with the 0.26% chance
> that my suspicions are ill-founded! ;>)

#13

Another comment: On the smaller cycle events, like say full houses,
you can use the following trick. Say you have accumulated 100 cycles
of data, one sigma is the square root, so sqrt(100) = 10. You have one
sigma confidence that the data should be within +/- 10 of the mean (90
to 110), two sigma for +/- 20, etc. One sigma is 68%, two sigma is
95%, three sigma is 99.75%, four sigma is 99.99%. I think, among other
things, this is what Harry is talking about. It's an approximation but
as has been shown in previous posts it's not far off from actual
data. About the smallest data set you can go with is 9 cycles with 3
sigma (0 to 18). So, for example, using 9/6 JOB below, 9 cycles of
full houses would be 782 hands, at which point you would expect to see
0 to 18 full houses in your data with three sigma confidence (99.75%).
16 cycles would be more accurate with three sigma being 4 to 28. As
Harry has pointed out, you don't care if you get too many of
something, that means the machine may be gaffed in your favor
(positive), so 3 sigma is actually 99.88% confidence of a negative gaff.

I don't think that's what that number means. Results that are 3
standard deviations off happen all the time on machines that are
generally considered fair. Even in the Wizard of Odds' article, he
gave no number for the probability that the results he was analyzing
were gaffed. It's apparently something that can't be expressed in
numbers, since too many incalculable factors are involved.

#14

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

dunbar_dra wrote:
>
> Harry, there are a couple of things in your post that are not

clear

> to me. You wrote:
>
> "The truth is that in general terms it isn't until you've

witnessed

> 20 cycles of an event that you have an inkling as to whether

you're

> truly experiencing anomalous results. By "anomalous", I'm

referring

> to results that deviate no more than 10% from expectation. And

even

> then, you only have 68% confidence that your results truly do
> represent an aberration. if you want 95% confidence, you need to

play

> through 60 cycles."
>
> I'm guessing that the cycles you give are for a deviation from
> expectation of exactly 10% instead of "no more than 10%".

Otherwise

> there could not be a single number of cycles that would fit the
> bill.

Well, that statement is certainly cause for pause, coming from

you.

However, I stand by my wording.

Well, let me qualify that ... I should have written "20%",

not "10%".

(I've been very intently working on a project this week ... the

4am

posting reflected an obsessive stirring from my sleep after only a
couple of hours in bed. Allow me that one lapse, ok? :wink:

In any case, what I suggest is that having played 20 cycles of

play,

68% of the time the number of time the related event will occur

within

the bounds of +/- 20% of 20, i.e. between 16 and 24 times. (This

can

be confirmed with a binomial distribution.)

The probability of a deviation of exactly +/- 20% (i.e., the event
being observed either 16 or 24 times) is 12%.

I'm still having a problem with your original wording, Harry. You
wrote:

"The truth is that in general terms it isn't until you've witnessed
20 cycles of an event that you have an inkling as to whether you're
truly experiencing anomalous results. By "anomalous", I'm referring
to results that deviate no more than [20%] from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration."

I now think you meant "results that deviate more than 20%" instead
of "...no more than 20%". If the "anomalous" result differed by a
mere 1%, then you would need a lot more than 20 cycles to get 68%
confidence. (In fact, there isn't such a thing as a 1% anomaly in
RF frequency until you get to 100 cycles!)

I'm 100% sure you understand the concept, but I just want to set the
wording straight. (I was so sure you understood it, that I accepted
your 10% figure without checking it. Just like I'm still not
checking your 20% figure!)

> Later, you wrote:
>
> "The truth is even if you've played through 10-15 cycles in that

time

> (400,000 to 600,000 hands) you haven't even come close to a

basis for

> a reasonable suspicion. If you've merely played through 6 cycles
> royalless, you haven't a ghost of a clue. But you're unlikely to
> convince some casual players of that. (You might gather that this
> isn't an entirely "off the top of my head" example ;)"
>
> You must be talking about the 10% deviation still, right?

Because

> if you are talking about 400,000 to 600,000 hands with no royal,

I'd

> have to disagree with you!

Absolutely (well ... make that 20% <sheepish grin>). This is a
continuation of a scenario in which the 20% deviation and 68%
confidence level are the selected thresholds for suspicion (which,

as

I separately discuss, are chosen in direct relation to one's

tolerance

for a deviation before suspicion).

> Even 6 cycles with no royal would be grounds for "reasonable
> suspicion" under the right circumstances. An example of wrong
> circumstances would be if the drought was counted from

immediately

> after an RF. (ie, it was really 1 RF in 240,001 hands instead

of no

> RF's in 240,000 hands). An example of what might be right
> circumstances would be if I walked into an Indian casino and

played

> my first 240,000 hands of JOB without an RF. An example of what
> (for me) would definitely be right circumstances would be if I
> walked into an Indian casino and said (to myself), "I am going

to

> play 240,000 hands of JOB, and if I don't hit at least 1 RF in

that

> stretch, I am going to quit." With a "test" structured like

that,

> there's only 1 chance in 380 that I would get no RF's in 240,000
> hands by chance alone. I'm willing to live with the 0.26%

chance

> that my suspicions are ill-founded! ;>)

Agreed, with the caveat that I raise in another post (and first
admirably noted by Tom Robertson). The version of this test that

most

players are likely to employ is, "If I don't hit at least 1 RF in a
stretch of any 240,000 hands, I'm going to quit". And, most often,
such a test is employed retroactively, after they become aware that
they've suffered a dry stretch.

That's a very good way to put it, and yes, I agree completely. Most
people do put too much weight on retroactively observed events with
fluid start and stop times.

You haven't suggested the test in that manner and I know that I

don't

need to tell you that such a "test" isn't an adequate measure of
gaffeness. However, I have little doubt that the great majority of
players who cry "gaffe" have done exactly that. In such a case,

it's

merely a flag that it may be reasonable to begin the clean test you
suggest starting with the next play.

Agreed. Also, as I know both you and NOTI understand very
well, there's nothing magic about 6 cycles. If someone is willing
to be wrong 2% of the time, he/she can use a 4-cycle drought as the
bailout threshold from a new game/casino. As long as they tell
themselves that ahead of time! ;>)

--Dunbar

#15

I don't think that's what that number means.

You're entitled to your opinion.

Results that are 3
standard deviations off happen all the time on machines that are
generally considered fair.

All the time??? Try 0.25% of the time. 1 out of 400.

Even in the Wizard of Odds' article, he
gave no number for the probability that the results he was analyzing
were gaffed. It's apparently something that can't be expressed in
numbers, since too many incalculable factors are involved.

I gave you the numbers, feel free to ignore them.

···

--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:

#16

dunbar_dra wrote:

I'm still having a problem with your original wording, Harry. You
wrote:

"The truth is that in general terms it isn't until you've witnessed
20 cycles of an event that you have an inkling as to whether you're
truly experiencing anomalous results. By "anomalous", I'm referring
to results that deviate no more than [20%] from expectation. And even
then, you only have 68% confidence that your results truly do
represent an aberration."

I now think you meant "results that deviate more than 20%" instead
of "...no more than 20%". If the "anomalous" result differed by a
mere 1%, then you would need a lot more than 20 cycles to get 68%
confidence. (In fact, there isn't such a thing as a 1% anomaly in
RF frequency until you get to 100 cycles!)

Kudos for reading what I meant, rather than merely what I wrote :wink:

Concerning the number of cycles I've cited (20 and 60 in examples,
thus far). Again, as I've stressed, the value is arbitrary and driven
by personal comfort level and intended action when the threshold is met.

A 20-cycle measurement is no where near a definitive test for
"gaffeness". But I suggest it's likely a good acid test from which
one can assess whether a machine bears closer scrutiny.

Further, a two prong test where the second trial is more sizable isn't
an unsurmountable barrier to a practical demonstration of machine
gaffeness. One thing I'll discuss later is that I find it VERY
unlikely that you would have cause to test RF occurrence as a
gaffeness measure ... I even find little or no reason to look at
quads. The focus will be on the very short cycle hands -- trips/FH,
S/F, etc. This makes assessment much more practical than most would
suspect. I'll explain further later.

- Harry

#17

I don't think that's what that number means.

You're entitled to your opinion.

That number means that assuming the machine isn't gaffed, that result
had a .25% chance of falling within a certain range. It says
virtually nothing about the chance that the machine is gaffed.

Results that are 3
standard deviations off happen all the time on machines that are
generally considered fair.

All the time??? Try 0.25% of the time. 1 out of 400.

Are you saying that as soon as you see one such event, that makes the
probability that the machine is gaffed 99.75%? You'd be including
every IGT machine, for starters. It's only a matter of time before
there's SOME result that's 3 standard deviations off. You posted that
6 cycles without a high pair in Jacks or Better is 28 hands. How many
IGT machines that have been around for more than, say, a year haven't
had just that result?

Even in the Wizard of Odds' article, he
gave no number for the probability that the results he was analyzing
were gaffed. It's apparently something that can't be expressed in
numbers, since too many incalculable factors are involved.

I gave you the numbers, feel free to ignore them.

What probability do you think there is that any given IGT machine is
gaffed?

···

--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:

#18

>> I don't think that's what that number means.
>
>You're entitled to your opinion.

That number means that assuming the machine isn't gaffed, that

result

had a .25% chance of falling within a certain range. It says
virtually nothing about the chance that the machine is gaffed.

Yes, it means there is a 0.25% chance that you would get a result
like that on a fair machine. How you interpret that info does
depend on your a priori assumptions (as I think you are suggesting).

If you believe that there is zero chance that the machine can be
gaffed, then you will not equate the 0.25% chance of an event with a
99.75% chance that the machine is cheating. However, if you come in
with no assumptions about a machine's fairness, and have devised a
well-defined test that comes back with a 0.25% probability of
occuring by chance, it's emininently reasonable to conclude that the
fairness of the machine is questionable. I might not want to equate
the 0.25% probability of occuring by chance with a 99.75% chance of
the machine being gaffed, but just saying "there's just a 0.25%
chance a fair machine would have yielded this result" is good enough
reason for me to high tail it out of there.

Your argument, Tom, seems to be that rare events do occur, so we
cannot take the observation of a rare event as evidence that
something is amiss. If you extend that argument, we'd never be able
to look at medical data for promising new treatments. We'd still be
arguing about whether smoking is dangerous to your health. Maybe
it's just a fluke that wearing a seatbelt results in a lower chance
of death from an accident.

Your point that seemingly unlikely events happen all the time in
video poker is well taken. In the course of a typical player's
experience, all sorts of weirdnesses routinely show up. But that's
different from setting out to test a particular game/machine that
one has for some reason begun to doubt. You will not be doing that
sort of test 10,000+ times.

It's extremely unlikely that I would be doing that sort of test on
an IGT game. But if I were getting hammered at an alarming rate on
what should be a very profitable opportunity, I might indeed set up
a test like that. And if the test came back showing a 0.25% chance
of occuring in a fair game, I'd be out of there like a shot with 99%
+ confidence that I was not leaving a fair game.

>> Results that are 3
>> standard deviations off happen all the time on machines that are
>> generally considered fair.
>
>All the time??? Try 0.25% of the time. 1 out of 400.

Are you saying that as soon as you see one such event, that makes

the

probability that the machine is gaffed 99.75%? You'd be including
every IGT machine, for starters. It's only a matter of time before
there's SOME result that's 3 standard deviations off. You posted

that

6 cycles without a high pair in Jacks or Better is 28 hands. How

many

IGT machines that have been around for more than, say, a year

haven't

had just that result?

That's a different question than what we are talking about. We are
talking about setting out to test a particular machine with a well
defined number of hands and a fixed starting and ending point. Not
every IGT machine is going to "fail" that kind of test. Just one in
865 fair machines will fail the JOB no-high-pair-in-28-hands test.

>> Even in the Wizard of Odds' article, he
>> gave no number for the probability that the results he was

analyzing

>> were gaffed. It's apparently something that can't be expressed

in

>> numbers, since too many incalculable factors are involved.
>
>I gave you the numbers, feel free to ignore them.

What probability do you think there is that any given IGT machine

is

gaffed?

Extremely small. But not zero.

--Dunbar

···

--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:

>--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@> wrote:

#19

dunbar_dra wrote:

<snip>

Your argument, Tom, seems to be that rare events do occur, so we
cannot take the observation of a rare event as evidence that
something is amiss.

No, I don't go that far. I was just objecting to the statement that
the likelihood that a fair machine would have produced a certain
result is therefore the likelihood that the machine isn't fair.

If you extend that argument, we'd never be able
to look at medical data for promising new treatments. We'd still be
arguing about whether smoking is dangerous to your health. Maybe
it's just a fluke that wearing a seatbelt results in a lower chance
of death from an accident.

Definitely. I'm all for revising a priori assumptions once results
are sufficiently inconsistent with them.

<snip>

What probability do you think there is that any given IGT machine
is gaffed?

Extremely small. But not zero.

I agree. It should never be 0.

#20

>> What probability do you think there is that any given IGT machine
>> is gaffed?
>Extremely small. But not zero.
I agree. It should never be 0.

Gaffing is intentional, there is also the possibility that a
particular machine is simply slightly defective. A casino will never
pull a tight machine (holds more than theoretical), as long as it
passes diagnostics and continues to get play. On the other hand, a
machine that is too loose (holds less than theoretical or has no hold)
will get attention, will get its paytable downgraded, and if that
doesn't solve the problem, will be disposed of, with possible action
taken against those playing it (the casino can't be sure if it's being
cheated or not).