IS THERE A 'POINT OF CERTAINTY' ???

[Raymond Baldwin]

Hi Everyone,

I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.

Has anyone heard about an ostensible physics law called Point of
Certainty ?

Thanks in advance for your kind replies-
RB

[Mason]

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB

Hope springs eternal in the human breast;
Man never Is, but always To be blest:
The soul, uneasy and confin'd from home,
Rests and expatiates in a life to come.

-Alexander Pope,
An Essay on Man, Epistle I, 1733

[Gerd Henjes]

Raymond...

Are you one of the famous Syracuse Baldwin brothers?

When I was a kid you could go up to Harlem and buy a dream book with the
daily numbers for future dates.

I didn't stick around long enough to find out how anyone did, but I had my
suspicions.

I also have to admit I never invested myself.

Maybe they still sell them and you should check it out for yourself and
report back on your results.

It's lucky for the Baldwin brothers that some can act.

Gerd

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB

[savgoose]

you mean like if i toss a fair 6 sided dice 1000 times I am certain the
number 1 wil come up once?

well i am certain orf that, but ask one of the math heads in here what are
the odds, and why i shouldnt bet the house on it,

or why a casino would only pay 1 penny if i did bet the house.

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB
.

[Nigel]

I've never heard of such a thing, but it sounds as though it might be a
misinterpretation of the "Birthday Paradox".

Take any particular ball in a 6 from 49 lottery.

The chances of not seeing it in the next draw are 43/49, ie 0.878.

The chances of not seeing it after the next two draws are (43/49) *
(43/49) ie 0.770.

The chances of not seeing it in any of the next 5 draws are (43/49)^5 ie
0.520.

The chances of not seeing it in any of the next 6 draws are (43/49)^6 ie
0.457.

So by the end of the 6th draw, you're more likely to have seen your
chosen number than not. However that doesn't mean that if it hasn't
appeared in the first 5 draws, it's magically more likely to appear in
the 6th draw than other numbers.

Evil Nigel

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB

[John Dingley]

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB

If its random, then each draw is just like the first ever draw. What balls
have been drawn before and in what frequency etc is irrelevant. So the
answer is if a ball has not been drawn for 30 weeks (say) it doesn't mean it
is more likely to be drawn than any other ball. In fact if there is some
mechanical or random generator defect or bias it probably means it it LESS
likely to be drawn.

The only factor that could give an "overdue" number an advantage is if the
balls are restacked in different orders prior to the drop, then this may
results in that ball suddenly showing up. If this did happen of course then
we would see a trend of overdue numbers suddenly appearing and getting
picked often until restacking takes place.

www.justlottery.com

[stacy_friedman]

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?

You're referring to the Law of Averages, also known as the Gambler's
Fallacy because it's false.

Start flipping a coin. Ask yourself whether it makes sense that if
you happen to flip 10 heads in a row, that implies the next flip is
more likely to be tails. If it does, ask yourself why that makes
sense in light of your understanding that heads and tails should both
occur with 50% probability.

[Robert Perkis]

Post by stacy_friedman

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?

You're referring to the Law of Averages, also known as the Gambler's
Fallacy because it's false.
Start flipping a coin. Ask yourself whether it makes sense that if
you happen to flip 10 heads in a row, that implies the next flip is
more likely to be tails. If it does, ask yourself why that makes
sense in light of your understanding that heads and tails should both
occur with 50% probability.

Point of Certainty means a starting point for a theory of which
you are certain. It also means a point of a percentage where
you're close enough to 100% for it not to matter.

For example, when a 3if6in49 wheel has reached 99.99789 it's a
point of certainty (virtually assured) you will contain the 3#
win even without closing the cover to 100%.

That's my opinion, who knows I could be right. ^_~ !

Robert Perkis / http://www.lotto-logix.com/

[CDEX]

Post by stacy_friedman
Start flipping a coin. Ask yourself whether
it makes sense that if you happen to flip
10 heads in a row, that implies the next flip is
more likely to be tails. If it does, ask yourself
why that makes sense in light of your understanding
that heads and tails should both occur with 50% probability.

Excellent point.

A related issue the coin flipper deals with is not knowing the previous
history of the coin.

If my 10 tosses are relevant to the next toss's outcome, then why not the
previous 10 (or 1000) tosses of the coin before I got it in my pocket?

You have two coins. (I have never seen them.)

You flip one coin 10 times and get 9 Heads. You flip the other coin 10
times and get 9 Tails.

You buy a candy bar, giving both coins to the cashier.

I am in line immediately behind you at the candy counter. I buy a candy bar
and receive the two coins in change. I have no knowledge of their previous
history.

The two coins appear identical (same denomination, same year, same mint). I
cannot tell the two coins apart.

I flip one coin 10 times and get 9 Heads. I flip the other 10 times and get
9 Tails.

I am now ready to flip each coin for my 11th toss.

How could I possibly suppose that either coin is more likely to result one
way, rather than the other, on my 11th toss?

Same question, different words:

... Does one coin now have 18 Heads and 2 Tails,
(and)
... The other coin now have 18 Tails and 2 Heads?

(or)

... Does each coin have 10 Heads and 10 Tails?

- - - -

Point?

Take a handful of coins that are jingling around in the pocket. No coin's
previous 'toss' history is known.

It's naive to suppose that none of those coins has been tossed before.

Take a toss. This will be the first toss you will make with any of those
coins. Note that we are referring to one toss here: your very next toss
with the coin, and only that one toss.

If we say that the coin's Heads/Tails probability on the next single toss is
0.5/0.5:

... It means that the history of all previous tosses with that coin is
irrelevant.

- - - -

Same thing, different words ...

You have two coins. One is direct from the mint, never tossed before. The
other is 20 years old. You can probably assume it has been tossed before,
at least for beers. Its history is unknown.

On the next single toss, does either the newly-minted coin or the
20-year-old coin have a next-toss Heads/Tails probability that is different
from 0.5/0.5?

Anybody want to toss for the next round of beers?

Obviously above we're dealing with fair coins. If a coin is somehow
weighted or worn through use so that it's more likely to fall one way than
the other, beer bets are off.

Joe

[gARY]

Post by CDEX

Post by stacy_friedman
Start flipping a coin. Ask yourself whether
it makes sense that if you happen to flip
10 heads in a row, that implies the next flip is
more likely to be tails. If it does, ask yourself
why that makes sense in light of your understanding
that heads and tails should both occur with 50% probability.

Excellent point.
A related issue the coin flipper deals with is not knowing the previous
history of the coin.
If my 10 tosses are relevant to the next toss's outcome, then why not the
previous 10 (or 1000) tosses of the coin before I got it in my pocket?
You have two coins. (I have never seen them.)
You flip one coin 10 times and get 9 Heads. You flip the other coin 10
times and get 9 Tails.
You buy a candy bar, giving both coins to the cashier.
I am in line immediately behind you at the candy counter. I buy a candy bar
and receive the two coins in change. I have no knowledge of their previous
history.
The two coins appear identical (same denomination, same year, same mint).

I

Post by CDEX
cannot tell the two coins apart.
I flip one coin 10 times and get 9 Heads. I flip the other 10 times and get
9 Tails.
I am now ready to flip each coin for my 11th toss.
How could I possibly suppose that either coin is more likely to result one
way, rather than the other, on my 11th toss?
... Does one coin now have 18 Heads and 2 Tails,
(and)
... The other coin now have 18 Tails and 2 Heads?
(or)
... Does each coin have 10 Heads and 10 Tails?
- - - -
Point?
Take a handful of coins that are jingling around in the pocket. No coin's
previous 'toss' history is known.
It's naive to suppose that none of those coins has been tossed before.
Take a toss. This will be the first toss you will make with any of those
coins. Note that we are referring to one toss here: your very next toss
with the coin, and only that one toss.
If we say that the coin's Heads/Tails probability on the next single toss is
... It means that the history of all previous tosses with that coin is
irrelevant.
- - - -
Same thing, different words ...
You have two coins. One is direct from the mint, never tossed before.

The

Post by CDEX
other is 20 years old. You can probably assume it has been tossed before,
at least for beers. Its history is unknown.
On the next single toss, does either the newly-minted coin or the
20-year-old coin have a next-toss Heads/Tails probability that is different
from 0.5/0.5?
Anybody want to toss for the next round of beers?
Obviously above we're dealing with fair coins. If a coin is somehow
weighted or worn through use so that it's more likely to fall one way than
the other, beer bets are off.
Joe

Very nice clarification of an "Excellent point" Joe.

However, Lotto 'test draws' (that we *never* see) sorta 'knock on the head'
using the said history function for gain in any lotto system.

The same as the scenario above or not?
gARY


--
Affordable Wheeling:-
http://www.justservices.com/9ukp.html

[stacy_friedman]

Post by gARY
However, Lotto 'test draws' (that we *never* see) sorta 'knock on the head'
using the said history function for gain in any lotto system.
The same as the scenario above or not?

Yes, with a minor caveat: If the history function shows a
statistically-significant bias toward a particular set of numbers, you
might be wise to favor those numbers. Similarly, if flipping a
particular coin favored heads, you'd be wise to assume the coin was
biased and to bet heads.

[QuiGon]

Post by stacy_friedman

Post by gARY
However, Lotto 'test draws' (that we *never* see) sorta 'knock on the head'
using the said history function for gain in any lotto system.
The same as the scenario above or not?

Yes, with a minor caveat: If the history function shows a
statistically-significant bias toward a particular set of numbers, you
might be wise to favor those numbers.

Except, of course, if that were the case then the machine would be
replaced....

[CDEX]

Post by gARY
...
However, Lotto 'test draws' (that we *never* see)
sorta 'knock on the head' using the said history
function for gain in any lotto system.
The same as the scenario above or not?
gARY

Indeed, what we never see is the action (if any) the lottery commission
undertook immediately after they ran the test draws. Did they change any
ball (or balls), or did they change the machine? In other words, what were
the results of the test draws?

We don't need to know the results of the test draws just for that
information alone. It relates to the condition of the ballset and machine
as it has been used prior to that test.

In other words, if a problem is detected in the test draws, that problem
must have been existing to some degree before that moment. That means, it
must have existed to some degree in the real results of the earlier draws.

- - - -

Example.

A hypothetical case only:

The commission draws several test draws with a ballset and machine. It's
done offstage and off-camera. The data are internal only.

To the commission, the results look biased in their eyes (we never see them
with our eyes).

So, they replace the ballset or the machine. King Arthur's machines
(Guinevere, Lancelot, Merlin) have already been retired, and now there's
Moonstone, Topaz, Amethyst, Opal, and the other new ones. All of a sudden
Opal is looking a little off-color in the pre-draw test results so she's
sent for repairs. Instead of Opal, Topaz is now tested and looks OK. Topaz
is run in the actual draw.

Opal had a problem. Problem is, Opal's problem has just now been discovered
in this pre-draw trial. Prior to this trial, she might have run a dozen
previous draws with her results biased to one side but "marginally" OK --
i.e., just inside the commission's limit for acceptance. If Opal's results
were getting out of balance due to wear over the past several weeks, she
didn't crap out all at once on just this one latest test drawing. If her
problem is due to wear and tear she must have been drifting toward going out
of tolerance for some draws before this test drawing.

The same thought applies to ballsets, as well as to machines. If the ball
"49" is rejected in the test draws for hitting above expectation, it wasn't
struck by lightning that afternoon. It must have been wearing gradually in
balance, bounce, weight and friction for some time prior to that test
drawing.

Same thing, different words. If there is such a thing as "lottery machine
or ballset retirement due to wear and tear", it cannot happen all at once,
overnight. It has to happen gradually over a series of uses.

If the commission retires the machine or ballset for having gotten out of
tolerance, logically they must be doing so because there's a perceived bias
in the results coming from that machine; otherwise they have no basis for
retiring it. There must have been some gradual, incremental, "creeping"
bias in the actual drawing results which that machine produced (i.e., in the
"real" Wednesday and Saturday numbers) prior to its retirement.

If the commission do not allow for the explanation of increasing wear and
tear as a cause of bias in the outcomes of the actual lottery drawings, why
should they retire machines and ballsets after pre-draw trials?

- - -

The California 5/39 Fantasy game drew 80 private,"pre-release" drawings,
before going public with the game. Those 80 draws have never been made
public. Oddly, when they began the actual public drawings, they counted the
first such drawing as number "81". In other words, the game began with
drawing 81.

Presumably those 80 private drawings were enough to convince them that the
machines and ballsets were working OK, so that they could begin the public
game.

Raises the question:

... If it takes 80 drawings to prove sufficient randomness ...

... and the Camelot (or California) game do not draw anything close to
80 pre-draw tests on Wednesday or Saturday night ...

... how do they know the machines are still functionally random?

Joe

[Robert Perkis]

Post by CDEX

Post by gARY
...
However, Lotto 'test draws' (that we *never* see)
sorta 'knock on the head' using the said history
function for gain in any lotto system.
The same as the scenario above or not?
gARY

Indeed, what we never see is the action (if any) the lottery commission
undertook immediately after they ran the test draws. Did they change any
ball (or balls), or did they change the machine? In other words, what were
the results of the test draws?
We don't need to know the results of the test draws just for that
information alone. It relates to the condition of the ballset and machine
as it has been used prior to that test.
In other words, if a problem is detected in the test draws, that problem
must have been existing to some degree before that moment. That means, it
must have existed to some degree in the real results of the earlier draws.
- - - -
Example.
The commission draws several test draws with a ballset and machine. It's
done offstage and off-camera. The data are internal only.
To the commission, the results look biased in their eyes (we never see them
with our eyes).
So, they replace the ballset or the machine. King Arthur's machines
(Guinevere, Lancelot, Merlin) have already been retired, and now there's
Moonstone, Topaz, Amethyst, Opal, and the other new ones. All of a sudden
Opal is looking a little off-color in the pre-draw test results so she's
sent for repairs. Instead of Opal, Topaz is now tested and looks OK. Topaz
is run in the actual draw.
Opal had a problem. Problem is, Opal's problem has just now been discovered
in this pre-draw trial. Prior to this trial, she might have run a dozen
previous draws with her results biased to one side but "marginally" OK --
i.e., just inside the commission's limit for acceptance. If Opal's results
were getting out of balance due to wear over the past several weeks, she
didn't crap out all at once on just this one latest test drawing. If her
problem is due to wear and tear she must have been drifting toward going out
of tolerance for some draws before this test drawing.
The same thought applies to ballsets, as well as to machines. If the ball
"49" is rejected in the test draws for hitting above expectation, it wasn't
struck by lightning that afternoon. It must have been wearing gradually in
balance, bounce, weight and friction for some time prior to that test
drawing.
Same thing, different words. If there is such a thing as "lottery machine
or ballset retirement due to wear and tear", it cannot happen all at once,
overnight. It has to happen gradually over a series of uses.
If the commission retires the machine or ballset for having gotten out of
tolerance, logically they must be doing so because there's a perceived bias
in the results coming from that machine; otherwise they have no basis for
retiring it. There must have been some gradual, incremental, "creeping"
bias in the actual drawing results which that machine produced (i.e., in the
"real" Wednesday and Saturday numbers) prior to its retirement.
If the commission do not allow for the explanation of increasing wear and
tear as a cause of bias in the outcomes of the actual lottery drawings, why
should they retire machines and ballsets after pre-draw trials?
- - -
The California 5/39 Fantasy game drew 80 private,"pre-release" drawings,
before going public with the game. Those 80 draws have never been made
public. Oddly, when they began the actual public drawings, they counted the
first such drawing as number "81". In other words, the game began with
drawing 81.
Presumably those 80 private drawings were enough to convince them that the
machines and ballsets were working OK, so that they could begin the public
game.
... If it takes 80 drawings to prove sufficient randomness ...
... and the Camelot (or California) game do not draw anything close to
80 pre-draw tests on Wednesday or Saturday night ...
... how do they know the machines are still functionally random?
Joe

This is my opinion only. We occasionally see in the Florida
draw history that a ballset or machine was rejected for a
draw.

The reason (outside of the machine not working properly) is
draws too alike for the lottery's comfort.

As we see the same ballsets and machines back in service in
later draws, and as I doubt ballsets can be repaired, I think
the lottery does this out of concern the mechanism of the
draw might have been tampered with to give certain numbers
a higher likelihood of being drawn.

The ballset and machine later tests normal and is restored.

If there were only one ballset and machine, these streaks of
too simular draws would be a real opportunity for sharp
lottery players. Even with test draws such streaks could
just as well come up every third drawing appearing as if
a continuous streak to the casual viewer.

The fact the lottery has these "problems" and randomly
rotates among ballsets and machines demonstrates the game
would be winnable if not for the interference.

Robert Perkis / http://www.lotto-logix.com/

[Nigel]

stacy_friedman wrote:
<snip>

Post by stacy_friedman
Start flipping a coin. Ask yourself whether it makes sense that if
you happen to flip 10 heads in a row, that implies the next flip is
more likely to be tails. If it does, ask yourself why that makes
sense in light of your understanding that heads and tails should both
occur with 50% probability.

Hi Stacey,

I'm firmly on the side of believing that history does matter, and I have
some lottery-related evidence that makes very interesting reading.

I'm not going to re-open old wounds and start the traditional "Oh yes it
does" "Oh no it doesn't" argument, but raise one of two issues.

To eliminate the effects of history, you must find a fair coin (which
itself is likely to render the experiment impossible), a fair tossing
process (which must involve some randomised process to eliminate the
sort of human bias reputedly exploitable at roulette) and you must
ensure the coin has never been tossed before, as historians might
maintain that it makes a difference whether you start from 11 heads in a
row or a tail then 10 heads. Your guinea pig then starts tossing the
coin and if a tail is thrown before 10 successive heads, the coin must
be rejected and the trial started with a new virgin coin.

Computer whizzes will advocate simulating the coin tossing with a random
number generator, but personally I would not assign them a lot of
street-cred. It's almost impossible to write a totally unbiased random
number program unless it relies upon some sort of physical trigger, and
that re-introduces the necessity of ensuring the trigger is virgin
before the trial starts etc.

Evil Nigel

[Gregg Cattanach]

Post by Nigel
Computer whizzes will advocate simulating the coin tossing with a random
number generator, but personally I would not assign them a lot of
street-cred. It's almost impossible to write a totally unbiased random
number program unless it relies upon some sort of physical trigger, and
that re-introduces the necessity of ensuring the trigger is virgin
before the trial starts etc.

You can go to http://random.org and get as many random numbers as you want
that are generated from random atmospheric noise. No seeds, counters or
other issues with PRNGs. The data is 'virgin' every time you get it.

Gregg C.

[stacy_friedman]

Post by Nigel
I'm firmly on the side of believing that history does matter, and I have
some lottery-related evidence that makes very interesting reading.

If history matters, the game is not one of independent trials. The
math for dependent games is far more complex. But the facts in
evidence don't indicate that dice, lottery, keno, roulette, or most
other casino games are games of dependent trials. For example, the
Nevada Gaming Control Board accepts the standard Keno formula for
hitting M of N picked spots as (N choose M) * ((80-N) choose (20 - M)
/ (80 choose 20). This formula is *invalid* if the probability of
each ball for each draw is not exactly 1/80.

Post by Nigel
To eliminate the effects of history, you must find a fair coin (which
itself is likely to render the experiment impossible), a fair tossing
process (which must involve some randomised process to eliminate the
sort of human bias reputedly exploitable at roulette)

This is all fine, and these two prerequisites are normally cited.

Post by Nigel
and you must
ensure the coin has never been tossed before, as historians might
maintain that it makes a difference whether you start from 11 heads in a
row or a tail then 10 heads. Your guinea pig then starts tossing the
coin and if a tail is thrown before 10 successive heads, the coin must
be rejected and the trial started with a new virgin coin.

This is nonsensical. If you have met your prerequisite of having a
fair coin, where fair is defined as p(heads) = p(tails) = 0.5, then
the historians are demonstrably incorrect. If it did make a
difference, the coin would not be fair, and you would have failed
meeting your initial prerequisites.

Post by Nigel
Computer whizzes will advocate simulating the coin tossing with a random
number generator, but personally I would not assign them a lot of
street-cred. It's almost impossible to write a totally unbiased random
number program unless it relies upon some sort of physical trigger, and
that re-introduces the necessity of ensuring the trigger is virgin
before the trial starts etc.

This is not true, and your insistence on "virginity" is misplaced.
There's a world of difference between "unbiased" and "physically
random". The Mersenne Twister is a very capable PRNG, yet it's
completely software-based. I would suggest additional reading before
hardening your opinion against PRNGs.

[Nigel]

Hi Stacy,

I apologise for misspelling your name, my wrist is firmly slapped.

stacy_friedman wrote:

<selective snipping>

Post by stacy_friedman
If history matters, the game is not one of independent trials.

It takes a difficult leap in understanding, but I would maintain that
lottery draws are near-enough random, physically independent, and yet
mildly predictable.

Post by stacy_friedman

Post by Nigel
and you must
ensure the coin has never been tossed before, as historians might
maintain that it makes a difference whether you start from 11 heads in a
row or a tail then 10 heads. Your guinea pig then starts tossing the
coin and if a tail is thrown before 10 successive heads, the coin must
be rejected and the trial started with a new virgin coin.

This is nonsensical. If you have met your prerequisite of having a
fair coin, where fair is defined as p(heads) = p(tails) = 0.5, then
the historians are demonstrably incorrect. If it did make a
difference, the coin would not be fair, and you would have failed
meeting your initial prerequisites.

No, this position is consistent with my beliefs above - if you can't
fulfill these prerequisites in a trial, then it doesn't constitute a
fair trial from a historian's point of view.

Post by stacy_friedman

Post by Nigel
Computer whizzes will advocate simulating the coin tossing with a random
number generator, but personally I would not assign them a lot of
street-cred. It's almost impossible to write a totally unbiased random
number program unless it relies upon some sort of physical trigger, and
that re-introduces the necessity of ensuring the trigger is virgin
before the trial starts etc.

This is not true, and your insistence on "virginity" is misplaced.
There's a world of difference between "unbiased" and "physically
random". The Mersenne Twister is a very capable PRNG, yet it's
completely software-based. I would suggest additional reading before
hardening your opinion against PRNGs.

I'm not an expert on random number generators, although I've debugged
one or two early ones and written one myself (based on the milliseconds
component of how long a backgammon player takes to enter the next move).
But bearing in mind my insistence on virginity, perhaps the operative
question should be "for this sequence of random numbers, would there
have been a previous one in the sequence if we had asked for it?" As far
as I can see, the previous respondee's reply about random numbers based
on atmospheric effects would fail this test.

Evil Nigel

[stacy_friedman]

Post by Nigel

Post by stacy_friedman
If history matters, the game is not one of independent trials.

It takes a difficult leap in understanding, but I would maintain that
lottery draws are near-enough random, physically independent, and yet
mildly predictable.

If the game is independent, previous draws cannot influence future
draws. If previous draws cannot influence future draws, the game
cannot be predicted. Your belief that
( "Each draw is independent" AND "The game can be predicted" )
is a logical contradiction, unless your method of prediction involves
some external information outside the history of previous draws.

Post by Nigel
No, this position is consistent with my beliefs above - if you can't
fulfill these prerequisites in a trial, then it doesn't constitute a
fair trial from a historian's point of view.

Your prerequisites involve starting from the beginning of time. No
historian worthy of the title would ever presume that history should
not exist. Think about the implications of what you're saying.

Post by Nigel
But bearing in mind my insistence on virginity, perhaps the operative
question should be "for this sequence of random numbers, would there
have been a previous one in the sequence if we had asked for it?"

The answer to this question is always "yes". No random number
generator in existence can fulfill the restriction of having time
itself start when your experiment does. Think about the implications
of what you're saying.

[Nigel]

Post by stacy_friedman

Post by Nigel

Post by stacy_friedman
If history matters, the game is not one of independent trials.

It takes a difficult leap in understanding, but I would maintain that
lottery draws are near-enough random, physically independent, and yet
mildly predictable.

If the game is independent, previous draws cannot influence future
draws.

The leap of understanding is too great, but you're in good company. It's
extremely difficult for most people with a scientific background to
question their preconceptions.

Post by stacy_friedman

Post by Nigel
But bearing in mind my insistence on virginity, perhaps the operative
question should be "for this sequence of random numbers, would there
have been a previous one in the sequence if we had asked for it?"

The answer to this question is always "yes". No random number
generator in existence can fulfill the restriction of having time
itself start when your experiment does. Think about the implications
of what you're saying.

Take the very first live UK national lottery draw. What was the result
of the previous draw? There wasn't one, it fulfills my virgin criterion.

Evil Nigel

[stacy_friedman]

Post by Nigel

Post by stacy_friedman
If the game is independent, previous draws cannot influence future
draws.

The leap of understanding is too great, but you're in good company. It's
extremely difficult for most people with a scientific background to
question their preconceptions.

Do you have another way to define "independent" such that the future
is, in fact, dependent on the past? If not, please explain how my
sentence is not a tautology.

Post by Nigel

Post by stacy_friedman

Post by Nigel
But bearing in mind my insistence on virginity, perhaps the operative
question should be "for this sequence of random numbers, would there
have been a previous one in the sequence if we had asked for it?"

The answer to this question is always "yes". No random number
generator in existence can fulfill the restriction of having time
itself start when your experiment does. Think about the implications
of what you're saying.

Take the very first live UK national lottery draw. What was the result
of the previous draw? There wasn't one, it fulfills my virgin criterion.

That's remarkably shortsighted, Nigel. The fact that the specific
balls had never been put in an official lottery bin before doesn't
mean that they couldn't have been drawn "had we asked for it". Do you
mean to imply that every draw of the UK national lottery is/was
different from the first one in some fundamental way?

Let's explore this further. You say that first draw of the UK
national lottery was virgin. By your criteria, the second draw would
not be.

1) Suppose a newly-manufactured lottery machine and lottery balls were
used for the second draw. Would that be "virgin"?

2) The answer must be yes, because if the same newly-manufactured
lottery machine and balls were used for the very first live French
lottery draw a week later, you wouldn't even consider the question.
If the answer were no, you'd have to consider all previous lottery
draws anywhere as ruining your "virginity", and moreover, all previous
random draws for anything (bingo, dice, divining sticks, etc). That
goes back thousands of years (or more), meaning that the first draw of
the UK national lottery clearly wasn't "virgin" as you've stated.

3) Now suppose the newly-manufactured lottery machine and lottery
balls were a molecular clone of the first lottery machine and balls.
That is, by any physical means of measuring, there is no difference
between the first lottery set and the second one.

4) If the first and second sets are physically identical, and drawing
the second draw using the second set is "virgin", then drawing the
second draw using the first set must also be "virgin".

5) Therefore, all draws are "virgin"; that is, your notion of
virginity has no valid meaning.

[Nigel]

This conversation has been going on a while, and it's cross-posted to 3
newsgroups - do people want us to take this private?

Post by stacy_friedman
Do you have another way to define "independent" such that the future
is, in fact, dependent on the past? If not, please explain how my
sentence is not a tautology.

I know the results I'm getting shouldn't be happening, and I don't have
a maths PhD or adequate resources to investigate properly, but the
conceptual "kludge" I've come up with is to seperate the concepts of
physical independence and logical independence. Hence all the live
published UK lottery draws are physically independent but in some way
logically dependent.

Post by stacy_friedman
That's remarkably shortsighted, Nigel. The fact that the specific
balls had never been put in an official lottery bin before doesn't
mean that they couldn't have been drawn "had we asked for it". Do you
mean to imply that every draw of the UK national lottery is/was
different from the first one in some fundamental way?

I agree it's not very satisfactory, but if we could turn back time, put
the balls in the bin and perform a minus oneth draw, that would in some
small way contribute to what we'd expect in the next draw.

Post by stacy_friedman
Let's explore this further. You say that first draw of the UK
national lottery was virgin. By your criteria, the second draw would
not be.
1) Suppose a newly-manufactured lottery machine and lottery balls were
used for the second draw. Would that be "virgin"?

That may well have happened, there were several machines available for
use, chosen at random by a member of the public. The answer is yes and
no - no if you're considering all live UK draws, yes if you're
considering draws by machine (something which may not be useful as the
original machines have been archived, and we don't know in advance which
one will be used in the next draw).

Post by stacy_friedman
2) The answer must be yes, because if the same newly-manufactured
lottery machine and balls were used for the very first live French
lottery draw a week later, you wouldn't even consider the question.

That's something I haven't had time to investigate, but it appears to be
valid to combine UK lottery and Extra draw information. I published a
'thought experiment' on rec.gambling.lottery about how conceptually that
could result in a form of causality that isn't bound by the speed of light.

Evil Nigel

[stacy_friedman]

Post by Nigel
I know the results I'm getting shouldn't be happening, and I don't have
a maths PhD or adequate resources to investigate properly

What are your results, and why shouldn't they be happening? Are you
saying this within a framework of statistical significance, or are you
just guessing?

, but the

Post by Nigel
conceptual "kludge" I've come up with is to seperate the concepts of
physical independence and logical independence. Hence all the live
published UK lottery draws are physically independent but in some way
logically dependent.

It's not a "kludge", Nigel, it's a made-up philosophy. Do you have a
legitimate reason for this "kludge", or are you just guessing?

Post by Nigel
I agree it's not very satisfactory, but if we could turn back time, put
the balls in the bin and perform a minus oneth draw, that would in some
small way contribute to what we'd expect in the next draw.

Does it merely *seem* like it has some contribution, or do you have
some factual reason for believing what you do? Can you describe the
small way, or are you just guessing?

Post by Nigel
I published a
'thought experiment' on rec.gambling.lottery about how conceptually that
could result in a form of causality that isn't bound by the speed of light.

I'm not going to debate you on the finer points of your personal
metaphysics. You're free to believe whatever you wish. If you want
to believe that independence doesn't actually mean independence, go
ahead. If you want to believe that past draws of the UK lottery can
influence the next Keno game at Caesar's Palace, go ahead. If you
want to believe that the phrase "causality that isn't bound by the
speed of light" has anything to do with simple arithmetic, go ahead.

I don't believe any of these things. I'll change my mind if you show
me why I should, but so far, it sounds like you're just guessing.

[Mason]

Post by Ion Saliu
but the
conceptual "kludge" I've come up with is to seperate the concepts of
physical independence and logical independence. Hence all the live
published UK lottery draws are physically independent but in some way
logically dependent.

Demosthenes may have missed out on "conceptual kludge" but he certainly had
a grasp on the gist of Nigel's thinking.

"A man is his own easiest dupe, for what he wishes to be true he generally
believes to be true."

[unknown]

That's the problem with most, simple computer generated random numbers
-- they begin the run at the next number from the residue of the
previous number. They are very much not virgin numbers. They are
mathematically related and actually reproducible.

Mike

On 25 May 2004 10:27:57 -0700, in rec.gambling.craps

Post by stacy_friedman

Post by Nigel

Post by stacy_friedman
If history matters, the game is not one of independent trials.

It takes a difficult leap in understanding, but I would maintain that
lottery draws are near-enough random, physically independent, and yet
mildly predictable.

If the game is independent, previous draws cannot influence future
draws. If previous draws cannot influence future draws, the game
cannot be predicted. Your belief that
( "Each draw is independent" AND "The game can be predicted" )
is a logical contradiction, unless your method of prediction involves
some external information outside the history of previous draws.

Post by Nigel
No, this position is consistent with my beliefs above - if you can't
fulfill these prerequisites in a trial, then it doesn't constitute a
fair trial from a historian's point of view.

Your prerequisites involve starting from the beginning of time. No
historian worthy of the title would ever presume that history should
not exist. Think about the implications of what you're saying.

Post by Nigel
But bearing in mind my insistence on virginity, perhaps the operative
question should be "for this sequence of random numbers, would there
have been a previous one in the sequence if we had asked for it?"

The answer to this question is always "yes". No random number
generator in existence can fulfill the restriction of having time
itself start when your experiment does. Think about the implications
of what you're saying.

[Gerd Henjes]

Mike... your statement indicates that you are a complete moron, you should
go hide now. Gerd

Post by unknown
That's the problem with most, simple computer generated random numbers
-- they begin the run at the next number from the residue of the
previous number. They are very much not virgin numbers. They are
mathematically related and actually reproducible.
Mike

[Cymbal Man Freq.]

I know 1 keno machine that agrees with Mike. One guy won huge on it. After a
power blackout, some guy counted so many results and wrote down the numbers. So
if the machine got unplugged again, the RNG would start over again repeating the
same pattern of results. This was maybe 10 years ago though, and he got busted.
But the RNG didn't fail that multiple big winner!

Now about those state lottery ping pong balls. Think German cryptography! No SOS
here, but maybe there is!?!

Post by Gerd Henjes
Mike... your statement indicates that you are a complete moron, you
should go hide now. Gerd

Post by unknown
That's the problem with most, simple computer generated random numbers
-- they begin the run at the next number from the residue of the
previous number. They are very much not virgin numbers. They are
mathematically related and actually reproducible.
Mike

[Ion Saliu]

• Point of Relative Certainty

There is no absolute certainty if we are to abide by the rules of
Reason…absolutely! Go to www.saliu.com and search for reason,
certainty, randomness.

This is a more mundane problem. It is a parlor favorite. It is also a
favorite reason to put up a fight. Just ask Kotskarr, or Shobolun, or
Kulai Parakelsus; or just ask yourself, or myself…
The question goes "If heads did not appear in 10 consecutive coin
tosses, is it more likely to come out in the 11th toss?" Many will
answer, I mean will shout right away "NOT! NOT! The probability of
heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is
always ½ or 0.5 or 50%. But that parameter simply represents the
number of expected successes in ONE trial; or, the number of favorite
cases over total cases. There is a lot more to a phenomenon such as
‘coin tossing'. For starters, we can analyze coin tossing by
calculating the ‘probability of the normal distribution'. The
‘probability of the normal distribution' refers to ‘EXACTLY M
successes in N trials'. In this particular case: what is the
probability of exactly 0 heads in 10 tosses? What is the probability
of exactly 0 heads in 11 tosses? You don't need to do all those
calculations manually. My freeware SuperFormula.EXE (version 11.0, May
2004) is a very convenient tool. Select option L (‘At Least' M
Successes in N Trials). Select next option 1, since we know the
probability p (p=0.5). Type 0 for number of successes M and 10 for
number of trials N. The program responds:


"The binomial probability of 0 successes in 10 trials
for an event of individual probability p = .5 is:
BDF = .0009765625
or .09765625 %
or 1 in 1024"


Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we
missed heads 10 times in a row. What is the probability to miss heads
in the very next toss? That is equivalent to missing heads 11 times in
a row!


"The binomial probability of 0 successes in 11 trials
for an event of individual probability p = .5 is:
BDF = .00048828125
or .04882812 %
or 1 in 2048"


We always use the constant p = .5, but the CHANCE to miss heads
worsens with the number of tosses! Tell you what, Krushbeck. Those
casino consultants, and game designers, and executives are not damn
idiots! Remember last time you lost all your money at the slot
machines? You remember that every time you won, a flashy-snazzy prompt
asked you to "Double your win". Why would the casinos offer you a good
chance to double your wins? Isn't the probability the same from one
spin to the next? Of course it is. But your chance (degree of
certainty) to win consecutively is lower. The casinos offer you the
"opportunity" to double your player's disadvantage. That is, one
method for the casino to double the house advantage! That's
mathematics. Read more:
http://www.saliu.com/keywords/casino.htm

Ok. We missed, this rare time, 11 consecutive tosses. What is the
degree of certainty to miss heads consecutively in 12 tosses?

"The binomial probability of 0 successes in 12 trials
for an event of individual probability p = .5 is:
BDF = .000244140625
or .02441406 %
or 1 in 4096"

If you will, the odds against missing heads in consecutive tosses
doubles with each toss. Those casino consultants, and game designers,
and executives are not damn idiots! They know how to boost their
wealth. They even pay pocket change to all kinds of ghiolbans and
tirtans to debate every conceivable public place. The ghiolbans and
tirtans "debate" with ardor that no matter how many times in a row an
event has skipped, your odds will remain eternally the same! If you
are stubborn and don't believe the ghiolbans and tirtans, guess what?
Those casino consultants, and game designers, and executives (who are
not damn idiots, ever!) will even offer players free "gambling
systems"! Ever heard of the "Turnaround" system? Read more:
http://saliu.com/bbs/messages/733.html

I've heard many times that heads can hit an infinity of times in a
row; or, miss an infinite number of consecutive tosses! My honest
question is, when does that infinity start? I wanna see a beginning,
if I were to believe in a certain end. Certain? Say what?

"For only Almighty Number is exactly the same, and at least the same,
and at most the same, and randomly the same. May Its Almighty grant us
in our testy day the righteous proportion of being at most unlikely
the same and at least likely different. For our strength is in our
inequities."

Jaqk Fowuru Disconqueror
------------------------

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper
expectations for roulette, baccarat, craps, keno, lotteries; meaning
that after a specfic number of no show outcomes then the due number is
most likely to appear.
Has anyone heard about an ostensible physics law called Point of
Certainty ?
Thanks in advance for your kind replies-
RB

[Mason]

Go to www.saliu.com and search for reason <snip>

Penn Jillette:

"My favorite thing about the Internet is that you get to go into the private
world of real creeps without having to smell them."

[Nick UK]

Post by Mason
"My favorite thing about the Internet is that you get to go into the
private world of real creeps without having to smell them."

.............................................................

If you are referring to Usenet Newsgroups.. I agree entirely.

With the recent extremely boring palaver about *coin tossing* a 'tossers'
subject which has been hammered to death for years here: this newsgroup..
(it seems) now has more than it's fair share of 'tossers'.

UK folks who post here will not need an explanation of the true meaning of
the word... 'tosser'.

Nick.
The r.g.l subscriber formerly known as 'lottoluk'.

[Mason]

Post by Nick UK

Post by Mason
"My favorite thing about the Internet is that you get to go into the
private world of real creeps without having to smell them."

.............................................................
If you are referring to Usenet Newsgroups.. I agree entirely.

Actually, Nick, I was referring to www.saliu.com, the previous posters
website.
The intended clue to the fact that I was referring to that citation was that
I referred to it.

[Nick UK]

Post by Mason
Actually, Nick, I was referring to www.saliu.com, the previous posters
website.
The intended clue to the fact that I was referring to that citation was
that I referred to it.
...............................................................

Is there a point of certainty?

Well, in my particular case, it is a certainty that I will *never* click on
links to tossers!

The non-intended clue is in the title of this thread.

Nick.
The r.g.l subscriber formerly known as 'lottoluk'.

[Gregg Cattanach]

. Point of Relative Certainty
"The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024"
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we
missed heads 10 times in a row. What is the probability to miss heads
in the very next toss? That is equivalent to missing heads 11 times in
a row!

WRONG. "What is the probability to miss heads in the very next toss?" and
"missing heads 11 times in a row!" are not '"equivalent" in ANY way. The
coin has NO IDEA that you just threw heads on the last 10 tosses.

If it DID then the formula for figuring out 11 tails in a row (0.5) ^ 11
would be wrong, becuase the (0.5) for the 11th toss would also be wrong and
way too high.

Gregg C.

[Ion Saliu]

For those who wondered what "ghiolbans" or "tirtans" are-
• Just look at some replies to my post. Intense visceral reactions. No
meaningful explanation as of why spilling their venom on my words.
They have no clue to what the probability of the binomial distribution
represents. No debate on the formulae; if my formulas and calculations
were wrong, what are the correct formulae?

The ghiolbans and tirtans are not regular idiots on their own feet.
They are the recipients of said pocket change…
They started as rare phenomena right at their birth. Their brains were
so diluted that there was the danger the "brains" would drain through
their ears, and eyes, and mouths, and nostrils. The doctors
encapsulated the sparsely floating gray-matter cells in bottles.
• They are liquidiots!

They grew as far as body matter is concerned, but those bottles lining
their skulls didn't. Yet, they developed the misconception that their
bottles were as large as the seas.
• They are squidiots!

Places they go stink as they do. Their only discovery is the
"pee-value of the null factor".
• They are peediots!


Jaqk Fowuru Disconqueror
"The Philosophical Science of Winning"
http://saliu.com/

[CDEX]

No, Ion.

You invent demons and rail against them. When the paranoia and
self-promotion are snipped from your material only the most trivial data
remains.

The only reason your 10-toss 1-in-1024 condition can go to your 11-toss
1-in-2048 condition (or stop) is because the next toss is 1-in-2.

The only reason your 11-toss 1-in-2048 condition can go to your 12-toss
1-in-4096 condition (or stop) is because the next toss is 1-in-2.

Regardless of how you got to your current condition the next condition is
based on 1-in-2. The same thing said in plain English is that the history
of previous tosses does not affect the outcome of the next toss.

Before you make 12 tosses your chance of getting all Heads or all Tails at
the end of those 12 tosses is 1-in-4096. At any step along that series the
next condition is based on 1-in-2. The same thing said in plain English is
that the history of previous tosses does not affect the outcome of the next
toss.

You can extrapolate that from 1 toss to a gazillion tosses with the same
principle applied. The same thing said in plain English is that the history
of previous tosses does not affect the outcome of the next toss.

Injecting any other conclusion into a thread on the subject of a "Point of
Certainty" is misleading. Probably not many people would want to weave a
narrative of paranoiac attacks on imaginary demons mingled with your own
self-promotion around some coin tosses.

Wisdom begins in wonder. (Socrates)

Joe

[stacy_friedman]

Post by Ion Saliu
They have no clue to what the probability of the binomial distribution
represents.

The binomial distribution is the way to calculate the probability of M
events in a total series of N being "winners", where the probability
of a winner is p and the probability of a loser is q = 1-p. It's a
relatively straightforward concept, especially with coin flipping.
What are the chances of getting 8 heads in 20 flips? Since p = q, all
permutations of the 20 flips are equiprobable so the answer is simply
20 choose 8.

Post by Ion Saliu
No debate on the formulae; if my formulas and calculations
were wrong, what are the correct formulae?

You seemed to imply that knowledge of the binomial formula would
enable you to know that if 10 heads were flipped in a row, for 11th
flip "p = q = 50%" is not true.

If this is your implication, it is incorrect. If not, I'm not sure
why you spent so much time writing about it.

[Raymond Baldwin]

First, I really apprecaite everyone's informative and candid
responses-

So OK its basically agreed that a fair coin, die, or ball has no
memory but it does produce a history of past performances. Still 50/50
on the next play , well how is it that in even chance games there are
never 50 consecutive heads, 50 consecutive blacks, 50 consecutive
passes or 50 consecutive banker hands?

Not being intentionally sarcastic but inquisitive.

Regards,
RB

Post by stacy_friedman

Post by Ion Saliu
They have no clue to what the probability of the binomial distribution
represents.

The binomial distribution is the way to calculate the probability of M
events in a total series of N being "winners", where the probability
of a winner is p and the probability of a loser is q = 1-p. It's a
relatively straightforward concept, especially with coin flipping.
What are the chances of getting 8 heads in 20 flips? Since p = q, all
permutations of the 20 flips are equiprobable so the answer is simply
20 choose 8.

Post by Ion Saliu
No debate on the formulae; if my formulas and calculations
were wrong, what are the correct formulae?

You seemed to imply that knowledge of the binomial formula would
enable you to know that if 10 heads were flipped in a row, for 11th
flip "p = q = 50%" is not true.
If this is your implication, it is incorrect. If not, I'm not sure
why you spent so much time writing about it.

[Mason]

Post by Raymond Baldwin
well how is it that in even chance games there are
never 50 consecutive heads

Actually you can expect 50 consecutive heads from a fair coin approximately
once in every 1,125,899,906,842,624 flips. (1/2)^50

That ain't often, RB, but it sure ain't never.

[Mason]

Post by Mason

Post by Raymond Baldwin
well how is it that in even chance games there are
never 50 consecutive heads

Actually you can expect 50 consecutive heads from a fair coin
approximately once in every 1,125,899,906,842,624 flips. (1/2)^50
That ain't often, RB, but it sure ain't never.

BTW, RB

Can you guess how often you can expect to get the following fifty fair coin
flip sequence .....
HTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHT

The answer is approximately once in every 1,125,899,906,842,624 flips.
(1/2)^50

Strange ... but true!

[Alan Shank]

Post by Mason
BTW, RB
Can you guess how often you can expect to get the following fifty fair coin
flip sequence .....
HTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHTHT
The answer is approximately once in every 1,125,899,906,842,624 flips.
(1/2)^50

Same thing. It's once every that many SETS of 50 flips.
The key here is order. If you only care about an even split between
heads and tails, then you are dealing with combinations, not
permutations, and instead of 1 there are 3.16 X 10^13 ways for that to
occur.
Cheers,
Alan Shank

[Alan Shank]

Post by Mason

Post by Raymond Baldwin
well how is it that in even chance games there are
never 50 consecutive heads

Actually you can expect 50 consecutive heads from a fair coin approximately
once in every 1,125,899,906,842,624 flips. (1/2)^50

I have to disagree here, Mason. I think that you can expect 50
consecutive heads once every 1,125,899,906,842,624 SETS of 50 flips, not
that many flips, which makes it even more unlikely. That number is
actually 2^50, which is the number of ways to arrange two things (H or
T) in 50 slots. 1/2^50 is 1 divided by that number.
Cheers,
Alan Shank

[Mason]

Post by Alan Shank

Post by Mason

Post by Raymond Baldwin
well how is it that in even chance games there are
never 50 consecutive heads

Actually you can expect 50 consecutive heads from a fair coin approximately
once in every 1,125,899,906,842,624 flips. (1/2)^50

I have to disagree here, Mason. I think that you can expect 50
consecutive heads once every 1,125,899,906,842,624 SETS of 50 flips, not
that many flips, which makes it even more unlikely. That number is
actually 2^50, which is the number of ways to arrange two things (H or
T) in 50 slots. 1/2^50 is 1 divided by that number.
Cheers,
Alan Shank

You are correct, Alan. I should have specified SETS of 50 flips for the
specific order and content of the of the flip set specified to be expected
to occur. Thus, the approximate number that I posted of
1,125,899,906,842,624 should be multiplied by 50 in order to be more
correct. This makes it 50 times more unlikely to occur.
Good catch!

[Alan Shank]

Post by Mason

Post by Alan Shank

Post by Mason

Post by Raymond Baldwin
well how is it that in even chance games there are
never 50 consecutive heads

Actually you can expect 50 consecutive heads from a fair coin

approximately

Post by Alan Shank

Post by Mason
once in every 1,125,899,906,842,624 flips. (1/2)^50

I have to disagree here, Mason. I think that you can expect 50
consecutive heads once every 1,125,899,906,842,624 SETS of 50 flips, not
that many flips, which makes it even more unlikely. That number is
actually 2^50, which is the number of ways to arrange two things (H or
T) in 50 slots. 1/2^50 is 1 divided by that number.
Cheers,
Alan Shank

You are correct, Alan. I should have specified SETS of 50 flips for the
specific order and content of the of the flip set specified to be expected
to occur. Thus, the approximate number that I posted of
1,125,899,906,842,624 should be multiplied by 50 in order to be more
correct. This makes it 50 times more unlikely to occur.

I still don't think that's right. The number you quoted is 2^50, which
is the total number of unique arrangements of Hs and Ts in 50 slots.
Since there is only one way to arrange 50 heads in 50 slots, the odds
against that happening are 1,125,899,906,623 to 1, which is the same
probability as .5^50. As you correctly pointed out, any UNIQUE
arrangement, including all tails and a string of 25 HT, is equally unlikely.
Cheers,
Alan Shank

[Allyn Boldt]

Post by Alan Shank
I have to disagree here, Mason. I think that you can expect 50
consecutive heads once every 1,125,899,906,842,624 SETS of 50 flips, not
that many flips, which makes it even more unlikely.

I have to disagree with you. I used to engage in a "friendly game of who
would buy the cokes". It was "odd man out untill 3 persons were flipping
coins and then the odd man bought for the crew.

A matter of repeating the coin flip, heads or tails. If you could not keep
a sequence of 7 or 8 after the first coin toss, you would wind up buying 5-8
cokes. Got expensive after a while. Took me several months to find out why
one guy never bought. He had a consistent coin flip. I started to carry a
silver dollar for coin flips. The heavier the coin the better the control
on how many turns until you catch the coin again. "Precision coin
flipping."

[stacy_friedman]

Post by Raymond Baldwin
First, I really apprecaite everyone's informative and candid
responses-
So OK its basically agreed that a fair coin, die, or ball has no
memory but it does produce a history of past performances. Still 50/50
on the next play , well how is it that in even chance games there are
never 50 consecutive heads, 50 consecutive blacks, 50 consecutive
passes or 50 consecutive banker hands?

There are, just rarely. In fact, the chances of 50 consecutive heads
are 1 in 2^50, or 1 in 1,125,899,906,842,620. That's not so likely
to ever happen in your lifetime, if you think about it.

However, the fact that you're thinking about it is why the rarity
seems odd. You are explicitly *not* thinking about series of coin
flips that don't seem "unusual" to you. Here's an example:

The series of coin flips that has 50 heads in order, that is:
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
seems to be quite unusual. And it is: it should occur once every 1.13
quadrillion hands (or so).

Now consider the series of coin flips that has 25 heads and 25 tails
in this order:
HHTHTTHTHHHHHHTHTTTHTTHHTHTTHTTTTTHTHHHTHTHTHHTTTH
That doesn't seem unusual at all, right? Well, it's just as unlikely
to happen as the series before: it too should occur once every 1.13
quadrillion hands (or so).

If you think about how there are a total of 1.13 quadrillion ways to
flip a coin 50 times, you'll realize that the first series is just one
way, and the second series is just another way. "But," you may ask,
"isn't it more likely to get 25 heads and 25 tails than all 50 heads?"
The answer is unequivocally "yes!" However, it is exactly as likely
to get all 50 heads as it is to get 25 heads and 25 tails in *exactly
that order*.

The difference is that there is only one way to arrange 50 heads in a
row. There are 126,410,606,437,752 ways to flip 50 times and still
get 25 heads and 25 tails. But each one of those 126.4 trillion ways
is equally likely, and just as likely as flipping 50 heads.

[unknown]

As I have said for decades: A string of 1's a mile long IS a random
number.

No, it won't happen very often, but it is as likely as any other
string of numbers that long.

Thanks for bringing this up.

On 24 May 2004 10:23:50 -0700, in rec.gambling.craps

Post by stacy_friedman

Post by Raymond Baldwin
First, I really apprecaite everyone's informative and candid
responses-
So OK its basically agreed that a fair coin, die, or ball has no
memory but it does produce a history of past performances. Still 50/50
on the next play , well how is it that in even chance games there are
never 50 consecutive heads, 50 consecutive blacks, 50 consecutive
passes or 50 consecutive banker hands?

There are, just rarely. In fact, the chances of 50 consecutive heads
are 1 in 2^50, or 1 in 1,125,899,906,842,620. That's not so likely
to ever happen in your lifetime, if you think about it.
However, the fact that you're thinking about it is why the rarity
seems odd. You are explicitly *not* thinking about series of coin
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
seems to be quite unusual. And it is: it should occur once every 1.13
quadrillion hands (or so).
Now consider the series of coin flips that has 25 heads and 25 tails
HHTHTTHTHHHHHHTHTTTHTTHHTHTTHTTTTTHTHHHTHTHTHHTTTH
That doesn't seem unusual at all, right? Well, it's just as unlikely
to happen as the series before: it too should occur once every 1.13
quadrillion hands (or so).
If you think about how there are a total of 1.13 quadrillion ways to
flip a coin 50 times, you'll realize that the first series is just one
way, and the second series is just another way. "But," you may ask,
"isn't it more likely to get 25 heads and 25 tails than all 50 heads?"
The answer is unequivocally "yes!" However, it is exactly as likely
to get all 50 heads as it is to get 25 heads and 25 tails in *exactly
that order*.
The difference is that there is only one way to arrange 50 heads in a
row. There are 126,410,606,437,752 ways to flip 50 times and still
get 25 heads and 25 tails. But each one of those 126.4 trillion ways
is equally likely, and just as likely as flipping 50 heads.

[Ion Saliu]

• The Probability of Losing or Winning N Consecutive Times

So, you saying that those casino consultants, and game designers, and
executives ARE damn idiots! How on earth have they been able to stay in
business this long??? Is that because the infinity hasn’t started yet?
You know, they offer this incredible bet: “Double your win?” as a way to
increase players’ gains, thus wiping out their own house advantage! You
mean, after an infinite number of trials, that huge mathematical mistake
will catch up with the casinos! I envision the gratitude of the kasinos
towards you. They believed that consecutive hits were less likely than
single-length hits! Now you have opened their eyes. They’ll spoil you
with…pocket change!

I know what you mean! I just looked at your data.
You provided the audience with plenty of real-life roulette spins… I
see! Wow! Those streaks are amazing! Look at the streaks of red. There
are more 100-length winning streaks than single streaks! You right, big
boys! Since p(ee) is always the same (18/38), the 100-length streak has
the right to go all the way to infinity! Godspeed!


Jaqk Fowuru Disconqueror
“The Philosophical Science of Winning”
http://www.saliu.com/

[Alan Shank]

Post by Ion Saliu
"The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024"
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we
missed heads 10 times in a row. What is the probability to miss heads
in the very next toss? That is equivalent to missing heads 11 times in
a row!
"The binomial probability of 0 successes in 11 trials
BDF = .00048828125
or .04882812 %
or 1 in 2048"
We always use the constant p = .5, but the CHANCE to miss heads
worsens with the number of tosses!

I hope that no one who reads this newsgroup is actually taken in by this
argument, but, in fact, I have known very intelligent people who cannot
seem to get their heads around the difference between the probability of
r successes in n trials and the probability of r successes in n trials
when you already have (r -1) successes in (n - 1) trials. It is the
foundation of the Gambler's Fallacy.

If we cut the problem down to size, we can see the difference more
easily. Let's consider the possibility of 0 heads in 4 trials.

We know the total ways to arrange Hs and Ts in 4 slots is 2^4, or 16;
Mr. Saliu's software would tell us that, if we didn't already know it.
Since there is only one way to arrange 4 Ts in 4 slots, the odds are 15
to 1 against this happening. Or, we can say the probability is 1/16, or
.0625.

Now, let's start the experiment. Let's toss the coin:

Heads!
What is the probability of 0 heads in (these particular) 4 trials now?
Let's not always see the same hands, please. >:-) Right, zero.

The chance of HHHH in THIS SERIES of 4 flips is gone. Where did it go?
The sum of all the probabilities of possible outcomes has to, at every
stage, be one! So, when a probability goes to zero, it has to be
re-distributed to the other remaining possibilities, right?

This proves that the probabilites CHANGE as we go through the
experiment, which is why Mr. Saliu's supposition that the chances of
gettting zero heads in THIS SERIES of 11 flips are still 1 in 2048 is
UTTER NONSENSE.
Cheers,
Alan Shank

[Raymond Baldwin]

As we use to say in Brooklyn, "Hey, not for notin but..." :-)
Back to the practical & mundane, anyone actually witness 50 roulette
red, blacks; baccarat bank hands, player hands; craps pass or no pass;
Sic Bo Big or Small ?

If not , everything considered, why not ?

Not being facetious, just trying to understand relative to the
original Point of Certainty inquiry-

Thanks again,
Raymond

Post by Alan Shank

Post by Ion Saliu
"The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024"
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we
missed heads 10 times in a row. What is the probability to miss heads
in the very next toss? That is equivalent to missing heads 11 times in
a row!
"The binomial probability of 0 successes in 11 trials
BDF = .00048828125
or .04882812 %
or 1 in 2048"
We always use the constant p = .5, but the CHANCE to miss heads
worsens with the number of tosses!

I hope that no one who reads this newsgroup is actually taken in by this
argument, but, in fact, I have known very intelligent people who cannot
seem to get their heads around the difference between the probability of
r successes in n trials and the probability of r successes in n trials
when you already have (r -1) successes in (n - 1) trials. It is the
foundation of the Gambler's Fallacy.
If we cut the problem down to size, we can see the difference more
easily. Let's consider the possibility of 0 heads in 4 trials.
We know the total ways to arrange Hs and Ts in 4 slots is 2^4, or 16;
Mr. Saliu's software would tell us that, if we didn't already know it.
Since there is only one way to arrange 4 Ts in 4 slots, the odds are 15
to 1 against this happening. Or, we can say the probability is 1/16, or
.0625.
Heads!
What is the probability of 0 heads in (these particular) 4 trials now?
Let's not always see the same hands, please. >:-) Right, zero.
The chance of HHHH in THIS SERIES of 4 flips is gone. Where did it go?
The sum of all the probabilities of possible outcomes has to, at every
stage, be one! So, when a probability goes to zero, it has to be
re-distributed to the other remaining possibilities, right?
This proves that the probabilites CHANGE as we go through the
experiment, which is why Mr. Saliu's supposition that the chances of
gettting zero heads in THIS SERIES of 11 flips are still 1 in 2048 is
UTTER NONSENSE.
Cheers,
Alan Shank

[CDEX]

Post by Raymond Baldwin
...
Back to the practical & mundane, anyone actually
witness 50 roulette red, blacks; baccarat bank hands,
player hands; craps pass or no pass; Sic Bo Big
or Small ?
...

On a wheel, 17 consecutive Reds once. All the Martingale and D'Alembert
players must have reached the house limit a bunch of times, renewing their
bets, and gone home broke.

A lottery number was out something like 70 draws once in the old Florida
6/49 Lotto, where the game's average was 8.2 draws.

Joe

[Alan Shank]

Post by Raymond Baldwin
As we use to say in Brooklyn, "Hey, not for notin but..." :-)
Back to the practical & mundane, anyone actually witness 50 roulette
red, blacks; baccarat bank hands, player hands; craps pass or no pass;
Sic Bo Big or Small ?
If not , everything considered, why not ?

Have you read this whole thread? Did you not see the odds against 50
consecutive tails. That's a big figure. It's not surprising at all that
no one reading this thread has even seen 50 consecutive anything. Even
events that have a greater-than-.5 probability do not appear 50 times in
a row often. Take a lay 4 (or 10) bet. The probability of winning it is
.66667, but the odds of winning 50 straight lay 4 bets are 637,621,499
to 1. OTOH, the odds against 50 dice rolls in a row without a 12 are
only about 3 to 1. We've all probably seen these (or 50 without a 2),
but we probably never noticed (unless we were betting on the 12).

Cheers,
Alan Shank

[Alan Shank]

Post by Raymond Baldwin
As we use to say in Brooklyn, "Hey, not for notin but..." :-)
Back to the practical & mundane, anyone actually witness 50 roulette
red, blacks; baccarat bank hands, player hands; craps pass or no pass;
Sic Bo Big or Small ?

I once rolled 56 times without a seven; the odds against this are
27,172.8 to 1.

"Awww, he ain't so shaggy." >:-)
Cheers,
Alan Shank

[TeddysDad]

What set were you using??..

Post by Alan Shank

Post by Raymond Baldwin
As we use to say in Brooklyn, "Hey, not for notin but..." :-)
Back to the practical & mundane, anyone actually witness 50 roulette
red, blacks; baccarat bank hands, player hands; craps pass or no pass;
Sic Bo Big or Small ?

I once rolled 56 times without a seven; the odds against this are
27,172.8 to 1.
"Awww, he ain't so shaggy." >:-)
Cheers,
Alan Shank

[Alan Shank]

Post by TeddysDad
What set were you using??..

Post by Alan Shank
I once rolled 56 times without a seven; the odds against this are
27,172.8 to 1.

None.
Cheers,
Alan Shank

[Golfer]

Post by Alan Shank

Post by TeddysDad
What set were you using??..

Post by Alan Shank
I once rolled 56 times without a seven; the odds against this are
27,172.8 to 1.

None.
Cheers,
Alan Shank

Imagine what could have happened with a 7 avoidance set.


Golfer

[Gregg Cattanach]

Post by Raymond Baldwin
As we use to say in Brooklyn, "Hey, not for notin but..." :-)
Back to the practical & mundane, anyone actually witness 50 roulette
red, blacks; baccarat bank hands, player hands; craps pass or no pass;
Sic Bo Big or Small ?
If not , everything considered, why not ?

Because the odds of 50 consecutive reds on roulette (or some other near
50/50 trial) are EXTREMELY small. ((18/38)^50). (or
16,809,491,491,404,623 to 1). However, the point (made about 1000 times
now) is that if you DID see 50 reds in a row, the odds of spin #51 coming up
red is still 18/38.

Gregg C.

[Ion Saliu]

• Point of Relative Certainty
There is no absolute certainty if we are to abide by the rules of Reason…absolutely! Go to the Saliu site and search for 'reason, certainty, randomness.'
This is a more mundane problem. It is a parlor favorite. It is also a favorite reason to put up a fight. Just ask Kotskarr, or Shobolun, or Kulai Parakelsus; or just ask yourself, or myself…
The question goes "If heads did not appear in 10 consecutive coin tosses, is it more likely to come out in the 11th toss?" Many will answer, I mean will shout right away "NOT! NOT! The probability of heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is always ½ or 0.5 or 50%. But that parameter simply represents the number of expected successes in ONE trial; or, the number of favorite cases over total cases.

There is a lot more to a phenomenon such as ‘coin tossing'. For starters, we can analyze coin tossing by calculating the ‘probability of the normal distribution'. The ‘probability of the normal distribution' refers to ‘EXACTLY M successes in N trials'. In this particular case: what is the probability of exactly 0 heads in 10 tosses? What is the probability of exactly 0 heads in 11 tosses?

"The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024"
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we missed heads 10 times in a row. What is the probability to miss heads in the very next toss? That is equivalent to missing heads 11 times in a row!
"The binomial probability of 0 successes in 11 trials
BDF = .00048828125
or .04882812 %
or 1 in 2048"

• https:/saliu.com/keywords/casino.htm

OK. We missed, this rare time, 11 consecutive tosses. What is the degree of certainty to miss heads consecutively in 12 tosses?
"The binomial probability of 0 successes in 12 trials
BDF = .000244140625
or .02441406 %
or 1 in 4096"
If you will, the odds against missing heads in consecutive tosses doubles with each toss. Those casino consultants, and game designers, and executives are not damn idiots! They know how to boost their wealth. They even pay pocket change to all kinds of ghiolbans and tirtans to debate in every conceivable public place. The ghiolbans and tirtans "debate" with ardor that no matter how many times in a row an event has skipped, your odds will remain eternally the same!

If you are stubborn and don't believe the ghiolbans and tirtans, guess what? Them casino consultants, and game designers, and executives (who are not damn idiots, ever!) will even offer players free "gambling systems"! Ever heard of the "Turnaround" system? Read more:
• https://saliu.com/bbs/messages/733.html

I've heard many times that heads can hit an infinity of times in a row; or, miss an infinite number of consecutive tosses! My honest question is, when does that infinity start? I wanna see a beginning, if I were to believe in a certain end. Certain? Say what?

"For only Almighty Number is exactly the same, and at least the same, and at most the same, and randomly the same. May Its Almighty grant us in our testy day the righteous proportion of being at most unlikely the same and at least likely different. For our strength is in our inequities."

Ion Saliu (royalty-name Parpaluck),
Founder of Gambling Mathematics

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper expectations for roulette, baccarat, craps, keno, lotteries; meaning that after a specific number of no-show outcomes then the due number is most likely to appear.
Has anyone heard about an ostensible physics law called 'Point of Certainty'?
Thanks in advance for your kind replies-
RB

The true idiots always boast this characteristic: “The Lizard of Odds Syndrome”. In a nutshell, the syndrome states that “the probability of getting 200 ‘heads’ in a row is always equal to the probability of getting 1 'heads' in a row”. Read more on how you can detect the bullish idiots:

• https://saliu.com/bbs/messages/204.html
• Wizard of Odds, Wizard of Vegas: Fallacy, Idiocy, Mysticism.

The undeniable universal Law states:

• The ‘degree of certainty DC’ rises exponentially with the increase in the ‘number of trials N’ while the ‘probability p’ is always the same or constant.


Ion Saliu,
Founder of Mathematics of Odds

[Ion Saliu]

• Point of Relative Certainty

There is no absolute certainty if we are to abide by the rules of Reason…absolutely! Go to the Saliu site and search for 'reason, certainty, randomness.'

This is a more mundane problem. It is a parlor favorite. It is also a favourite reason to put up a fight. Just ask Kotskarr, or Shobolun, or Kulai Parakelsus; or just ask yourself, or myself…

The question goes "If heads did not appear in 10 consecutive coin tosses, is it more likely to come out in the 11th toss?" Many will answer, I mean will shout right away "NOT! NOT! The probability of heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is always ½ or 0.5 or 50%. But that parameter simply represents the number of expected successes in ONE trial; or, the number of favorite cases over total cases.

There is a lot more to a phenomenon such as ‘coin tossing'. For starters, we can analyze coin tossing by calculating the ‘probability of the normal distribution'. The ‘probability of the normal distribution' refers to ‘EXACTLY M successes in N trials'. In this particular case: what is the probability of exactly 0 heads in 10 tosses? What is the probability of exactly 0 heads in 11 tosses?

You don't need to do all those calculations manually. My probability software SuperFormula.EXE ( https://saliu.com/formula.html ) is a very convenient tool. Select option L (‘At Least' M Successes in N Trials). Select next option 1, since we know the probability p (p=0.5). Type 0 for number of successes M, and 10 for number of trials N. The program responds:

The binomial probability of 0 successes in 10 trials
for an event of individual probability p = .5 is:
BDF = .0009765625
or .09765625 %
or 1 in 1024

Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we missed heads 10 times in a row. What is the probability to miss heads in the very next toss? That is equivalent to missing heads 11 times in a row!

The binomial probability of 0 successes in 11 trials
for an event of individual probability p = .5 is:
BDF = .00048828125
or .04882812 %
or 1 in 2048

We always use the constant p = .5, but the CHANCE to miss heads worsens with the number of tosses! Tell you what, Krushbeck. Those casino consultants, and game designers, and executives are not damn idiots!

Remember last time you lost all your money at the slot machines? You remember that every time you won a flashy-snazzy prompt asked you to "Double your win". Why would the casinos offer you a good chance to double your wins? Isn't the probability the same from one spin to the next? Of course it is. But your chance (degree of certainty) to win consecutively is lower.

The casinos offer you the "opportunity" to double your player's disadvantage. That is, one method for the casino to double the house advantage! That's mathematics. Read more:
• https://saliu.com/keywords/casino.htm

OK. We missed, this rare time, 11 consecutive tosses. What is the degree of certainty to miss heads consecutively in 12 tosses?

The binomial probability of 0 successes in 12 trials
for an event of individual probability p = .5 is:
BDF = .000244140625
or .02441406 %
or 1 in 4096

If you will, the odds against missing heads in consecutive tosses doubles with each toss. Those casino consultants, and game designers, and executives are not damn idiots! They know how to boost their wealth. They even pay pocket change to all kinds of ghiolbans and tirtans to debate in every conceivable public place. The ghiolbans and tirtans "debate" with ardor that no matter how many times in a row an event has skipped, your odds will remain eternally the same!

If you are stubborn and don't believe the ghiolbans and tirtans, guess what? Them casino consultants, and game designers, and executives (who are not damn idiots, ever!) will even offer players free "gambling systems"! Ever heard of the "Turnaround" system? Read more:
• https://saliu.com/bbs/messages/733.html

I've heard many times that heads can hit an infinity of times in a row; or, miss an infinite number of consecutive tosses! My honest question is, when does that infinity start? I wanna see a beginning, if I were to believe in a certain end. Certain? Say what?

• "For only Almighty Number is exactly the same, and at least the same, and at most the same, and randomly the same. May Its Almighty grant us in our testy day the righteous proportion of being at most unlikely the same and at least likely different. For our strength is in our inequities."

Ion Saliu (royalty-name Parpaluck),
Founder of Gambling Mathematics

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper expectations for roulette, baccarat, craps, keno, lotteries; meaning that after a specific number of no-show outcomes then the due number is most likely to appear.
Has anyone heard about an ostensible physics law called 'Point of Certainty'?
Thanks in advance for your kind replies-
RB

• The true idiots always boast this characteristic: “The Lizard of Odds Syndrome”. In a nutshell, the syndrome states that “the probability of getting 200 ‘heads’ in a row is always equal to the probability of getting 1 'heads' in a row”. Read more on how you can detect the bullish idiots:

• https://saliu.com/bbs/messages/204.html
• Wizard of Odds, Wizard of Vegas: Fallacy, Idiocy, Mysticism.

The undeniable universal Law (the famed FFG) states:

• The ‘degree of certainty DC’ rises exponentially with the increase in the ‘number of trials N’ while the ‘probability p’ is always the same or constant.

• N = log (1 - DC) / log (1 - p)
or
• DC = 1 – (1 – p) ^ N


Best of luck from Parpaluck!

Ion Saliu,
Founder of Mathematics of Odds

[Ion Saliu]

Post by Ion Saliu
• Point of Relative Certainty
There is no absolute certainty if we are to abide by the rules of Reason…absolutely! Go to the Saliu site and search for 'reason, certainty, randomness.'
This is a more mundane problem. It is a parlor favorite. It is also a favourite reason to put up a fight. Just ask Kotskarr, or Shobolun, or Kulai Parakelsus; or just ask yourself, or myself…
The question goes "If heads did not appear in 10 consecutive coin tosses, is it more likely to come out in the 11th toss?" Many will answer, I mean will shout right away "NOT! NOT! The probability of heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is always ½ or 0.5 or 50%. But that parameter simply represents the number of expected successes in ONE trial; or, the number of favorite cases over total cases.
There is a lot more to a phenomenon such as ‘coin tossing'. For starters, we can analyze coin tossing by calculating the ‘probability of the normal distribution'. The ‘probability of the normal distribution' refers to ‘EXACTLY M successes in N trials'. In this particular case: what is the probability of exactly 0 heads in 10 tosses? What is the probability of exactly 0 heads in 11 tosses?
The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we missed heads 10 times in a row. What is the probability to miss heads in the very next toss? That is equivalent to missing heads 11 times in a row!
The binomial probability of 0 successes in 11 trials
BDF = .00048828125
or .04882812 %
or 1 in 2048
We always use the constant p = .5, but the CHANCE to miss heads worsens with the number of tosses! Tell you what, Krushbeck. Those casino consultants, and game designers, and executives are not damn idiots!
Remember last time you lost all your money at the slot machines? You remember that every time you won a flashy-snazzy prompt asked you to "Double your win". Why would the casinos offer you a good chance to double your wins? Isn't the probability the same from one spin to the next? Of course it is. But your chance (degree of certainty) to win consecutively is lower.
• https://saliu.com/keywords/casino.htm
OK. We missed, this rare time, 11 consecutive tosses. What is the degree of certainty to miss heads consecutively in 12 tosses?
The binomial probability of 0 successes in 12 trials
BDF = .000244140625
or .02441406 %
or 1 in 4096
If you will, the odds against missing heads in consecutive tosses doubles with each toss. Those casino consultants, and game designers, and executives are not damn idiots! They know how to boost their wealth. They even pay pocket change to all kinds of ghiolbans and tirtans to debate in every conceivable public place. The ghiolbans and tirtans "debate" with ardor that no matter how many times in a row an event has skipped, your odds will remain eternally the same!
• https://saliu.com/bbs/messages/733.html
I've heard many times that heads can hit an infinity of times in a row; or, miss an infinite number of consecutive tosses! My honest question is, when does that infinity start? I wanna see a beginning, if I were to believe in a certain end. Certain? Say what?
• "For only Almighty Number is exactly the same, and at least the same, and at most the same, and randomly the same. May Its Almighty grant us in our testy day the righteous proportion of being at most unlikely the same and at least likely different. For our strength is in our inequities."
Ion Saliu (royalty-name Parpaluck),
Founder of Gambling Mathematics

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper expectations for roulette, baccarat, craps, keno, lotteries; meaning that after a specific number of no-show outcomes then the due number is most likely to appear.
Has anyone heard about an ostensible physics law called 'Point of Certainty'?
Thanks in advance for your kind replies-
RB

• https://saliu.com/bbs/messages/204.html
• Wizard of Odds, Wizard of Vegas: Fallacy, Idiocy, Mysticism.
• The ‘degree of certainty DC’ rises exponentially with the increase in the ‘number of trials N’ while the ‘probability p’ is always the same or constant.
• N = log (1 - DC) / log (1 - p)
or
• DC = 1 – (1 – p) ^ N
Best of luck from Parpaluck!
Ion Saliu,
Founder of Mathematics of Odds

You can get lost easily in public forums like this Usenet group. THERE ARE WAY TOO MANY POSTS!!! The overwhelming proportion of such “scribbles” are nothing more or above garbage, nonsense, one-liner bullshitting, fights, controversies… or a few cryptic numbers meant to “beat” the lottery!

To solve the problem, I created a thread referring to the most relevant articles, materials, debates, systems, fights, etc. I keep it updated and make sure it shows at the top of this Google group:

• https://groups.google.com/forum/?hl=en#!topic/rec.gambling.lottery/TztssQOdv9M
• The Best RGL Posts, Contents: Lottery, Strategies, Systems, Software.

Ion Saliu (royalty-name: Parpaluck),
Founder of Lottery Mathematics
Founder of Lotto Programming Science

• https://saliu.com/lottery3-software.html
• High-Powered Lottery Software for 3-Digit Lotteries.

[Ion Saliu]

• Point of Relative Certainty
There is no absolute certainty if we are to abide by the rules of Reason…absolutely! Go to the Saliu site and search for 'reason, certainty, randomness.'
This is a more mundane problem. It is a parlor favorite. It is also a favourite reason to put up a fight. Just ask Kotskarr, or Shobolun, or Kulai Parakelsus; or just ask yourself, or myself…
The question goes "If heads did not appear in 10 consecutive coin tosses, is it more likely to come out in the 11th toss?" Many will answer, I mean will shout right away "NOT! NOT! The probability of heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is always ½ or 0.5 or 50%. But that parameter simply represents the number of expected successes in ONE trial; or, the number of favorite cases over total cases.
There is a lot more to a phenomenon such as ‘coin tossing'. For starters, we can analyze coin tossing by calculating the ‘probability of the normal distribution'. The ‘probability of the normal distribution' refers to ‘EXACTLY M successes in N trials'. In this particular case: what is the probability of exactly 0 heads in 10 tosses? What is the probability of exactly 0 heads in 11 tosses?
The binomial probability of 0 successes in 10 trials
BDF = .0009765625
or .09765625 %
or 1 in 1024
Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we missed heads 10 times in a row. What is the probability to miss heads in the very next toss? That is equivalent to missing heads 11 times in a row!
The binomial probability of 0 successes in 11 trials
BDF = .00048828125
or .04882812 %
or 1 in 2048
We always use the constant p = .5, but the CHANCE to miss heads worsens with the number of tosses! Tell you what, Krushbeck. Those casino consultants, and game designers, and executives are not damn idiots!
Remember last time you lost all your money at the slot machines? You remember that every time you won a flashy-snazzy prompt asked you to "Double your win". Why would the casinos offer you a good chance to double your wins? Isn't the probability the same from one spin to the next? Of course it is. But your chance (degree of certainty) to win consecutively is lower.
• https://saliu.com/keywords/casino.htm
OK. We missed, this rare time, 11 consecutive tosses. What is the degree of certainty to miss heads consecutively in 12 tosses?
The binomial probability of 0 successes in 12 trials
BDF = .000244140625
or .02441406 %
or 1 in 4096
If you will, the odds against missing heads in consecutive tosses doubles with each toss. Those casino consultants, and game designers, and executives are not damn idiots! They know how to boost their wealth. They even pay pocket change to all kinds of ghiolbans and tirtans to debate in every conceivable public place. The ghiolbans and tirtans "debate" with ardor that no matter how many times in a row an event has skipped, your odds will remain eternally the same!
• https://saliu.com/bbs/messages/733.html
I've heard many times that heads can hit an infinity of times in a row; or, miss an infinite number of consecutive tosses! My honest question is, when does that infinity start? I wanna see a beginning, if I were to believe in a certain end. Certain? Say what?
• "For only Almighty Number is exactly the same, and at least the same, and at most the same, and randomly the same. May Its Almighty grant us in our testy day the righteous proportion of being at most unlikely the same and at least likely different. For our strength is in our inequities."
Ion Saliu (royalty-name Parpaluck),
Founder of Gambling Mathematics

Post by Raymond Baldwin
Hi Everyone,
I understand that there is a fascinating formula on sleeper expectations for roulette, baccarat, craps, keno, lotteries; meaning that after a specific number of no-show outcomes then the due number is most likely to appear.
Has anyone heard about an ostensible physics law called 'Point of Certainty'?
Thanks in advance for your kind replies-
RB

• https://saliu.com/bbs/messages/204.html
• Wizard of Odds, Wizard of Vegas: Fallacy, Idiocy, Mysticism.
• The ‘degree of certainty DC’ rises exponentially with the increase in the ‘number of trials N’ while the ‘probability p’ is always the same or constant.
• N = log (1 - DC) / log (1 - p)
or
• DC = 1 – (1 – p) ^ N
Best of luck from Parpaluck!
Ion Saliu,
Founder of Mathematics of Odds

• There is a new useful feature for reading the Usenet posts in Google Groups. The vast majority of newsgroup members use GROUPS.GOOGLE.COM to post and read on the Internet pioneering service, Usenet.

One drawback of the Google service, very useful otherwise, is the default font. It is a proportional font (of variable-width, that is). However, initially Usenet was written and shown in a monospace font.

Many of the statistical reports I posted did not show up in an acceptable format. The original format was in the typewriter format 9the Courier font). I shall inventory the most important posts in this newsgroup and refer the readers to this important thread. Viewing will be better off overall.

It is quite easy and simple to add this useful feature to two of your browsers: Chrome and Firefox. Just read this axiomatic thread:

• https://groups.google.com/g/rec.gambling.lottery/c/xj1oUsXz5oo?hl=en
• Usenet Redivivus! Best Post Viewing in Google Groups

[Nan]

Certainty only exists in the nature of Godness. Refer to thethe tests I proposed in the year of 2019 with yes/no questions, witnessed and participated in by Nigel.
Nan

[Ion Saliu]

Post by Nan
Certainty only exists in the nature of Godness. Refer to thethe tests I proposed in the year of 2019 with yes/no questions, witnessed and participated in by Nigel.
Nan

Driveling Yak 驅動犛牛

STFU, delirium-tremens-imbecile!
Ce-ai ba, mielu turbat al lu Mnezau and S'nt Ketru? What's with you, rabid lamb of G'd and S'int Keter?

[Nan]

blah blah blah....
how do you approve the non-existence of certainty in quantum entanglement?

[Nan]

certainity tests

https://groups.google.com/forum/m/#!topic/rec.gambling.lottery/pQ8khr0Zcfs