From ???@??? Wed Aug 21 09:37:39 2002

Date: 21 Aug 2002 09:37:39 EDT

From: Gregory Leibon

Subject: At Luarie Snell's request

To: rdellison@netzero.net

Dear Rick D. Ellison,

Laurie Snell has asked me to look over your claims at
http://www.ildado.com/article12.html

as well as a sequence of question you posed him. I must
admit that at first it looked to me that questions you presented where simply a
question of semantics, and not the realm of a mathematician at all.
However after going to the above website I realized the true content of
you questions and am quite intrigued. Please tell me if you think the following
are fair deduction to be made from
your article at http://www.ildado.com/article12.html.

Claim 1: A truly accurate model for roulette will allow a
given spin to be affected by past
spins.

Claim 2:I have devised a method, the 3Q/A procedure, that
gives evidence in support of Claim 1.

Claim 3: I have tried out the 3Q/A procedure 7500 times,
and found

I can produce an expected payment off p =1.0794 per
dollar gambled, as opposed to the usual expected payoff of .9474.

If understand these claims correctly and assume that the
experiment in claim 3 was a controlled experiment (and in particular that you decided
on the 7500 and the 3Q/A strategy before performing the experiment), then the
results are EXTREMELY impressive; and worthy of investigating further Claim 1. In fact, if I am interpreting
your experiment correctly, then your claimed result is no less than 70 standard deviations better than what
would be expected! Under such
circumstances, I would be forced
to accept your that Claim 1 has content, and very interested in attempting to
replicate the experiment in Claim 3.
I ask you the following:

Question: Would say that your experiment was performed in
a controlled manner (at least with
regards to the pair of senses
mentioned above)?

If you could describe to me the experiment, and the
protocol used in performing it, I'd be able to more accurately judge the
evidence

that supports
Claim 1.

Gregory Leibon

From ???@??? Wed Aug 21 20:39:40 2002

Date: Wed, 21 Aug 2002 20:40:35 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory Leibon <Gregory.Leibon@Dartmouth.EDU>

Subject: Re: At Laurie Snell's request

References: <63660521@vixen.Dartmouth.EDU>

Hello Gregory,

Thank you so much for your note. This is exactly the kind
of response I have been seeking for quite some time. I will try to answer all
your questions, and I have some comments also:

Gregory Leibon wrote:

> Dear Rick D. Ellison,

>

> Laurie Snell has asked me to look over your claims
at http://www.ildado.com/article12.html

> as well as a sequence of question you posed him. I
must admit that at first it looked to me that questions you presented where
simply a question of semantics, and not the realm of a mathematician at all.
However after going to the above website I realized the true content of you
questions and am quite intrigued. Please tell me if you think the following are
fair deduction to be made from your article at
http://www.ildado.com/article12.html.

Just a note: the article at my own website at this
address: <http://www.gamble2win.com/thebiglie.htm> is probably more
concise and to the point. I hope you can check it out.

> Claim 1: A truly accurate model for roulette will
allow a given spin to be affected by past spins.

I am not sure what you're saying, but I do claim that
results at a roulette table are influenced by the previous results at that
table, through what I call Statistical Propensity.

> Claim 2:I have devised a method, the 3Q/A procedure,
that gives evidence in support of Claim 1.

Yes. It is one of several pieces of evidence I have to
support the claim above.

> Claim 3: I have tried out the 3Q/A procedure 7500
times, and found I can produce an expected payment off p =1.0794 per dollar
gambled, as opposed to the usual expected payoff of .9474.

I am not a mathematician, so I don't know if those
figures are the correct translation, but the 3qA strategy gives the player a
7.94% edge over the casino (larger than what the casino normally pays itself)
in two samplings of documented roulette spins that exceed 7,500 spins, which
equate to 372 sessions, or 881 bets. And I am quite sure that no other strategy
for roulette could stand up to that many trials.

> If understand these claims correctly and assume that
the experiment in claim 3 was a controlled experiment (and in particular that
you decided on the 7500 and the 3Q/A strategy before performing the
experiment), then the results are EXTREMELY impressive; and worthy of
investigating further Claim 1. In fact, if I am interpreting your experiment
correctly, then your claimed result is no less than 70 standard deviations
better than what would be expected! Under such circumstances, I would be forced
to accept your that Claim 1 has content, and very interested in attempting to
replicate the experiment in Claim 3. I ask you the following:

>

> Question: Would say that your experiment was
performed in a controlled manner (at least with regards to the pair of senses
mentioned above)?

I think my experiment would meet your definition of
'controlled,' because the proof is public information. That is, if you play per
the rules, and use the two prescribed system testers as verification, you will
arrive at the 7.94% figure I mentioned earlier. These system testers are
available to the public.

> If you could describe to me the experiment, and the
protocol used in performing it, I'd be able to more accurately judge the
evidence

> that supports Claim 1.

>

> Gregory Leibon

I would be happy to send you a complimentary copy of my
book (which contains the strategy & rules), along with a copy of the 3qA
Verification Statistics, which are meant to be accompanied by two published
system testers, which are now in circulation. We can also discuss perhaps the
lending of those system testers, so you can see that the numbers add up.

I hope this answers your questions for now. Thank you so
much for taking the time to look at this, and to write (using email), and for
your courtesy in writing.

Rick D. Ellison

From ???@??? Thu Aug 22 12:04:43 2002

Date: 22 Aug 2002 12:04:43 EDT

From: Gregory Leibon

Subject: My mailing adress

To: rdellison@netzero.net

--- You wrote:

<http://www.gamble2win.com/thebiglie.htm> is
probably more concise and to the point. I hope you can check it out.

--- end of quote ---

At this website, I think you understate a bit the results
of your 3Q/A experiment. The
current MODEL of phenomna, like the game of roulette, includes the HYPOTHESIS that the events are independently
determined. ( Though I'm
using this term as a mathematician, which is quite distinct from how you use
it. Especially judging from
comments like "And anything that moves in a predictable fashion

cannot be
independent"; since, to a mathematician, independent events behave in some of the most dramatically
predictable ways imaginable - things like the central limit theorem , weak law
of large numbers, law of the iterated logarithm, etc... This is perfectly alright with us, and, in fact, it's what makes
independently produced events so interesting to study.) As a mathematician am interested
in models that predict the outcomes of experiments, and not in arguing about
what the word independent should mean.
Hence my interest in your work is that your 3Q/A evidence suggest that this usual MODEL is flawed,
and, in particular, that the independence HYPOTHESIS may need to altered to
more accurately capture the results of experiments. This would be a truly
incredible discovery, and not just some semantics game.

--- You wrote:

I would be happy to send you a complimentary copy of my
book (which contains the strategy & rules), along with a copy of the 3qA
Verification Statistics, which are meant to be accompanied by two published
system testers, which are now in circulation. We can also discuss perhaps the
lending of those system testers, so you can see that the numbers add up.

--- end of quote ---

I look forward to seeing this material.

Gregory Leibon

Department of Mathematics

6188 Bradley Hall

Dartmouth College
Hanover, NH 03755-3551

From ???@??? Thu Aug 22 21:17:10 2002

Date: Thu, 22 Aug 2002 21:18:00 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory Leibon <Gregory.Leibon@Dartmouth.EDU>

Subject: Re: My mailing adress

References: <63710874@vixen.Dartmouth.EDU>

Hello,

Thank you for writing. I will put copies of the book
& booklet in the mail tomorrow.

Regarding the issues of definitions, I think that was Mr.
Snell's doing. I spent months trying to convince him that my phrasing was the
standard argument, held dear by virtually every gaming author. But he kept
challenging the basic premise, and tried to re-write it in a way that stripped
out all its meaning. So we had to go down the road of making sure we concurred
on our definitions. He never gave me a chance to convey that I could have
forwarded emails to him, sent to me by over a dozen top-selling gaming authors,
who all concurred on the definition I offered. And/or, I could have directed
him to the exact pages of published books, where he would find the same thing.
For reference, what they all say is that table events at roulette are
independent because the wheel has no memory. That is the sum and substance

of their argument. And I'm saying that the wheel was
constructed to perform a task that simulates memory, which removes the only
supporting ledge upon which the "independent events" argument stands!

I look forward to continuing our dialogue. You sound like
you are truly interested in the subject matter, and that is a refreshing chance
from what I've been dealing with to date. Much obliged!

Rick D. Ellison

Gregory Leibon wrote:

> --- You wrote:

> <http://www.gamble2win.com/thebiglie.htm> is
probably more concise and to the point. I hope you can check it out.

> --- end of quote ---

> At this website, I think you understate a bit the
results of your 3Q/A experiment. The current MODEL of phenomna, like the game
of roulette, includes the HYPOTHESIS that the events are independently
determined. ( Though I'm using this term as a mathematician, which is quite
distinct from how you use it. Especially judging from comments like "And
anything that moves in a predictable fashion

> cannot be independent"; since, to a mathematician,
independent events behave in some of the most dramatically predictable ways
imaginable - things like the central limit theorem , weak law of large numbers,
law of the iterated logarithm, etc... This is perfectly alright with us, and,
in fact, it's what makes independently produced events so interesting to
study.) As a mathematician am interested in models that predict the outcomes of
experiments, and not in arguing about what the word independent should mean.
Hence my interest in your work is that your 3Q/A evidence suggest that this
usual MODEL is flawed, and, in particular, that the independence HYPOTHESIS may
need to altered to more accurately capture the results of experiments. This
would be a truly incredible discovery, and not just some semantics game.

>

> --- You wrote:

> I would be happy to send you a complimentary copy of
my book (which contains the strategy & rules), along with a copy of the 3qA
Verification Statistics, which are meant to be accompanied by two published
system testers, which are now in circulation. We can also discuss perhaps the
lending of those system testers, so you can see that the numbers add up.

> --- end of quote ---

>

> I look forward to seeing this material.

>

> Gregory Leibon

> Department of Mathematics

> 6188 Bradley Hall

> Dartmouth College Hanover, NH 03755-3551

From ???@??? Mon Sep 2 17:20:48 2002

Date: 02 Sep 2002 17:20:48 EDT

From: Gregory Leibon

Subject: Re: Confirmation requested

To: rdellison@netzero.net

--- You wrote:

Can you
please confirm receipt?

--- end of quote ---

I did, and thank you. I have been out of town for a while
and have not had a chance to look through the materials yet. I will get back to
you as soon as I get chance to look through your book.

----You Wrote

I would also like to hear your comment on what I said at
the end of the

second paragraph of my message of August 22 (regarding
the accepted

definition of independent events at casino games).

--- end of quote ---

I assume you are referring to the following

----You Wrote

what they all say is that table events at roulette are
independent because the wheel has no memory. That is the sum and substance

of their argument. And I'm saying that the wheel was
constructed to perform a task that simulates memory, which removes the only supporting
ledge upon which the "independent events" argument stands!

--- end of quote ---

As I understand it, I disagree with this argument. However in your description it is not
clear what is meant by "independent events", so perhaps this is why
we disagree. In order to
eliminate this possibility, I will now describe a mathematician's view of
independence (also this will allow you more easily follow the below paragraph, where I describe my problems with the above reasoning). A
mathematician's articulation of the
independence hypothesis: Experiments A and B are independent means that
the probabilities with which
experiment A takes on its possible outcomes does not depend on the out comes of experiment
B.

The memoryless property is traditionally utilized in modeling roulette by requiring, in the model, that the outcome of the
"experiment" of spinning a roulette wheel is independent of the outcomes of previous spins, in the above
sense. This is an extremely rigid property, and
conforming to it forces phenomena to behave in incredibly rigid ways (like the
weak law of large numbers, etc..).
One should NOT think of the memoryless property as saying that we know
nothing about the out come of an event, it saying quite the opposite: we are claiming to know the exact probabilities with which the
experiment will take on its
possible outcomes - which is an ENORMOUSLY rigid assumption. I certainly do not see any conflict between obeying these laws (which I
believe you refer as a "simulation of memory") and the independence hypothesis. In fact, quite the opposite: to a
mathematician, these rigid laws (the "simulation of memory") are born
of the independence hypothesis.
Quite literally the laws of
probability follow DUE to the
mathematical articulation of the independence hypothesis - not in spite of it!

What
interest me about your roulette experiment is that it suggest that utilizing
the above independence hypothesis is NOT a good way to model roulette, which
would shake the very foundation of how to apply probability to the world. If so, your discovery of this phenomena
would rank among the greatest scientific discoveries of all time. I admit that I am
sceptical, but I sincerely hope that my scepticism proves unfounded, and that
your experiments can be replicated under controlled circumstances (which I hope
to soon have time to implement).

Sincerely,

Gregory Leibon

From ???@??? Mon Sep 2 13:13:05 2002

Date: Mon, 02 Sep 2002 13:14:06 -0400

From: "R.D. Ellison" <rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: Confirmation requested

Hello Gregory,

You should have received the parcel containing my two
books about a week

ago. Can you please confirm receipt? Also, please let me
know if you

would like to borrow the reference books I mentioned in a
previous

message.

I would also like to hear your comment on what I said at
the end of the

second paragraph of my message of August 22 (regarding
the accepted

definition of independent events at casino games).

Thank you for your time. Sincerely,

Rick D. Ellison

From ???@??? Fri Aug 23 16:33:45 2002

Date: Fri, 23 Aug 2002 16:34:42 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: Parcel

Hello,

The parcel containing my book and booklet was sent out
this morning by

priority mail. You should be receiving it early next
week.

I wanted to comment on my last message. I try to answer
all my emails

each night, but having a dial-up connection, I have only
a 15-minute

window to do so before I get bumped offline. So, my
attempt to give you

an honest appraisal of what had previously occurred was
hastily composed

and did not adequately reflect my appreciation for Mr.
Snell‚s efforts

to help me. I hope you will overlook this. Thanks again
for your help.

Sincerely,

Rick D. Ellison

From ???@??? Mon Sep 2 21:48:34 2002

Date: Mon, 02 Sep 2002 21:48:51 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: probability and predestination

Hello,

Thank you so much for taking the time to articulate those
thoughts. This

is precisely the type of interchange I have been hoping
for. I only wish

I understood „mathspeak‰ a little better.
Every so often a word comes up

that raises questions as to how it should be interpreted.
So, let me

start with what I think I understand. Please forgive me
if I

misinterpret your intent.

I‚m not sure I agree that a 1 in 38 probability
represents a rigid

property or assumption. If we agree that a miscast ball
is disqualified

from consideration, then the ball has to land in one of
those 38 slots.

Your use of the term „exact probabilities‰
tends to make it sound like

we can pin an event down to one number, when in fact the
entire field of

38 is understood to be possible.

Also, I question the sentence: „Quite literally the
laws of probability

follow due to the mathematical articulation of the
independence

hypothesis ˆ not in spite of it.‰
Independence, as I understand it,

means free from influence. Conversely, probability
implies

predestination; that is, that a certain behavioral
pattern is expected

to occur. How can an event that is considered to be
predictable also be

described as „free from influence‰? The two
concepts conflict.

One of the reasons I‚m raising these questions is
observations made over

a period spanning two decades, which have led me to
understand more

clearly (than most) how these numbers behave in large
groups. One

observation I‚ve made is that no even-chance
proposition seems to be

capable of winning as many as 30 consecutive decisions.
Not once, ever.

Another, is that in ANY sampling of 300 roulette spins
(for example),

ALL numbers will have come up at least once. This will
happen every

time, without exception. From these and other examples I
could offer, I

think it can be safely deduced that this
Œevening-out process‚ is not

merely a persistant coincidence, as the
Œindependence guys‚ would have

us think. Instead, the behavior of these numbers is
influenced by the

equivalent of a countdown that adjusts itself with every
spin of the

wheel. This is the only explanation I know of, that
doesn‚t lead to

conflict or contradiction somewhere along the continuum
of the

independence premise.

Thanks again for your help. You are very kind, and your
efforts are very

much appreciated!

Sincerely,

Rick D. Ellison

From ???@??? Tue Sep 3 16:12:41 2002

Date: 03 Sep 2002 16:12:41 EDT

From: Gregory Leibon

Subject: Re: probability and predestination

To: rdellison@netzero.net

--- You wrote:

$E3exact probabilities$E4 tends to make it sound like

we can pin an event down to one number, when in fact the
entire field of

38 is understood to be possible.

--- end of quote ---

Exactly the opposite. Exact probabilities in this setting is the claim that EACH of the

38 possibilities is EQUALLY likely, an extremely rigid
assumption. Different real world experiments may or may not respect such an assumption.

--- You wrote:

Independence, as I understand it,

means free from influence. Conversely, probability
implies

predestination; that is, that a certain behavioral
pattern is expected

to occur. How can an event that is considered to be
predictable also be

described as $E3free from influence$E4? The two concepts
conflict.

--- end of quote ---

No.
Independence to a mathematician, is exactly the claim in the previous
e-mail (which resembles the above claim
but only in a certain naive senses). In particular, one assumes that
they have an understanding of the probabilities of a given experiment,
regardless of its dependence or independence of other experiments. Like all events, independent events are
assumed to experience the above
sense of "predestination", and there would be no notion of
probability at all if events in
the real world did not often mimic
this assumption. If you wish to familiar your self with the
mathematician view of these notion I highly recommending looking over Laurie's
book at

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html

--- You wrote:

One

observation I$E2ve made is that no even-chance
proposition seems to be

capable of winning as many as 30 consecutive decisions.

--- end of quote ---

Using standard probabilistic results you could only
rightfully hope see such a streak
to occur if you
performed around 10 billion
consecutive even odds experiments! Furthermore it would be hopelessly unlikely
if you only performed say a
million (then you would expect to see a longest streak of about 17-23), to see such a streak . I'm not sure how to evaluate your
claim, since I'm not sure what magnitude of experiments your talking
about. The expected size of a longest streak in N experiments is
"usually" in
[log(N/2)/log(2)-2,log(N/2)/log(2)+4]. So you can use your own estimate of the number experiments,
N, that you feel you have witnessed in order to see how long of a streak you
should have expected to see.

(I found these estimetes in the excellent article : Mark F. Schilling, The Longest Run of
Heads, Coll. Math. J. 21 (1990), 196-207.
This article is actually not ridiculously "mathy", and you may
enjoy it. )

--- You wrote:

Not once, ever.

Another, is that in ANY sampling of 300 roulette spins
(for example),

ALL numbers will have come up at least once. This will
happen every

time, without exception.

--- end of quote ---

Using the standard independence model, the probability of
this happening is about 1 in 3,000.
How many experiments have you tried? You would need to have performed more than 3,000 such 300 run experiments before such a claim would have a statistical
significance.

--- You wrote:

Instead, the
behavior of these numbers is influenced by the

equivalent of a countdown that adjusts itself with every
spin of the

wheel.

--- end of quote ---

In order to evaluate such a claim would I would need to note the scope of the
above experiments (i.e. the approximate number of even odd experiment N and the
number M of 300 spin experiments that you have witnessed.) If N < 10 billion or

M not a fair bit more than 3,000 then your claims would support rather than
contradict the independence hypothesis! Also, in the future, always provide an estimate of you
experiment sizes so that I can accurately evaluate the experiment's meaning.

Sincerely,

Gregory Leibon

From ???@??? Wed Sep 4 22:51:01 2002

Date: Wed, 04 Sep 2002 22:25:52 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: Reply to message of Sept 3

Hello,

Regarding your email message of 9-3-02: questions,
comments, and

observations:

1) Thank you for directing my attention to Laurie‚s
book. I was not

aware he was published. I have ordered a copy through the
AMS (online)

bookstore.

2) How can I get a copy of the article by Mark F.
Schilling you

mentioned?

3) Regarding my Œprobability implies
predestination,‚ to which you

replied that it is not unusual for independent events to
mimic this

assumption. . .I think what I said still stands. There is
a big

difference between a chance copycat occurrence and a
predetermined

expectation.

4) One point I am trying to convey was stated on page 5
of the book I

sent to you. The second paragraph poses the question: do
you think it

would be possible for a given roulette table to fail to
produce the

number 5 (for example) in twenty million spins? This is
the big flaw in

the Œindependence‚ argument: we both know that
no roulette table will

ever skip over a number for that long, don‚t we?
And yet, if there is

not a force in the world that makes the number 5 come up,
then there

would be times when it would never come up! That
'non-event' would in

itself be a chance occurrence!

As Frank Barstow said in his book, Beat the Casino (page
28), 'Dice and

the wheel are inanimate, but if their behavior were not
subject to some

governing force or principle. . .there could be no games
like craps or

roulette, because there would be no way of figuring
probabilities and

odds.'

What I‚m getting at, is that we need to take this
thought to the next

level, where you question things like whether
probabilities CAN be

assigned, in the first place, to independent events. I
agree with Mr.

Barstow in saying that we can‚t expect
nonconforming events to be pinned

down to a precise expectation.

Please also bear in mind that the theoretical math
you‚re using to

challenge my points is the same theoretical math that I
claim to be at

least partially invalid. But I prefer to avoid making
assumptions, and

am very much enjoying our dialogue! Thank you.

PS: Please correct any misinterpretations I may have
made.

R.D. Ellison

From ???@??? Thu Sep 5 09:01:40 2002

Date: 05 Sep 2002 09:01:40 EDT

From: Gregory Leibon

Subject: Re: Reply to message of Sept 3

To: rdellison@netzero.net

--- You wrote:

do you think
it

would be possible for a given roulette table to fail to
produce the

number 5 (for example) in twenty million spins? This is
the big flaw in

the independence$E2 argument: we both know that no
roulette table will

ever skip over a number for that long, don$E2t we?

--- end of quote ---

We do and we do not. One of us believes it is impossible
and the other believes it to be incredibly unlikely. Under the independence
hypothesis this could conceivably
occur. I do not feel this is a
flaw in the hypothesis since it gives a chance of only

(1-1/38)^(20000000), which is an INCREDIBLY remote! So we
would all agree that in practice for a fair roulette wheel to suffer such a
phenomena would be
astonishing, though, we would
phrase the situation differently.
I would say that the chances of this occurring are so slim that we can expect
that it will never occur in the world; I would certainly NOT say that it
inconceivable (only that it is incredibly unlikely). In practice, maybe only a mathematician would think of
(1-1/38)^(20000000) as not equal to zero, but from a philosophical point of
view this is a serious discrepancy between your belief and utilizing the
independence hypothesis.

In part, because how do you set the cut off between
extremely rare events that you consider impossible and extremely rare event
that you simply consider extremely rare.

--- You wrote:

where you question things like whether probabilities CAN
be assigned

--- end of quote ---

Indeed this is a reasonable question. Much more so in other settings (like
quantum mechanics and finance), but it has little to do with the independence
hypothesis. If you'd like to
see a beautiful introduction of how to actually analyze games WITHOUT utilizing
the conventional wisdom about probabilities, I highly recommend looking at the
introduction to Probability and
Finance: It's Only a Game!

by Shafer and Vovk at

http://www.cs.rhul.ac.uk/~vovk/book/

You might
like this approach to probability better than the conventional approach, since
its mathematical articulation is much closer to philosophical roots. It allows one to make sense of
statements like "rare event don't occur" in sound way. You might also like chapter 2
where various issue concerning the philosophical foundations of probability are
addressed in a beautifully crafted historical context.

--- You wrote:

Please also bear in mind that the theoretical math
you$E2re using to

challenge my points is the same theoretical math that I
claim to be at

least partially invalid.

--- end of quote ---

Perhaps I misunderstood your argument. It sounded to me as though you were
attempting to find data that was inconsistent with this "theoretical math", and, in particular, with
its independence hypothesis. If you were, then I was simply pointing out that your evidence was, in fact ,
completely consistent the conventional beliefs and tools. Hence it gives one no reason to
look for alternative tools. If you want to change the way people think about
these thing you will need a replicable experiment that actually produces
results inconsistent with
those expected utilizing
conventional techniques. The data
in your previous e-mail certainly did not do this.

Once again, I am not a philosopher and I am really only
interest in discussing philosophical aspect of probability if there is DATA
that suggest such a discussion has value.
Your anecdotal data certainly did not qualify as such, and I was merely
attempting to explain why.

--- You wrote:

2) How can I get a copy of the article by Mark F.
Schilling you

mentioned?

--- end of quote ---

I would be happy to mail you a copy. Please send me your mailing address.

Gregory Leibon

From ???@??? Fri Sep 6 10:57:29 2002

Date: Fri, 06 Sep 2002 10:58:20 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: contradictions

Hello,

As I understand it, you wish to avoid a philosophical
debate, and

concentrate on the facts. That would be my choice as
well, if it were

practical. But our discussion has already taken us to an
example that

would require more than a lifetime of data accumulation.
For example, my

last letter posed a question for which you offered
(1-1/38) ^ (20000000)

as the answer. I don‚t know what that works out to,
but the problem is,

neither of us could ever aspire to witness such an event.

For the moment, it would seem to be more fruitful for us
to focus on the

contradictions I perceive in the existing theory. This is
not exactly

philosophy. It is a quest for a logical explanation.

In my last letter, I questioned whether probabilities can
be assigned to

something as random and unstructured as Œindependent
events.‚ You

granted that it was a reasonable question, but I could
find no answer in

your reply. You also wrote that it has little to do with
the

independence hypothesis, but offered no reason for that
view. I am ready

for your answer now.

Regarding the contradictions I mentioned: as I understand
it, gaming

authors, statisticians and math experts alike all agree
that, given a

large enough sampling, any group of unbiased numbers
(that have been

formally assigned a statistical expectation) will
ultimately conform to

that expectation. My question is, how do they do that in
the absence of

a compelling force? In a controlled environment where a
statistical

certainty is involved, there has to be a cause, and an
effect. The

effect is that the numbers conform to a statistical
expectation. Are you

saying there is no cause? That this is willy-nilly random
chance that

conforms solely through unabated coincidence?

Thank you for your time. I really appreciate your
efforts.

Sincerely,

Rick D. Ellison

PS: I was unable to get through to the latest website you
referred me

to, but I will keep trying.

From ???@??? Sat Sep 7 12:56:36 2002

Date: 07 Sep 2002 12:56:36 EDT

From: Gregory Leibon

Subject: Re: contradictions

To: rdellison@netzero.net

--- You wrote:

For the moment, it would seem to be more fruitful for us
to focus on the

contradictions I perceive in the existing theory. This is
not exactly

philosophy. It is a quest for a logical explanation.

--- end of quote ---

If you want logical explanation, this is easy
enough. Any standard probability
text will show you how the laws of averages, etc.. are consistent, and in fact
derivable from, a set up that assumes the independence hypothesis. This is not a simple or intuitive
thing, but you will find it done very nicely in Laurie's text. In particular, there you will see that
there is no contradiction in assuming the usual independence hypothesis,

though this hypothesis is perhaps unlikely to capture
your definition of independence.
You should read Laurie's text and decide for yourself.

--- You wrote:

Regarding the contradictions I mentioned: as I understand
it, gaming

authors, statisticians and math experts alike all agree
that, given a

large enough sampling, any group of unbiased numbers
(that have been

formally assigned a statistical expectation) will
ultimately conform to

that expectation. My question is, how do they do that in
the absence of

a compelling force?

--- end of quote ---

This is highly dependent on the sense in which you mean
conform.

Once again the sense in which a mathematician means this
is standard, and I can not do it justice in an e-mail correspondence; since it
is a little involved. Fortunately
I don't have to, since, in chapter
8 of Laurie's book, you can
explicitly see that such a compelling force most certainly can and does
exist, in the presence of the
standard in independence hypothesis.
In fact, your proposal would probably have it conform too well. It is known that if you flip a fair coin N times that it very unlikely that
the number of heads that shows up,H, to be too close to N/2 ( of course H/N
will be near 1/2 but the H will NOT be near N/2). In fact, the number of heads
will satisfy the normal distribution, see Laurie's chapter 9, at least in the presence of the independence
hypothesis. The normal distribution would be unlikely to arise if one removed the independence
hypothesis, as you propose; however it is well known that actual statistics conform very well to
this normal distribution.

--- You wrote:

Are you

saying there is no cause? That this is willy-nilly random
chance that

conforms solely through unabated coincidence?

--- end of quote ---

No. As in
the previous e-mail , this is due to the fact that we believe there is some

underlying tendency that is articulated as a
probability. For example, for a
fair coin, if

we assume that the coin has the same chance of coming up as heads as it does of
coming up tails when flipped, together with the independence hypothesis, then
the law of averages follows logically.
This is carefully done in any book on probability, and in particular in
Laurie's book (chapter 8).
Since you don't like this assumption...

--- You wrote:

I questioned whether probabilities can be assigned to

something as random and unstructured as independent
events.$E2 You

granted that it was a reasonable question, but I could
find no answer in

your reply. You also wrote that it has little to do with
the

independence hypothesis, but offered no reason for that
view. I am ready

for your answer now.

--- end of quote ---

Your question is reasonable, from a certain point of
view, and invite to look at Vovk's
and Shafer's book to see what this point of view is. Their arguments are much to involved to discuss over e-mail,
but are very nicely expressed in there treatise. You should
decide for yourself whether the ideas there are of interest to you. Here is
another address were you can find their book (I hope this one works).

http://www.cs.rhul.ac.uk/home/vovk/book/

Gregory Leibon

From ???@??? Sat Sep 7 12:15:42 2002

Date: Sat, 07 Sep 2002 12:16:35 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: my postal address

Hello,

I neglected to include my mailing address in my last
message, as had

been previously discussed. It is:

Rick D. Ellison

P.O. Box 27429

Cincinnati, OH
45227

Thank you for your kind offer to forward that article to
me. L8er,

Rick

From ???@??? Sun Sep 8 09:51:32 2002

Date: Sun, 08 Sep 2002 09:52:30 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory.Leibon@Dartmouth.EDU

Subject: cause & effect (reprise)

Hello,

Thank you for your email of 9-7-02. I am sorry to say, I
was unable to

find a straightforward answer to any of my questions. So,
I guess I will

have to keep probing.

You wrote:

. . .though this hypothesis is perhaps unlikely to capture
your

definition of independence.

And also wrote:

This is highly dependent on the sense in which you mean
conform.

I do not have personal interpretations for the words I
use. My

definitions concur with whatever is in the dictionary. In
this context,

the applicable definition of the word independent is
<free from the

influence, guidance, or control of another or others>
and for the word

conform, it is <to be in accord or agreement; to
comply> These were

derived from the American Heritage College Dictionary. Do
we concur on

these definitions? This must be established.

Regarding the <cause and effect> issue, I had asked
if your position was

that there is no <cause> to the <effect> that
numbers conform to their

inherent statistical expectations.

You wrote:

. . .this is due to the fact that we believe there is
some underlying

tendency that is articulated as a probability.

That right there is the heart of the issue, but you have
stopped short

of the mark. You need to take your explanation at least
one step

further. There has to be a CAUSE for that underlying
tendency. It

doesn‚t just pop up out of nowhere and exist for no
reason. There has to

be a driving force that makes it happen. What is the
cause of this

<underlying tendency>?

I am not sure my budget can justify the expenditures
involved in these

very expensive books you defer to ($90 + shipping for the
latest),

because I happen to believe that the philosophies therein
are built upon

a flawed premise. The fact that you seem unable to
summarize the

arguments contained therein tends to confirm that belief.
So, please

don‚t take offense if I ask you to try to
encapsulate each argument so

that I can receive something that resembles a direct
response to my

queries.

Again, thank you very much for your time. Sincerely,

Rick D. Ellison

From ???@??? Sun Sep 8 11:28:34 2002

Date: 08 Sep 2002 11:28:34 EDT

From: Gregory Leibon

Subject: Re: cause & effect (reprise)

To: rdellison@netzero.net

--- You wrote:

Do we concur
on

these definitions? This must be established.

--- end of quote ---

The American Heritage College Dictionary

certainly will certainly not do if you wish to have a
logical debate! A dictionary definition has many distinct interpretations, and
much more often than not, I find,
any argument utilizing such definitions will be wholly semantic; hence
not interesting to me (at all). If
you are going to discuss

these topics with a mathematician, or hope to make
logical conclusions via the use of such definitions, you must precisely articulate the use of your terminology. For example, utilizing the
mathematician's definition of
independence (see page 130
of Laurie's book) the following
events are independent: Suppose we have a fair coin, that produces a head or
tail when flipped. Let A be the
event that the first toss is a head and

B be the event that the two tosses are the same. The A and B are independent! Clearly the ou come of A
"influences" the outcome of B, but the probabilities of the
associated outcomes do not depend
on each other, and this IS the mathematician's definition. This is the notion of
independence that is used by statistician when articulating the law of large
numbers, etc.. . Ask
yourself: Do you think it agrees
with your definition? If not then
our argument would only be about semantics (meaning our view of these
definitions) and not about the content of our arguments.

--- You wrote:

There has to
be a CAUSE for that underlying tendency.

--- end of quote ---

This is not the realm of a mathematician, but if you need a CAUSE, then the cause
could be that there really IS some
underlying tendency that is articulated via a probability. In the world this tendency could
be born in many ways. In terms of gaming, one has the standard
argument that it is too complicated to set up initial conditions that
allow one to predict the outcome, hence it is "reasonable" to view
all the outcomes as equally likely.
This will automatically imply ("cause") the numbers to behave as the laws of
probability indicate, and has been very accurately confirmed
exprimentally. If you control the
initial conditions, then indeed this hypothesis is no longer
"reasonable" and such a model
would not be utilized. (I
should say in places like quantum mechanics it is believed that this tendency
IS an actual physical phenomena, not born simply of an inability to keep track
of the appropriate initial conditions; but in gaming situations the above
justification is, I believe, the
standard one.)

--- You wrote:

So, please

don$E2t take offense if I ask you to try to encapsulate
each argument so

that I can receive something that resembles a direct
response to my

queries.

--- end of quote ---

Such a debate
would only be on a semantic level until we agree on a precise use of
terminology. As seen above we are no where even remotely near such a
state. If you want to argue
semantics over e-mail, then I suggest finding someone involved in the
philosophy of probability; this does not interest me. If you want to have a conversation with a
mathematician on these topics you will need to see how we articulate these
notions so you can point out at
which point you feel these interpretations are bad, and propose how to modify
them. Then these
modifications can be implemented and compared to experiment. Laurie's book is free on line (at
the address I gave you), and reading it might put you in position to have such
a dialog. Also I believe my refusal is justified since, when I teach
probability these argument take at 15 lectures to demonstrate! Since they are standard (and available
for free online!) I refuse to communicate them over e-mail. I apologize that Vovk's book is so expensive,
you might want to check and see if
your local library has a loan system. Also, when I point out references which I claim state my position much clearer than I
could via an e-mail communication, I mean it! These are good references
(especially Laurie's book - which is, after all, free!), and hope that you will
look them over carefully before our next communication. Once my apologies that I am a
mathematician and not even a wee bit of a philosopher.

Gregory
Leibon

From ???@??? Sun Sep 8 16:32:53 2002

Date: Sun, 08 Sep 2002 16:32:57 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory Leibon <Gregory.Leibon@Dartmouth.EDU>

Subject: clarifications

Hello,

Thank you again for your latest email.

I would like to start out by saying that I appreciate
your forbearance

in a situation that is probably as frustrating for you as
for me. Please

bear with me. I believe we are on the verge of a mutual
discovery that

may benefit the scientific community.

I want to respect your suggestion that I partake of the
reading material

before we proceed, but there are clarifications I can
make at this time,

that do not call for that need. These are:

You wrote:

If you are going to discuss these topics with a
mathematician, or hope

to make logical conclusions via the use of such
definitions, you must

precisely articulate the use of your terminology.

These were noted in my last letter. I will repeat:

Independent ˆ free from the influence, guidance, or
control of another

or others.

Conform: to be in accord or agreement; comply.

This is what I believe these words to mean. If you feel
these

definitions need to be amended or expanded to be made
suitable for a

mathematical application, by all means do so. The answer
you offered, I

am sorry to say, did not make sense to me. You made an
opening statement

and then drew a conclusion, without explaining its
relevance, or how it

was derived.

To my claim that there has to be a cause for the
underlying tendency,

you wrote:

In terms of gaming, one has the standard argument that it
is too

complicated to set up initial conditions that allow one
to predict the

outcome, hence it is "reasonable" to view all
the outcomes as equally

likely.

That reply raises many questions, and does not explain
the cause.

Perhaps, instead, you can answer this question for me: is
there a

compelling force behind this underlying tendency, or not?
If Yes, what

is the source of this compelling force? If No, how can it
exist in the

absence of a reason to exist?

By the way, I looked for both the expensive books in the
main library

downtown. They are not on record. I did, however, learn
that Laurie

apparently wrote four other books from 1960-1966.

As I am sure you have a demanding schedule, please take
your time in

replying. Thank you.

Sincerely,

Rick D. Ellison

From ???@??? Sun Sep 8 22:54:53 2002

Date: Sun, 08 Sep 2002 22:55:52 -0400

From: "R.D. Ellison" <rdellison@netzero.net>

To: Gregory Leibon <Gregory.Leibon@Dartmouth.EDU>

Subject: Two breakthroughs!

Hello!

We have just had two breakthroughs. The first is that I
now understand

most of what you wrote. It took many readings, but it now
makes sense

(to me). You are saying that the numbers conform through
mans perception

of those numbers. No no no. MAN is merely the observer.
No amount of

wishing on the mans part is going to influence what the
numbers do. It

happens through the numbers themselves. The numbers are
the ones doing

the work. Which brings us to the second breakthrough: I
am positive that

the quantum mechanics angle is the applicable argument.
This is a

physical phenomenon that is created through the
craftsmanship of the

device (e.g., roulette wheel), or the fairness of the
trial environment

(e.g., flip of a fair coin).

That was the stumbling block. Do you see it now?

R.D. Ellison

From ???@??? Mon Sep 9 10:09:44 2002

Date: 09 Sep 2002 10:09:44 EDT

From: Gregory Leibon

Subject: A summary of the standard argument

To: rdellison@netzero.net

--- You wrote:

You are saying that the numbers conform through mans
perception

of those numbers.

--- end of quote ---

Perception plays a role but the statement GREATLY
distorts the argument. I will now
try and explain it carefully, in hopes that it will clarify the standard
position.

In order to justify me putting any more time into this I
ask permission to use any of our e-mail communications for pedagogical
purposes. If I'm going to put
energy into carefully restating standard arguments then I want to be able to archive these debates and
utilize in them in the future. Is
this acceptable to you?

back to the argument... It would be much more accurate to
say the numbers conform BECAUSE of man's lack of precision (though such a position should be
restricted to a setting that resembles the gaming world). It is conventional
in the gaming situation to view the situation as not inherently random
(one would take the opposite view in the quantum mechanics setting), but rather
as modeling a lack of precision. A
good view of the standard working hypothesis would be something along these
lines...

WORKING HYPOTHESIS: " The spinner lacks the precision necessary to make a spin obey
any laws other than those that
follow logically from the belief
that all the outcomes are equally
likely with respect to in a given spin and the outcome of any spin is
independent of the outcomes of any
other spins."

Note: this hypothesis utilizes the notion of independence
I defined in our previous correspondence (or equivalently the one from Laurie's
book), not the dictionary definition, which fits the above well, but could lead to meaningless semantic debate.

A careful articulation of "the belief that all the outcomes are equally likely with
respect to in a given spin and the outcome of any spin is independent of the outcomes of any other spins"
is accomplished in Laurie's book (or any book on probability).

About the hypothesis: You are FREE to reject this
hypothesis and of course in many situations it will fail.

For example,
if the spinner is utilizing a roulette wheel or a spinning technique
that is rigged in some way then this hypothesis fails. It is justified in standard gaming situations in two
steps. The first is that it is believed,
with very compelling physical evidence,
that the final position of the ball is INCREDIBLY sensitive to the
initial

position and velocity of the spin; and it is also
believed that any spinner you
would choose to deal with would not put in the effort necessary, or naturally
be consistent enough, to reproduce such sensitive initial conditions. Secondly, via an application of Occum's
razor, if the initial conditions cannot be replicated then all the outcomes should be viewed as
equally likely with respect to a given spin, and the outcome of any spin should
be viewed as independent of the
outcomes of any other spins. As any application of Occum's razor, this is not a precise argument but
rather a commonly accepted and wildly beneficial vantage point. Namely utilizing the next
CONCLUSION one find that real numbers behave as if this hypothesis is true.
Note: Since such an argument is based on Occum's razor, I have NO URGE to argue this hypothesis unless there
is DATA suggesting that the following conclusion is false in a setting where the hypothesis seems reasonable
to me.

CONCLUSION: The laws of probability (like the law of
large numbers, the central limit theorem, etc...) can be applied to
numbers derived from
gambling experiments that satisfy the above hypothesis.

The step from the
HYPOTHESIS to the
CONCLUSION CANNOT be argued
without changing accepted definitions or abandoning logic, and I invite you
once a gain to look into Laurie's book to see how this accomplished. In particular, LIKE IT OR NOT, the HYPOTHESIS alone is CAUSE enough
for the number to obey there known laws and satisfy the CONCLUSION. You can feel free to debate the
hypothesis, but any debate which does not lead to a different conclusion
(namely a testable difference in the laws of probability that come from the above CONCLUSION)
would not interested me.

Gregory Leibon

From ???@??? Mon Sep 9 22:41:18 2002

Date: Mon, 09 Sep 2002 22:03:13 -0400

From: "R.D. Ellison"
<rdellison@netzero.net>

To: Gregory Leibon <Gregory.Leibon@Dartmouth.EDU>

Subject: Breakthrough, part two

Hello,

--You wrote:

In order to justify me putting any more time into this I
ask permission

to use any of our e-mail communications for pedagogical
purposes.

--end of quote--

Thank you for the compliment! Permission is most
definitely granted. May

I also have reciprocal permission from you? This is an
excellent time

for us to establish this, because my last letter set the
stage for a

very powerful argument, which I will split between this
letter and the

next.

All it takes to make this effective point is to compare
two roulette

wheels. One of these is an $8000 perfectly-balanced
professional wheel,

as used in casinos, and the other is a toy that cost $39.
We must add

this caveat: both are capable of hitting all the playable
numbers.

Question: which one of these two wheels is more likely to
produce

numbers that conform to their inherent statistical
expectations, in the

long run?

This is a no-brainer: the expensive wheel will be more
accurate in the

long run. Do we concur? If Yes, then in the next letter,
you will see

very vividly what I have been trying to say all along!

Thank you.

Rick D. Ellison