J. Laurie Snell/R.D. Ellison - Dialogue 2
The following are the
transcripted email messages that form the second dialogue (of two) between
R.D. Ellison and Dr. J. Laurie Snell, which took place between October 26
and January 26 of 2003. In between, Dr. Snell asked that the dialogue be
continued by his associate, Professor Gregory Leibon (documented
separately).
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Dr.
J. Laurie Snell (picture from
website): |
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Subject:
Re: RD asked me to have you look at this Hi, I
am sorry to be so late in answering your note that Greg forwarded to me. Of
course gambling devices could be made to have a “memory” or at least
make them not well-described by an independent trials model. This would be
particularly easy for modern slot machines that are run by computers and
the outcome has nothing to do with how you pull the arm. The computer
decides everything and could easily be programmed to let the next outcomes
depend on the previous outcome. This
would be harder with a roulette wheel but it would be easy if they just
had the outcome of the ball determined by the computer rather than the
throw of the ball. So
I guess you have a point. The roulette wheel could have a memory. Which
reminds us once more that mathematicians develop probability models such
as independent trials and the question of whether they apply to a
particular situation has to be based on looking at data to see how well
the predictions of the model are verified. There
have, of course, been examples where players have made money by detecting
that a wheel is imbalanced and at least one group has claimed to have made
money by solving differential equations based on what happens when you
throw a ball on the wheel. However, it seems to me that the casino has plenty of reasons to try to make the wheel behave as closely as possible to the independent trials model which predicts that they will make about 5% of all the money put on the table. Cheers Laurie |
Subject: synthetic memory
Date: 27 Oct 2002 18:17:47 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
It is good to hear from you
again. You wrote:
< So I guess you have a
point. The roulette wheel could have a memory.>
THAT is the affirmation I have
been looking for ever since beginning our dialogue! Now, if we have confirmed
that the wheel could have a <memory>, does this not cast doubt on whether
those events are independent? As I understand it, the <wheel has no
memory> is the standard (and sole) argument supporting the theory that the
numbers produced from a roulette wheel are independent events.
This would also apply to coin
flips, except that the <fairness of the trial environment> replaces the
<precision craftsmanship> as the primary guiding force in making
those events <dependent.>
I am enjoying your book. I am
now on Chapter 6.
Thanks for your time.
R.D. Ellison
Subject: Four questions
Date: 17 Nov 2002 09:39:56 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
You may have learned by now
that my dialogue with Mr. Leibon has ended. I encouraged him to bow out because
his unwillingness to deal seriously with the subject matter had risen to the
place where no one’s purpose was being served.
One thing I learned from our
dialogue is that no expert is going to willingly or easily concede that a
non-expert knows more than him! To ensure that his knowledge is not questioned
and his career is not thus jeopardized (if that scenario comes up), his best
move is to force a stalemate. And that is precisely what happened in our case.
This sort of thing makes it very difficult for me to promote recognition of my
discovery.
To give you an example, Mr.
Leibon interpreted your admission that <the wheel could have a memory> to
mean that a diabolical force would have to be involved, such as rigging the
wheel with magnets that could be turned off and on at will. I do not think you
intended your statement to be limited to that interpretation, so I am seeking a
clarification from you.
Also, Mr. Leibon seemed to
believe that roulette table results are considered to be independent events only
because of man’s inability to predict the result, forcing him to assume that
every possible result is equally likely. In other words, the physicality of the
wheel is irrelevant. A $39 wheel will perform the same as an $8000 wheel, and a
wheel that is biased to favor certain numbers does so only through man’s
perception, as opposed to a mechanical reason. I do not believe this is the
standard logic in general use by mathematicians, and so I am asking you to
tell me whether or not you concur with that logic.
I am also seeking a reply to
the question posed in my email of Sunday, October 27, which was a follow-up to
your message containing your <wheel could have a memory> quote, noted
above.
If you are unable to help me or
don’t wish to be bothered with new discoveries at this late stage in your
career, could you advise me as to how I might establish a dialogue with someone
who might be more willing to confront the issue and seek the truth? As you
probably know, I am looking for someone to help me write a book about this, as I
do not know how such a book should be formatted.
To summarize, the last four
paragraphs each contain a question of some kind, from which I am seeking a reply
from you. I apologize for any inconvenience. Thank you for your time.
R.D. Ellison
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Subject:
Re: Four questions Hi, As
Greg and I have tried to explain many times, mathematical probability was
developed to shed light on chance experiments. In general it has an
impressive record of doing just that. However, in any specific application
of probability the only way to decide whether a probability model is a
good one is by doing experiments. If you do not want to do this, but
rather rely on an expert to agree with you that the standard probability
model for roulette is not completely satisfactory, you can quote one of
the greatest statisticians of this century. As we write in our probability
book: The
statistician Karl Pearson analyzed a large number of outcomes at certain
roulette tables and suggested that the wheels were biased. He wrote in
1894: Clearly,
since the casino does not serve the valuable end of huge laboratory for
the preparation of probability statistics, it has no scientific raison
d’etre. Men of science cannot have their most refined theories
disregarded in this shameless manner! The French government must be urged
by the hierarchy of science to close the gaming salons; it would be, of
course, a graceful act to hand over the remaining resources of the Casino
to the Acadaemie des Sciences for the endowment of a laboratory of
orthodox probability; in particular, of the new branch of that study, the
application of the theory of chance to the biological problems of
evolution, which is likely to occupy so much of men’s thoughts in the
near future. Pearson,
Science and Monte Carlo, Fortnightly Review, vol. 55 (1894), p. 193; cited
in S.M. Stigler, The History of Statistics (Cambridge: Harvard University
Press, 1986) Actually,
he should not have been so negative about the casinos since experiments
like this led Pearson to develop the chi-square test which is the standard
test to see how well a probability model fits data. I
am sorry that you feel that neither of us have been much help to you but I
really believe that we have tried. Cheers Laurie |
Subject: request
Date: 17 Nov 2002 20:25:55 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
I am not sure what point you
were trying to make in your reply of today. You appeared to suggest that a
roulette wheel is not a worthy instrument for probability study, then you backed
away from saying that. The only thing that is certain is that you did not answer
any of my four questions.
Perhaps I did not make it clear
that a roulette wheel need not be the proving ground. The gist of my arguments
can also be proven through coin flips, or any other probability technique where
a fair trial environment is assured.
In your letter, you said that
you really believe you have tried to help. The real test of that is whether you
can provide straightforward answers to my questions. As you know, very little
(of these issues) can be proven empirically because of the need for billions of
trials, which are not realistically achievable. Do you understand that? If so,
then you should also realize that in such cases, the best way to get at the
truth is to ask questions. When one side takes a long time to answer, or offers
ambiguous replies, this is an indication that they do not really have the
answer. At that point, it begins to become clear who is right and who is not. I
too would prefer empirical proof, but when that is not feasible, we must use
whatever techniques are available.
With the above in mind, do you
understand that abrogating the dialogue before having made every effort to get
at the truth tends to expose a need to suppress the truth?
I will ask the questions again:
1) When offered the opinion
that <the wheel could have a memory>, were you referring only to
diabolical influences, such as a gaffed wheel, as Mr. Leibon claimed? (We really
do need to be clear on your intent.)
2) If No to the question above,
how did you mean for that statement to be interpreted? (Please be explicit
enough to cover all basic applicable categories.)
3) Is it the common belief
among mathematicians, as Mr. Leibon also claims, that the chief reason we
consider roulette results/coin flips to be independent events is through our
inability to guess the result?
4) If Yes to the above, are you
saying that the physicality of the trial environment is irrelevant?
Those are all the questions I
have for now. These are simple questions that pertain to your specific area of
expertise, so there is really no reason for you to decline to answer them.
Thank you for your time.
R.D. Ellison
Subject: Interim reply
requested
Date: 30 Nov 2002 16:33:12 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
As it has been nearly three
weeks since my last email was sent to you, this follow-up is written to make
sure that the message and the questions it contained were received. If in fact
they were but you need more time to formulate your replies, I would appreciate
if you could forward to me an estimate for when you will be able to respond.
One of the four questions from
that message is of particular interest, because it involves a statement you had
made in a previous message to me, which initiated a dispute between Gregory
Leibon and myself. The statement is:
<So I guess you have a
point. The roulette wheel could have a memory.>
It is important that we are
clear on your intent, because Mr. Leibon interpreted that statement to mean that
a <diabolical influence> would have to be involved, such as rigging the
wheel with magnets. And I strongly disagreed with that characterization, because
you were responding to an argument of mine that made no mention of that type of
influence. And yet, he ended up using that characterization to support a related
argument of his.
Therefore, we need a
clarification from you. Surely you cannot expect us to spend an eternity trying
to second-guess what you intended when you wrote those words!
And, if by chance you intend to
disregard my other questions from that same message, could you please specify a
reason for your refusal to do so, or acknowledge that the subject matter is over
your head, or state that you have no interest in pursuing the truth in a matter
that could change the way mathematics are scientifically applied in probability
issues? I ask this because, with all due respect, in the absence of choosing one
of those three options, it tends to appear that you are avoiding the issue to
avoid losing the argument.
Therefore, I am seeking a
formal reply from you to clarify your overall intent. I think I am being fair in
asking you to either agree to continue our dialogue, or conclude your
involvement in a fair, honest, and forthright manner, which leaves no dangling
issues, and no doubt as to your position and ultimate intent. Thank you.
R.D. Ellison
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Subject:
Re: Interim reply requested Hi, I
think my original answer was very clear. All
I said was that I assume that a casino could make a roulette wheel where
the outcome of individual plays were such that the assumption of
independence would not be reasonable. I also said that I personally did
not think they would do this. What
is unclear about that? Let’s
stick to this question until you understand what I’m saying. . . Laurie |
Subject: clear / unclear
Date: 01 Dec 2002 21:00:02 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
Thanks for getting back to me.
--- You wrote:
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I
think my original answer was very clear. All
I said was that I assume that a casino could make a roulette wheel where
the outcome of individual plays were such that the assumption of
independence would not be reasonable. I also said that I personally did
not think they would do this. What is unclear about that? |
--- end of quote ---
What is unclear is that I am
not sure if we may have lost sight of the original argument. The heart of my
argument – to which you were responding – was that a poorly-made roulette
wheel (e.g., a $39 toy) is not as likely to produce results that conform to
their statistical expectation as a well-made, perfectly-balanced wheel (e.g.,
an $8000 device). Therefore, the craftsmanship of the wheel is the key factor in
determining how statistically balanced the table results will be. So in other
words, the more precise the device, the more precise its memory (which is built
in) will be.
I was under the impression that
this is the point I made to which you replied:
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I guess you have a point. The roulette wheel could have a memory. |
Do you concur with that
interpretation?
--- You wrote:
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Let’s stick to this question until you understand what I’m saying. |
--- end of quote ---
Good idea.
RD
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Subject:
Re: clear / unclear --- You wrote: |
What is unclear is that I am
not sure if we may have lost sight of the original argument. The heart of my
argument – to which you were responding – was that a poorly-made roulette
wheel (e.g., a $39 toy) is not as likely to produce results that conform to
their statistical expectation as a well-made, perfectly-balanced wheel (e.g., an
$8000 device). Therefore, the craftsmanship of the wheel is the key factor in
determining how statistically balanced the table results will be.
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---
end of quote --- I
agree with this. I would not use memory without a more careful statement
about what we mean by memory since I think most people associate this with
living creatures. I realize that we used it and what I have learned from
this discussion is that this usage can cause confusion. Laurie |
Subject: the illusion of memory
Date: 02 Dec 2002 19:23:36 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
--- R.D. Ellison wrote (paraphrasing):
A $39 toy wheel is not as likely to produce results that conform to their statistical expectation as a well-made, perfectly-balanced wheel. Therefore, the craftsmanship of the wheel is the key factor in determining how statistically balanced the table results will be.
--- end of quote ---
--- You wrote:
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I agree with this. I would not use memory without a more careful statement about what we mean by memory since I think most people associate this with living creatures. I realize that we used it and what I have learned from this discussion is that this usage can cause confusion. |
--- end of quote ---
Hello Laurie,
I can appreciate your
reluctance to use the word memory toward a mechanical device. In my dialogue
with Mr. Leibon, and at my website, I have referred to it as <the illusion of
memory> or <the equivalent of a memory>. I believe you concur with my
meaning.
I am pleased to hear that you
agree with my assertion that the device is what causes the level of statistical
balance in the numbers that are generated. This is all the more evident when one
considers that a biased wheel will favor certain numbers because it is
mechanically defective, and will cease to do so after it is repaired.
Thus, it would seem that this
is an area of quantum mechanics, if I correctly understand the term. Do you
agree with that characterization?
RD
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Subject:
Re: the illusion of memory Dear
Rick, The
“illusion of memory” is a good solution to the terminology problem. I
would think that classical physics would be sufficient for studying bias
but then I really don’t know enough about Quantum theory to know if that
would help. You
might be interested in Thorp’s experience with roulette wheels that you
can read at: http://www.bjmath.com/bjmath/thorp/tog2.pdf Cheers Laurie |
Subject: relationship of mutual
dependence
Date: 06 Dec 2002 21:08:59 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
Thank you for your message of
Dec 5, and the article by Thorp. He seems to agree with me in that the
mechanical soundness of the wheel is what keeps it unbiased and therefore
unbeatable: <The unbeatability of the roulette wheel is based on the
mechanical perfection of the wheel.>
Thorp’s seemingly innocuous
claim, however, actually conflicts with the conventional logic that is and has
been applied for years. On the surface it does not appear to be a contradiction,
but if you follow the statement to its logical conclusion, this becomes evident:
1) If a perfect wheel has the
capability to distribute the numbers perfectly, then:
2) The precision in the distribution would have to correspond to the precision
in the wheel construction.
3) Since perfect distribution requires the equivalent of a memory to compensate
for those numbers that under- or over-perform, then:
4) A synthetic memory would have to be built into the device, which in turn
means that:
5) The numbers are, in effect, following the orders given to it by the device
itself, so therefore:
6) All numbers generated from that device would have a relationship of mutual
dependence.
I am trying to step my way from
premise to conclusion as smoothly as possible. The above says what I want to
say, but I am sure there is room for improvement. This is where I could use your
help. But first I must ascertain whether you agree in principle with this, or
perceive a possible weakness in the logic.
Thanks for your time.
RD
Subject: Thanks
Date: 09 Dec 2002 19:12:53 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello,
Thank you very much for keeping
me informed.
RD
“J. Laurie Snell” wrote:
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Hi, I
have to try to finish my Chance News this week so I will get back to you
later about Thorp. Laurie |
Editor’s note: Mr. Snell’s
original message was lost,
but its content is shown in its entirety in the above reply.
Subject: 11 days
Date: 17 Dec 2002 20:26:50 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
I don’t know why, but it
seems that after 11 days or so go by, I get to wondering if maybe you forgot
about our dialogue. And it has been 11 days since I wrote you last (not counting
my courtesy message).
I do want you to take the time
you need to finish up your newsletter business, and to give consideration to the
argument I presented in my last message. So, I hope you don’t mind if I ask if
you think you can get back to me before the end of the year, or give me some
kind of timeframe to work around? Thanks,
RD
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Subject:
Re: 11 days Hi, Well,
at my age it takes a long time to do anything but I am aiming to finish
Chance News by Christmas. Sorry for the delay. Laurie |
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Subject:
Re: request Dear
Rick, Well,
Chance News is finished and took longer than I thought. Now I have a
colleague coming to work with me until Tuesday. Then I have to go to math
meetings so I guess you should just give up on me unless you can wait
until I finish these trips. Sorry. Laurie |
Editor’s note: Mr.
Ellison’s original message was lost, which was
a request for an estimate as to when the dialogue could continue.
The above is Mr. Snell’s reply to that inquiry.
Subject: Re: request
Date: 03 Jan 2003 21:10:36 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Laurie,
Thank you for your note. Can
you tell me what kind of timeframe we’re talking about (until you will have
time to look at my last message?
You may be reading more into
this than it deserves. I am merely looking for your comments on the matter I
referred to your attention. I can understand that you might be reluctant to put
on paper anything that could be construed as an affirmation of some kind, but
surely there must be some comment you can offer, without turning it into a big
deal?
If you find this to be too
exhausting, could you tell me who I might contact at the AMS, or Dartmouth, or
any one of your colleagues who could look at what I’m saying? After all, we
have come pretty far, and you seem to feel that there is some merit to my words,
and the underlying principle behind those words tends to indicate that we may be
onto something that could conceivably change history. Please don’t drop out on
me now!
Thanks,
R.D. Ellison
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Subject:
Re: relationship of mutual dependence Hi, I
cannot seem to find Thorp’s paper again. Did I give you a URL or did I
send the paper? Either way, can you help me find it again? Thanks. Laurie |
Subject: Thorp’s link
Date: 11 Jan 2003 19:42:01 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Laurie,
Great to hear from you again. I
believe this is the link you are looking for:
http://www.bjmath.com/bjmath/thorp/tog2.pdf
L8er,
RD
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Subject:
Re: Thorp’s link Hi, Yes
that was what I wanted. I’ll read it on my trip and then try to answer
your questions related to it. Thanks. Laurie |
Subject: (Not urgent)
Date: 18 Jan 2003 10:06:54 –0500
From: R.D. Ellison (web address deleted)
To: J. Laurie Snell (web address deleted)
Hello Mr. Snell,
I am not looking for a quick
reply to this note; just wanted to give you some more food for thought.
I am currently engaged in a
similar dialogue with another gaming author, and I am finding that even those
who want to agree with me are having difficulty reaching that state of deep
thought necessary to grasp the concept. But I see this as a good thing, because
it is forcing me to find a more efficient way to explain it. The following is
the essence of an email message I sent to him yesterday. I am hoping it helps
clarify my view:
<We are in agreement that
man is capable of producing a device (such as a roulette wheel) that can
distribute the numbers fairly and somewhat equally. But you do not concur that
this means that, to make this possible, the wheel would have to possess the
equivalent of a memory. Let me put it this way: (we also agree that) a biased
wheel does not produce numbers that conform to the statistics. But when the same
wheel is repaired, it WILL conform to the statistics. What is the difference
between the two? The former is mechanically impaired. In effect, it does not
“remember” to process the numbers proportionately. (That is its job, right?)
Ergo, the state of mechanical perfection, or lack thereof, is what makes the
difference between a wheel that “remembers” to distribute the numbers
correctly, and one that does not. To recap: unbiased wheel: perfect memory.
Biased wheel: impaired memory. That is the effect, is it not?>
By the way, the only part of
the Thorp article that I referenced (to you) was on the first page. (That is the
only place he talks about his views on the significance of mechanical
perfection.)
L8er,
RD
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Subject:
J. Laurie Snell – Automatic Reply I will be away until Monday January 20. Laurie |
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Subject:
Re: (Not urgent) Dear
Rick, I
finally read Thorp’s discussion of his ideas on how to beat roulette.
Thorp is one of my heroes so I enjoyed reading it. A similar account of
attempts to beat roulette are described in the book “The Eudaemonic
Pie” by Thomas A. Bass. You probably have read this since it was quite a
popular book. I
then read your questions about it and found indeed that I could have
answered then long ago since, of course, I don’t agree with your third
remark in which you say “the perfect distribution requires the
equivalent of a memory to compensate for those numbers that under- or
over-perform. I
then read your most recent note and note that I have company. We
are back to the beginning of our discussion. If by perfect distribution
you mean the distribution implied by the standard mathematical model then
if the model is any good we would expect that it would pass standard
statistical tests. If the wheel is known to be biased we would expect that
it would fail these tests. We have to look at the data! Cheers Laurie |
Subject: Agree or disagree?
Date: 21 Jan 2003 22:00:23
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
Hello Mr. Snell,
I’m sorry I don’t follow you. I was trying to confirm that you concurred with me that the wheel would have to have a “mechanical memory” in order to be able to distribute the numbers fairly. I thought you had already “agreed to agree” with that, so are you recanting, or do I misunderstand?
Perhaps it would help if I clarify MY position with the following, which I posted at a web message board earlier today:
<Let’s say that a given roulette wheel has a mechanical flaw, which prevents the number 17 from ever coming up. Is the law of large numbers applicable at that table? Does the normal statistical expectation for the group of numbers 0, 00 and 1 through 36 apply? Obviously, not. The number 17 would be missing from the equation, thereby throwing off all the averages of the group itself. So, what made this happen? The mechanical condition of the wheel was impaired. This means that the wheel’s state of mechanical perfection, or lack of perfection, is what determines whether that wheel can produce numbers that will conform to the statistical expectation. This in turn means that the wheel itself is calling the shots (so to speak), and would have to have a “mechanical memory” (for lack of better words) to be able to do that.>
My point is: it doesn’t take volumes of data to figure out that when a normally playable number is prevented from coming up because of a mechanical flaw, statistical expectations for the group as a whole will not be met. Do you dispute this? If so, we need to put our focus right here, on this question, and get it cleared up, because this stuff is elementary.
RD
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Subject:
Re: Agree or disagree? Hi, I guess the current confusion is caused by my misinterpreting what you meant by “perfect distribution” in your remark: |
“the perfect distribution
requires the equivalent of a memory to compensate for those numbers that under-
or over-perform.”
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Perhaps
you can explain this in more detail so I can see if we are indeed still in
agreement about what a “mechanical memory” means. Cheers Laurie |
Subject: Perfect Distribution
Date: 22 Jan 2003 21:30:16
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
Hello Laurie,
<Perfect Distribution> simply means that the numbers generated (from a roulette wheel) will ultimately conform to the inherent statistical expectation of that group of numbers. This is the same general concept Thorp stated regarding the <mechanical perfection of the wheel.>
By the way, can you tell me what book of Thorp’s that article was taken from? Thanks.
RD
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Subject:
Re: Perfect Distribution The
Thorp book is Mathematics
of Gambling It is out of print but you can view the whole book at http://www.bjmath.com/bjmath/thorp/tog.htm If we agree that you mean the traditional mathematical model for roulette then it is not clear to me what your statement. . . |
Since perfect distribution requires the equivalent of a memory to compensate for those numbers that under- or over-perform
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.
. .means. The
mathematical model predicts allows for all kinds of strange behavior which
would appear to represent under- or over-perform. For example if you toss
a coin a sequence of times it predicts that streaks of heads arbitrarily
large will occur sometime. I do not know any way to make
“under-or-over-perform” other than statistical tests. Laurie |
Subject: question repeated
Date: 24 Jan 2003 01:13:45
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
Hello Mr. Snell,
Perhaps you did not notice that – for the moment – we are no longer talking about over- and under-performing numbers. This decision was made because it appears that we are not ready to address that question yet, for it will lead to an unprovable dead end. More specifically, to a place that requires more computations than can be processed in a lifetime.
Unless you intend for this dialogue to conclude at the aforementioned dead end, we will first have to set a proper foundation for that question. That foundation can be laid by addressing the question posed in my letter of Tuesday, January 21, 2003. It is reprinted below, as it appeared in that message:
<Let’s say that a given roulette wheel has a mechanical flaw, which prevents the number 17 from ever coming up. Is the law of large numbers applicable at that table? Does the normal statistical expectation for the group of numbers 0, 00 and 1 through 36 apply? Obviously, not. The number 17 would be missing from the equation, thereby throwing off all the averages of the group itself. So, what made this happen? The mechanical condition of the wheel was impaired. This means that the wheel’s state of mechanical perfection, or lack of perfection, is what determines whether that wheel can produce numbers that will conform to the statistical expectation. This in turn means that the wheel itself is calling the shots (so to speak), and would have to have a “mechanical memory” (for lack of better words) to be able to do that.
My point is: it doesn’t take volumes of data to figure out that when a normally playable number is prevented from coming up because of a mechanical flaw, statistical expectations for the group as a whole will not be met. Do you dispute this?>
Please respond to this argument. Thank you.
RD
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Subject:
Re: question repeated --- You wrote: |
My point is: it doesn’t take volumes of data to figure out that when a normally playable number is prevented from coming up because of a mechanical flaw, statistical expectations for the group as a whole will not be met. Do you dispute this?
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I agree with this. Laurie |
Subject: the next step
Date: 25 Jan 2003 11:07:33
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
“J. Laurie Snell” wrote:
--- You wrote (quoting RD):
My point is: it doesn’t take volumes of data to figure out that when a normally playable number is prevented from coming up because of a mechanical flaw, statistical expectations for the group as a whole will not be met. Do you dispute this?
--- end of RD Ellison quote ---
--- You replied:
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I agree with this. Laurie |
--- end of Laurie Snell quote ---
Hello Mr. Snell,
Thank you for your reply, and also for the referral to the Thorp book.
Now that we have found something on which to agree, we need to delve further into the paragraph that preceded the quoted paragraph above. I am reprinting the appropriate part of that paragraph below:
<Let’s say that a given roulette wheel has a mechanical flaw, which prevents the number 17 from ever coming up. Is the law of large numbers applicable at that table? Does the normal statistical expectation for the group of numbers 0, 00 and 1 through 36 apply? Obviously, not. The number 17 would be missing from the equation, thereby throwing off all the averages of the group itself. So, what made this happen? The mechanical condition of the wheel was impaired. This means that the wheel’s state of mechanical perfection, or lack of perfection, is what determines whether that wheel can produce numbers that will conform to the statistical expectation.>
I would expect for you to agree with everything up to the last sentence, and am asking for your input on that premise. However, if you dispute anything leading to that statement, I need for you to single it out and then please convey to me the nature of your disagreement. Thanks for your time.
RD
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Subject:
Re: the next step --- You wrote: |
This means that the wheel’s state of mechanical perfection, or lack of perfection, is what determines whether that wheel can produce numbers that will conform to the statistical expectation.
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---
end of quote --- While
I tend to believe this, this is not a consequence of mathematical models
for roulette. There are serious people who believe that quantum theory
allows esp to influence such things. While I am skeptical I have no reason
to know that they are wrong. The
rest of the paragraph is fine with me. Laurie |
Subject: Re: the next step
Date: 25 Jan 2003 13:59:05
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
--- You wrote:
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While I tend to believe this, this is not a consequence of mathematical models for roulette. There are serious people who believe that quantum theory allows esp to influence such things. While I am skeptical I have no reason to know that they are wrong. |
--- end of quote ---
What is needed at this time is a clear Yes or No answer. If it is Yes, we can move to the next step. If it is No, a clear and concise expression of your doubts is needed. And just to clarify my position, let us assume for the sake of this argument that things like ESP are explicitly ruled out.
RD
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Subject:
Re: the next step Well,
if I have to say yes or no I will have to say no. I do not agree with the
statement since I don’t believe one can ever be sure what produces
physical behavior. Laurie |
Subject: contradiction?
Date: 26 Jan 2003 04:50:49
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
Hello,
I had previously written that:
<the wheel’s state of mechanical perfection, or lack of perfection, is what determines whether that wheel can produce numbers that will conform to the statistical expectation.>
To which you replied:
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< Well, if I have to say yes or no I will have to say no. I do not agree with the statement since I don’t believe one can ever be sure what produces physical behavior.> |
If I may say, it appears that you are contradicting what you just previously agreed to.
We have established that if a wheel is mechanically impaired to the point that the number 17 (for example) is prevented from coming up, the statistical expectation for the entire group (0, 00, plus 1 through 36) will not be met.
Question 1) Is it not obvious
to you that these statements say the same thing?
Question 2) Being mechanically
impaired is a lack of perfection, is it not?
(And in using the word ‘perfection,’ I am using it in the same context as Thorp, when he wrote that <the unbeatability of the roulette wheel is based on the mechanical perfection of the wheel.>)
Please respond to questions 1 and 2 above. I would appreciate if you could be as explicit as you can.
RD
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Subject:
Re: contradiction? Well,
you are probably right. I don’t think one can ever say with certainty
what a physical object will do so perhaps I should not have agreed to your
previous statement. However, I interpreted your previous statement as
meaning that you made the hypothesis that 17 could not come up and under
this hypothesis any reasonable probability model would assign probability
0 to 17 coming up. However,
all this shows that we are getting into silly philosophical arguments
which I am no good at and don’t particularly enjoy. If
I can help you at all it is in questions related to the mathematics of
probability or statistics and tests of significance for specific models. Cheers Laurie |
Subject: skewed motives
Date: 26 Jan 2003 14:48:38
–0500
From: R.D. Ellison (web address
deleted)
To: J. Laurie Snell (web
address deleted)
Hello Laurie,
I vigorously protest your characterization that the below is a <philosophical argument.> There is nothing philosophical about realizing that a ball cannot land in a slot that is blocked!
Your attempt to exit this argument when you find yourself losing that argument is a disgraceful cop-out! I have spent nearly a year pursuing this dialogue with you in the interests of science, and for you to now cry <philosophy!> is a betrayal of the trust I put in you, and the integrity I believed you to have.
But I do understand your motives. If it turns out that I am right, a considerable part of your foundational teachings will be discredited, won’t it, because part of it was built on a flawed premise?
As Victor Hugo once said, <A legion of armies can be resisted, but not an idea whose time has come.> Meaning, in this context, that you can try to suppress this great discovery through your questions about semantics, your accusations of philosophy, your forgetfulness, stall tactics and long delays, but at the end of it all, the truth will come out, and when it does, your name will be that much more shamed through the public awareness (at that future point in time) that you had a chance to contribute to the presentation of this obvious discovery, and chose to keep your head in the sand.
For the last time, I am urging you to respond to an argument that would be plainly evident to any fourth-grader, and all the more so to a man of your prominence and experience.
Cheers?!
R.D. Ellison
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Subject:
Re: skewed motives I
guess that the honest answer is that I do not want to continue a
conversation with someone who thinks my motives are dishonorable. If you
want to interpret this as a victory that is your business not mine. Laurie |
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