—seventeen math and/or gaming experts
J. Laurie Snell
—Dr. J. Laurie Snell, Dartmouth College Math Professor (retired)
(See J. Laurie Snell Dialogue 2, dated 26 Oct 2002 16:42:49 EDT - link below)
R.D. Ellison
Gregory Leibon
06 Sep 2002 10:58:20 -0400:
Ellison: "The experts agree that any group of unbiased numbers will ultimately conform to their assigned statistical expectation. My question is, how do they do that? This is a cause-and-effect situation. The effect is that the numbers conform to the statistical expectation. Are you saying that there is no cause? (paraphrased for brevity)
07 Sep 2002 12:56:36 EDT:
Leibon: "This is due to the fact that we believe there is some underlying tendency that is articulated as a probability."
08 Sep 2002 09:52:30 -0400:
Ellison: "What is the cause of this underlying tendency?"
08 Sep 2002 11:28:34 EDT:
Leibon: "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."
08 Sep 2002 16:32:57 -0400:
Ellison: "That reply does not explain the cause. Is there a compelling force behind this 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? (Editor's note: the question was never answered.)
There's something happening here; what it is ain't exactly unclear. It
seems that none of the relevant experts (gaming authors, mathematicians,
and statisticians) can explain contradictions in the Gambler's Fallacy,
the principle upon which much of their teachings are based.
On balance, the experts agree
that, given time, any set of numbers produced in a regulation environment
(e.g., an unbiased craps or roulette table) will ultimately conform to
their statistical expectations. But none of them can explain what makes
this happen. In a controlled environment where a statistical certainty is
invoked, a cause-and-effect situation exists.
The effect is that the numbers will ultimately form a very precise
statistical balance among themselves. But what is the cause of this infallibly
predictable behavior? And how can "independent events" (as most
experts believe them to be) conform to anything? Does that not belie the
core meaning of "independence"?
R.D. Ellison's Theory of
Statistical Propensity answers these questions. Its foundational principle
is that these are NOT independent events. They are collectively dependent
upon the proper use and functionality of the device. If the device is
mechanically flawed or improperly used, the numbers will not conform to
the probabilities. If it IS properly maintained, they will. To be properly
distributed, the numbers depend upon the correctness of the device.
The premise of the Gambler's
Fallacy is the biggest load of crap ever perpetrated upon civilized
society. One
day, the experts will acknowledge this. The question is, how long are they
going to keep pretending to miss something so obvious?
This matter, and the theory of
Statistical Propensity,
which replaces the Gambler's Fallacy, is discussed in more depth in
R.D. Ellison's next book, Advanced Craps, available May 2005.
Side note: At this writing,
part of the dialogue between Professor Leibon and RD Ellison is posted at
the Dartmouth College website, at http://www.math.dartmouth.edu/~m5f02/files/ellis.htm.
The only reason this version is posted is because at the Dartmouth site,
the text was cut off just as it appeared to be getting interesting. And
the author, having just learned of that posting from a reader, decided to
post a more complete version.
6-16-02 to 8-20-02 8-21-02 to 10-22-02 10-26-02 to 01-26-03
