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Applying The Law of Statistical Propensity
American Roulette Is Now
Mathematically Beatable
by R.D. Ellison
Whenever a system becomes
completely defined, some damn fool
discovers something that either
abolishes the system or expands it
beyond recognition.
--Brooke's Law
From the moment the first casino
opened, there has been an ongoing
controversy as to whether table
game decisions are affected by
previous results. Many players
believe that past results do
matter. They wait for an even money
proposition to win three or four
decisions in a row, and then bet on
the opposite choice, figuring that
it is statistically due. But this
kind of thinking is ridiculed by
gaming experts, authors, and
purists, because it infers that the
dice or roulette wheel react to
past events. The wheel has no
memory, they say of roulette.
Therefore, those who believe that
past events influence future
results are frequently considered
to be misguided or naïve.
If you ask ten gaming experts if
gaming decisions are independent of
all previous decisions, you'll hear
the word "yes" approximately ten
times. That figure, in fact, was
derived from a recent survey I
conducted of gaming authors[1],
which assumed there was no bias
from any mechanical defect or
external influence. One of the
objectives of this article,
however, is to prove that all ten
of those answers are wrong.
Is it possible to prove that gaming
decisions can be influenced by past
results? Answering this question
begins with a premise: For a
roulette wheel to be deemed
suitable for live gaming, it would
have to show no bias towards or
against any of the playable
numbers. This could be reasonably
established from a trial run of
perhaps 3000 spins. At the end of
that trial, if the table decisions
do not demonstrate a marked
deviation from the mathematical
expectation, there shouldn't be a
problem. But if the number 8, for
example, doesn't turn up once in
all of those spins, then there is a
problem. For the wheel to pass the
test, all the numbers would have to
come up in a pattern that resembles
a fairly even distribution.
But let's take a closer look at the
implications of this. If every
table game result is an independent
event, how can we ever expect any
particular number to come up at
all? We can't, because there would
be nothing to stop the wheel from
selecting a different number, every
time. And yet, the same people who
say that these numerical events are
immaculately independent, expect
the numbers to conform with the
probabilities. But if such events
were truly independent, there would
never be a moment, or even a
sustained period, when any number
could be expected to show up.
There is a causative force that
compels numerical events to seek
their legitimate place within their
assigned probabilities. Whether the
dice or wheel have a memory is
irrelevant. The influence
originates from the effects of
statistical propensity, the
authority that governs the
probabilities of random numerical
events.
The key to getting a clear handle
on this lies in seeing the
difference between viewing table
decisions one at a time, or in
groups. On a one-by-one basis, it
is true that there will never be a
time when any number is mandated to
appear or not appear. But even in a
sampling as small as 3000 spins,
you will never see what might be
regarded as a catastrophic
deviation from the statistical
expectation. There's not an
unbiased roulette table on earth
that can make it through that many
spins without our number 8 coming
up at least two or three dozen
times times.
To understand why this is the case,
one must know a little something
about the characteristics of the
numbers that form the table
decisions at roulette. Toward that
end, let us look at the 15,000
actual casino spins, as they appear
in Erick St. Germain's Roulette
System Tester[2]. These spins are
broken down into thirteen sessions
in a Single Number Distribution
Chart that appears at the end of
the book. This chart shows how many
times each of the 38 playable
roulette numbers came up in the
course of thirteen groups of 1,140
documented spins apiece.
To get the ball rolling, we will
look at the occurrences of the
number 7. In all of the groups of
1,140 spins, the 7 came up at least
25 times, but never more than 38
times. That averages out to an
occurrence every 30 spins on the
low end, and every 45.6 spins on
the high end. What's the average of
those two figures? 37.8. That's
just two-tenths away from the exact
statistical expectation of 1 in 38.
Something is making that happen.
Independent events are not that
obedient or precise, particularly
in a sampling that small!
But then, could that just be a
fluke? Might we get a whole
different set of results from
another one of those numbers? Let's
take a look at the entire group:
Taking all 38 numbers into
consideration, the least number of
times any number showed up was 16,
and the most number of times was
50. This is a wider range, which
accounts for the greater
possibility of unconventional
trends in a larger sampling, but
not one of the 38 numbers tried to
escape from the corral. Meaning,
each one was compelled to show up a
minimum number of times, but not
too many times.
This is pretty much how the numbers
fall in any group that size.
Conformity with this pattern, by
and large, is as reliable as a
Swiss watch. You never know when a
given number will appear, but at
the end of the day, every number
will have taken its turn in the
spotlight. The numbers have not the
inclination or the means to
overlook the mathematics of
statistical destiny.
If every gaming result were truly
independent, then it would be
possible for a roulette table to
fail to produce the number 7 in
twenty million consecutive spins,
because there would be nothing to
enforce that occurrence. But in the
real world, unless the wheel is
biased, there is a 100 percent
chance that won't happen. Anyone
who understands the numbers knows
that an unbiased table would never
make it past the first thousand
spins without a 7 coming up.
Assuming the above is true, the
only logical conclusion that can be
drawn is that it is not possible
for gaming results to be truly
independent, for those results are
constantly bending, however
imperceptibly, toward a state of
perfect statistical balance. To
presume that this is nothing more
than a persistent coincidence (that
never stops occurring) is not a
credible argument!
There's just one tiny problem with
all of this. The consensus of
gaming experts and mathematicians
is that in such matters, past
events have no bearing on future
results. And this consensus has
evolved for generations, and has
withstood the test of time
throughout that period. How could
all those experts be so wrong?
Actually, quite a few of these
authorities have been dancing along
the edge of this issue for many
years:
In his book, Winning at Casino
Gambling[3], author Lyle Stuart
said that he once witnessed an even
money wager at baccarat win 23
consecutive times. He said this was
the longest streak he had ever seen
in all his years of playing. It is
also the longest streak that I have
ever read about, heard about, or
witnessed. If this is (roughly) the
farthest a numerical pattern is
likely to stray from the norm in
what amounts to trillions of gaming
decisions, this is no accident, or
coincidence.
In another book, Beat the
Casino[4], Frank Barstow follows up
that thought with "Dice and the
wheel are inanimate, but if their
behavior were not subject to some
governing force or principle,
sequences of 30 or more repeats
might be commonplace, and there
would be no games like craps or
roulette, because there would be no
way of figuring probabilities." He
goes on to talk about his Law of
Diminishing Probability, which is,
in effect, one of the subordinate
laws of Statistical Propensity.
But these are gaming authors. What
do they know? All right; let's see
what an expert in statistics has to
say. In his book, Can You Win[5],
author and statistician Mike Orkin,
describing the Law of Averages,
seemed to agree with this
philosophy when he wrote: "In
repeated, independent trials of the
same experiment, the observed
fraction of occurrences of an event
eventually approaches its
theoretical probability." In other
words, what goes up, must come
down. Given enough trials, a
statistical balance will be
compelled.
The only reason the laws of
numerical science have not been
modified to allow for this logic is
because everyone pussyfoots around
the issue. It's just too hot to
handle. Indirectly, they embrace
the concept, or make obscure
references to it, but they don't
challenge the existing philosophy.
And I'd be doing the same thing, if
not for having developed a betting
scheme that gives the player a
mathematical advantage over the
game of roulette. For it is the
implementation of this concept that
makes that possible.
So, the most compelling evidence I
have to support my theory that past
events do influence future results,
is in my ability to harness this
power in a wagering strategy for
roulette, which has been named the
3Q/A Reverse Select. What sets this
apart from other strategies is a
technique for processing the table
data. Utilizing this procedure, a
careful analysis of the past table
decisions enables the player to
foretell future table results with
enough precision to reverse the
house edge. This in turn enables
him to win more than the math of
the game would otherwise allow.
Nothing else could explain the
phenomenal success of the 3Q/A,
which has been independently
verified to yield a 7.94% player
advantage, in a sampling of over
7,500 live roulette spins. This
figure represents a spread of
13.20% over the established house
edge of 5.26% for American
roulette. And while the size of
that sampling is limited by the
structure of the 3Q/A, no other
strategy or system for roulette
would still look good after being
subjected to the same testing
ground.
Consequently, for players of the
3Q/A, the game of roulette has been
transformed from a game of chance,
to a game of skill.
But how is this possible? And what
makes the 3Q/A work? There is no
simple explanation, and if there
was, it would be a trade secret.
But this much can be said: the 3Q/A
is a two-pronged strategy. Each of
these two categories covers roughly
one-third of the layout, and pays
2-1. What you're doing is playing
the one against the other. If you
see one of the two betting
categories in a state of activity,
you choose the other prong as your
betting choice for that session. In
effect, you're looking for a trend
that is occurring inside of a
non-trend.
Because of the way the numbers of
each respective group are spaced
along the wheel itself, the two
form a symbiotic relationship, by
virtue of the effects of the dealer
signature.
The root problem in all other
systems is their one-size-fits-all
approach, which pays no heed to the
inclination of the table. Only
through an evaluation of the
table's past results can a player
aspire to anticipate the direction
of trend development, enabling him
to gain valuable insights into what
the future may hold at that table.
The real art lies in the ability to
read the data that is constantly
streaming from the table. You have
to follow the information labyrinth
until you come to the right
doorway. Then it becomes a simple
matter of timing the strike.
This is where the 3Q/A excels.
But there's another issue here:
even if such a system works as
claimed, wouldn't the casinos
install countermeasures? Not an
insurmountable problem. The 3Q/A
falls into the surgical strike
category, which calls for sessions
that are, above all, brief. This
helps the player avoid getting
trapped when the table is churning
out unfriendly patterns. And, since
it's a two-pronged strategy, he
won't always be playing the same
bets. Thus, it is not hard for such
moves to be cloaked in the garment
of routine play. The dealer won't
know what has happened until after
the winner is paid.
Well then, could this invention
actually kill the game of roulette?
Very unlikely. Most of the new
players attracted to the game won't
have the patience to stick
religiously to the procedure. They
could never aspire to maintain the
same level of discipline the
casinos rigorously impose on their
staff.
Make no mistake: professional
gambling is brutal. I don't think
an occupation exists that is so
lonely, ungratifying, and
unfulfilling (with the possible
exception of forced slavery, or
data entry).
One may recall a time when the
casinos were terrified of card
counters at their blackjack tables.
So they imposed harsh rules, which
ended up alienating their
clientele. In time, they did their
homework, and realized the
non-experts were bringing in more
money than what the counters were
taking out. So the new rules were
relaxed, and now they are not much
different from the old days. And so
it will be for the 3Q/A.
What about the sample size? Are
7,500 results adequate to pin down
a reliable percentage representing
the player advantage? Not
precisely, but it does offer a
strong indication that this
strategy is far superior to
anything that has ever been offered
to the public. And the sampling is
large enough to provide reasonable
assurance that the 7.94% figure
would not be likely to slip by more
than a couple points. And that
would still translate to a strong
advantage over the casino.
Why wasn't a computer simulation of
perhaps a million spins performed?
The short-term nature of this
approach is not adaptable to
computer trials, which are designed
to process nearly infinite strings
of numbers. Such cannot duplicate
the effect of moving from table to
table, and 'qualifying' each one
before the start of play.
What impact might this strategy
have on the way casinos do
business? Probably less than what
one might expect, because having a
winning strategy is not even half
the battle. Only a small percentage
of those who use it are likely to
have the fortitude to weather the
unexpected downturns that crop up
periodically, and the relentless
monotony of processing the same
damn numbers, the same damn way,
endlessly and forever. To win at
this game, you have to embrace the
notion of spending your workday
surrounded by numbers that react to
everything you do with anesthetic
indifference.
Even if the 3Q/A retains its 7.94%
player advantage after having been
played a million times, those who
run the casinos probably won't be
too concerned. They've seen this
sort of thing before. They've dealt
with card counters, dice mechanics,
and wheel clockers, and they're
still standing. They know that most
of their clientele can't handle the
reality of this brand of long-term
emotional deprivation. Maybe some
players will be able to hold up for
short periods, but for most, the
structure of player ambition will
inevitably collapse.
This is just one reason why the
casinos win, and will always
continue to do so. That is, until
the next wave of technology
disproves these words, just as the
3Q/A has disrupted the beliefs of
quite a few experts in the gaming
industry.
For players who are up to such a
task through faithful devotion to
the reward, there is nothing out
there that gives them a stronger
chance to win over this tough
opponent, the casino. And if enough
people can stick to it, there may
be some changes ahead. But don't be
cashing in your MGM stock just yet.
It's going to take more than the
3Q/A to bring that monster down.
[1] Gaming authors contacted:
Frank Scoblete, John Robison,
Walter Thomason, John May, Avery
Cardoza, John Grochowski, John G.
Brokopp, Henry Tamburin, David
Sklansky, Nelson Rose.
Collectively, they have written
more than 60 gaming-related books.
(All ten asserted that past results
have no influence on future results
at roulette.)
Sources:
[2] Copyright 1995 by Zumma
Publishing Company, Arlington, TX
[3] Copyright 1995 by Barricade
Books, Inc., New York NY 10011
[4] Copyright 1984 by Pocket Books,
New York, NY 10020
[5] Copyright 1991 by W.H. Freeman
and Company, New York, NY
By R.D. Ellison, author, Gamble to
Win series of books.
R.D. Ellison, the architect of the
3Q/A strategy for roulette, is one
of the world’s leading authorities
on casino gambling. The success of
this breakthrough procedure is
attributed to his discovery of
statistical propensity, the force
that compels gaming decisions to
ultimately conform to their
statistical expectation. For more
information about the book
containing the 3Q/A strategy,
please visit the author's website
at
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