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2 PLUS System / Diamond system

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Markus Funk

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Jul 21, 1998, 3:00:00 AM7/21/98
to
Hi,

I have tried out both systems (referring to J. H. Koehlers Book The science
of pocket Billiards).

Both systems do work quite well but only if you alter english and force of
the hit on almost each shot. My questions to the group: does anyone has made
the same experience ? If anybody else uses this system...How do you alter
english and speed??

The Chicago End Rail System by Wal Harris by the way is the most accurate
one I have seen so far.

Markus
"It`s no disaster getting beaten by a master"
Old chinese wisdom


LMoss18701

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Jul 23, 1998, 3:00:00 AM7/23/98
to
>From: "Markus Funk"

>The Chicago End Rail System by Wal Harris by the way is the most accurate
>one I have seen so far.

just wanted to say "ditto" on the chicago system. also the "sid system.
it has saved many a day for me.

linda moss

Robert Raiford

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Jul 24, 1998, 3:00:00 AM7/24/98
to
For those interested, the Sid system can be viewed here:

http://www.billiardsatlas.com/sid.html

Here's why Sid and Chicago (really the same system) are so accurate. It uses
easy to remember numbers that are extremely close to the 'theoretical' numbers
that are calculated assuming 'angle in = angle out'. This is a valid
assumption because it is a dead ball system using medium-soft speed. The
actual numbers are a ratio as follows:

2nd rail # = (10*d) / (d+8)

where d = distance in diamonds from the 1st rail to the 2nd
rail target (measured along 2nd cushion from the corner).

For example, the 2.5 2nd rail point in the Sid system is 3 diamonds from the
corner, so with d = 3, 2nd rail # = (10*3)/(3+8) = 2.73

Compare:

Sid Theoretical
-------------------
1.0 1.11
2.0 2.00
2.5 2.73
3.0 3.33
3.5 3.85
4.0 4.29
4.5 4.67
5.0 5.00

As you can see, these numbers are close enough considering the other variables
such as speed/rail conditions/etc. As many have found out, this can be very
accurate once you test a particular table for the proper speed of the shot. I
also like the fact that this system underestimates most of the actual values
so you can play into the first rail numbers instead of opposite them (which is
more theoretically sound :) In general I prefer visualization to using
numbers, but this one is so simple and quick that you might as well use it!

Rob

Markus Funk

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Jul 24, 1998, 3:00:00 AM7/24/98
to
Hi steve,

you can find it also in Walt Ahrris Book "The Billuard Atlast on Systems and
Techniques" on Page 199.

Do you know some more systems that your are willing to share??
TIA
Markus,
Germany

Steve Perry schrieb in Nachricht ...
>x-no-archive: yes In article
><199807230539...@ladder01.news.aol.com>, lmoss...@aol.com


>(LMoss18701) wrote:
>
>> just wanted to say "ditto" on the chicago system. also the "sid system.
>> it has saved many a day for me.
>

>Where can I find info on the chicago system? TIA.........

dst...@mediaone.net

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Jul 25, 1998, 3:00:00 AM7/25/98
to
Why not just post the system to the group?

Systems and methods are not copyrightable... only the particular
expression of an idea is copyrightable.

Dave


Robert Raiford

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Jul 25, 1998, 3:00:00 AM7/25/98
to
In my previous message I posted a link to the Sid system which I will
repeat here:

http://www.billiardsatlas.com/sid.html

The Chicago side rail system is really identical to the Sid system with
the short rail taking the place of the long rail in the sid system, and
all distances scaled accordingly (i.e. divided by 2). In other words,
the short rail half diamonds in the Chicago system are numbered the same
as the long rail diamonds in Sid. In the above link, imagine the
bottom rail is gone and the shots are taking place in the 'kitchen',
above the headstring, which is essentially a 2x4 diamond 'table'.

Rob

Robert Raiford

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Jul 25, 1998, 3:00:00 AM7/25/98
to
Markus Funk wrote:

> Both systems do work quite well but only if you alter english and force of
> the hit on almost each shot.

Doesn't sound like working "quite well" to me. How is it systematic to have to
make so many alterations on each shot (which the system doesn't tell you how to
account for anyway)?

> My questions to the group: does anyone has made the same experience ? If
> anybody else uses this system...How do you alter english and speed??
>

> The Chicago End Rail System by Wal Harris by the way is the most accurate
> one I have seen so far.

While I don't use them now, I used these systems (plus-2 & corner-5) in my
earlier years of banking study mainly because, although the exhibited the
problems you mention, they were commonly available/accepted and there weren't
many decent alternatives. I have since put them (and all others I have come
across) under the microscope to understand their limitations and discover where
the numbers came from. In doing this, I have gained a much greater
understanding of multiple-rail banking, and my pool and 3-cushion game have
improved as a result. I don't number rails much anymore to calculate shots, but
there is no doubt that my analysis of these common systems was important in my
development as a player.

I have written a little about this before (see 'diamond system' in deja news)
but, in summary, here are the essential problems with the plus-2 and corner-5:

plus-2: I think Bob Byrne's characterization of the system as 'dreaded' is very
appropriate. The calculations use the cueball origin and 3rd rail destination
on the long rail to find an aiming point on the short (1st) rail. System
numbers indicate that a 1/2-diamond difference on the short rail becomes a full
diamond difference on the long (3rd) rail for a given cueball origin. This
would only be possible if the 1st rail were parallel to and halfway between the
cueball origin and the 3rd rail point, which it is not. This type of error is
very common in systems that calculate an aiming point on a cushion that is not
parallel to the destination point.

corner-5: A similar thing happens here. Throughout the system's many
variations, the cueball origin numbers are on two rails, long and short, and a
1st rail aim point is calcuated using the cueball origin and the desired 3rd
rail destination. Fortunately, the 1st rail is parallel to the 3rd rail for
long cushion cueball origins, but is not for short rail cueball origins. Right
off this should get you suspicious of its performance from short cushion cueball
origins (which is lousy, and accounts for the fact that most variants of this
system alter numbers that affect short cushion calculations). For long rail
cueball origins, the 1st rail is halfway between the cueball origin and the 3rd
rail destination, but the system numbers indicate that, for a given cueball
origin, a 1/2-diamond difference on the 1st cushion creates a 1/2-diamond
difference on the 3rd cushion, instead of the proportionally correct 1-diamond
difference. You may wonder at this point why anyone would use such a lousy
system with such gross inaccuracies, and how could such a far off system become
so popular and widely accepted as perfect ;) In reality, the system seems to
work OK for certain positions (as does the plus-2) and on some tables it is very
forgiving when it comes to spin applied to the cueball. How can this be? Of
course believing it to be true and fudging the speed/spin (unconsciously or not)
to make it work is one possibility. Another interesting answer lies in the fact
that usually 'thru' aiming points (into the diamonds) are used instead of
'opposite' ones (opposite the diamonds in the track along the rail). A previous
post in dejanews elaborates on this, but the basic idea is that, from certain
cueball origins, a 1-diamond spread of 'thru' points on the 1st rail is larger
than and roughly equivalent to a 1/2-diamond spread of 'opposite' points or the
same rail. This interesting coincidence happens for more 'natural' angles,
which is where the diamond system is most accurate (or least inaccurate :)
Also, I haven't even mentioned spin on the cueball, which has different effects
depending on the angle into the 1st cushion. In brief, sometimes additional
english makes the ball go longer, and sometimes it makes it go shorter.
Curiously, banks aimed at the 2nd diamond on the 3rd rail (which many assume
'goes to the corner') tend to be the most forgiving when it comes to variation
in applied english, and some tables will accept anywhere from zero to maximum
running english for this shot and still follow the same 3rd to 4th rail path.
Bottom line: banking is not easy! There are many variables to account for, and
aiming point is just one of them. Of course it is possible to quantify and
calibrate just about any of them if you really want to, but if you are going to
use a system, make sure you understand why it works ( or doesn't :) and
therefore understand its approximations and limitations.

Rob

BTW, I realize that I have just been criticizing without offering alternatives
or improvements, of which there are many. This was to keep the post to an
almost reasonable length. If anyone is interested in some of these alternatives
or cares to offer up their favorite system for analysis, let me know. I find
this topic very interesting and hope others here do as well :)


Deno J. Andrews

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Jul 25, 1998, 3:00:00 AM7/25/98
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Robert Raiford wrote:
Snippapalooza-

> BTW, I realize that I have just been criticizing without offering alternatives
> or improvements, of which there are many. This was to keep the post to an
> almost reasonable length. If anyone is interested in some of these alternatives
> or cares to offer up their favorite system for analysis, let me know. I find
> this topic very interesting and hope others here do as well :)

I think you bring up some very good points regarding the diamond
systems. I truly believe that it is easier to learn the path of the cue
ball without the numbers than with them. There are so many adjustments
that need to be made on every shot, and then on every different table.
I also used to use many systems, now I am down to just one or two, and
they are only used in a certain type of shot that is not too common.

I also think if someone wants to know a good system to start with, they
can learn the spot on the wall system. It is just as accurate as any
number system offered, and it is much easier to remember. Nice post
Robert.
Deno J. Andrews

Patrick Johnson

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Jul 25, 1998, 3:00:00 AM7/25/98
to
Fascinating, Rob. Your point about all these systems needing constant reality
adjustment is right on the money, and should be taken to heart by anyone who thinks
any one of them can be used right out of the box. I like to think of all these
systems as checks and balances for one another, and try to "overlay" more than one
on a single shot in hopes that they will tend to correct each other's inaccuracies
and alert me if I'm using one of them incorrectly (I do the same with aiming
systems). In the end, they're all just reference tools for shots you have to learn
yourself.

It reminds me of a bleary night at the pool table with a friend. I was trying,
after too many drinks, to aim a long straight-in shot, and complained that I was
seeing three balls instead of one. My friend's advice was characteristically
practical: "Shoot the one in the middle!"

Pat Johnson


Graham Toal

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Jul 25, 1998, 3:00:00 AM7/25/98
to
Robert Raiford wrote:

> While I don't use them now, I used these systems (plus-2 & corner-5) in my
> earlier years of banking study mainly because, although the exhibited the
> problems you mention, they were commonly available/accepted and there weren't
> many decent alternatives. I have since put them (and all others I have come
> across) under the microscope to understand their limitations and discover where
> the numbers came from. In doing this, I have gained a much greater
> understanding of multiple-rail banking, and my pool and 3-cushion game have
> improved as a result. I don't number rails much anymore to calculate shots, but
> there is no doubt that my analysis of these common systems was important in my
> development as a player.

I profess woeful ignorance of this area in as much as I didn't even realise there
were systems and only since coming to america have I even been aware of
the measured diamonds around tables. Either we didn't have them in Europe
or I was singularly unobservant at the time.

Anyway, I've always played your average bank shot in a fairly pedestrian
fashion, but one vacation in the Netherlands my friends took me out for a
game of billiards on the proper sort of table with no pockets. Turns out my
friends were no experts and didn't even play 1-cushion, so I wasn't as
embarassed as I thought I'd be, *but* I did get a chance to watch some of
the old guys playing 3-cushion and I realised that I knew *nothing* about
bank shots compared to these guys, so I devised a series of drills to improve
my game: firstly, I put just one ball on the table, and then had to hit it again
and again, but always playing off a cushion first. The object of the game was
simply to hit the ball ten times in a row, consistently. Although they were
simple kick shots that I thought I would always make, when I started counting
I was scared at first to see I was lucky if I could make 5 shots in a row.
Eventually
I got it down a little better. After that I've been moving up through two cushions
to three cushions, however I've also been moving down from making 10 consecutive
hits to making a lot fewer :-( Nevertheless I keep practicing. I give myself bonus

points if I can make a pot as well as a hit. My intention once I get good enough
at simply hitting a ball via 3 cushions is to then move to making cannons and
actually
take up 3-cushion billiards, but I'm a few years off I think by my current play.
Also
I'm not sure if people play 3-cushion billiards on tables with pockets. I suppose
you can, as a natural extension of British rules billiards, but it seems a little
strange
to me.

G

Robert Raiford

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Jul 25, 1998, 3:00:00 AM7/25/98
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Deno J. Andrews wrote:

> [SNIP]

> I also think if someone wants to know a good system to start with, they
> can learn the spot on the wall system. It is just as accurate as any
> number system offered, and it is much easier to remember. Nice post
> Robert.
> Deno J. Andrews

I agree, Deno. As you know, the 'spot on the wall' principle can be used with
practically any known tracks to find modified aiming points. This is really what
system numbers are trying to calculate (emphasize TRYING) to eliminate the need for
visualization.
For the benefit of those starting out, I would also add that when using the 'spot on
the wall' system (I prefer to call it the 'distant point' method), it is important to
pick a spot the correct distance on the other side of the 1st rail. This distance is
ideally the same distance behind the 1st rail as the length of the shot from the 1st
rail to the target point. The problem with using a real wall/chair/knee/etc is that
it might be too different from the ideal distance to have the shot path converge
properly. Therefore, forget where the actual wall/carpet stain/spectator's arm/etc is
and imagine a point in free space that is as close to the ideal distance beyond the
1st rail as you can get it. This skill is easily acquired with a little practice.
For example, if you are converging on a 3rd rail point going long-short-long (like
typical corner-5 natural), the shot path crosses 1 table width from the 1st to the 3rd
cushion. Therefore, a handy way to find the correct imaginary point beyond the 1st
rail is to erect your own imaginary 'wall' exactly one table width beyond and parallel
to the 1st rail, and notice where it intersects the aim line of the known track that
you want to modify. To converge on a 4th/5th rail point along this known track, do
the same thing, but put up the imaginary wall TWO table widths beyond and parallel to
the 1st rail (because the cueball travels across the table twice from the 1st to
4th/5th rail). Once you understand the principle, its easy and accurate! That's a
nice (and rare) combination, indeed :) Whenever I show this to people, especially
those that like to put their opponents to sleep while calculating shots to 1/10ths of
diamonds (or worse), they invariably say that they prefer their [tedious] calulations
(which are only approximations anyway). When asked why, they either respond with
doubt as to its accuracy because it involves imprecisely imagined points, or else
claim inability to do such visualization (without trying of course) and that I have
some special ability to do this. This 'special ability' came with diligent practice,
of course, and as for its accuracy, it is very forgiving as long as you get the
general magnitude of the distance correct (1 width vs. 2 widths, as in above
example). Once in the very small ballpark, your knowledge and feel for spin/speed/etc
(which you gained from the known track) and visualization of the shot path (which you
are forced to do while practicing this) will take care of the rest with amazing
accuracy. Of course, don't just take my word for it, get on the table and try it
out! Try it with known tracks for any type of shot: one rail, two rail, plus-2,
corner-5, umbrellas, cross tables, double the rails, etc...

Rob

LMoss18701

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Jul 26, 1998, 3:00:00 AM7/26/98
to
>From: Robert Raiford

>> Both systems do work quite well but only if you alter english and force of
>> the hit on almost each shot

i use both the sid and chicago system and follow walt harris inststructions on
how to hit the cueball which works quite well.
his instructions for hitting the cueball and i quote "stroke is very important.
absolute dead ball english and "roll ball" softly, much like a lag....short
bridge, cuestick hits up. "

linda moss

dst...@mediaone.net

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Jul 26, 1998, 3:00:00 AM7/26/98
to
Could you draw an ASCII picture to help me visualize what you are
saying?

Thanks - Dave

Robert Raiford

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Jul 26, 1998, 3:00:00 AM7/26/98
to
Oops, Linda, gotta watch those quotes :) You've got my name attached to some
quotes from the message by Markus Funk that I was responding to. Also, the quote
refers to the subject "2 PLUS System / Diamond system" and not the Sid and chicago
systems, which Markus did say he found to be accurate.

Rob


LMoss18701 wrote:

> >From: Robert Raiford
>
> >> Both systems do work quite well but only if you alter english and force of

Robert Raiford

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Jul 26, 1998, 3:00:00 AM7/26/98
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dst...@mediaone.net wrote:

Darn it, I was afraid someone would go and ask for a simple picture,
when I was trying my best to offer the requisite 1000 words instead ;)
Please remember all of the usual caveats for ASCII pictures, including
but not limited to: use fixed width font/crossing your eyes may help/I'm
an engineer not an art major, captain/etc...and remember, you asked for
it ;)

Step 1. Pick a known track. I'll take the infamous corner-5 system
track to the corner which goes(counter-clockwise in the diagram):
corner->diamond 3->diamond 2->corner using running english of a certain
amount. Of course, almost any type of track will do, but I probably
have a better chance of drawing one that is familiar instead of some
crazy reverse spin-out-of-the-corner or something. Anyway, its probably
better to print this one out...

distant point ----> x
for 4th rail target / :
/ :
/ :
distant point for target / :
between 3rd & 4th rail / :
along known track ----> x :
/ :
/ :
/ :
distant point ----> x :
for 3rd rail target / : :
/ : :
__________________ / : :
| /\ | / : :
| / \ | / : :
| / \ | / : :
|/ \ | / :<---imaginary---->:
2|oo <-3rd rail \ | / : 'walls' :
| \ target \|/ : :
| \ /|3 : :
| \ / | : :
|mid-> oo / | : :
|way \ / |<---one table---->: :
|target /\ | width : :
| / \ | : :
| / \ |<----------two table widths--------->:
| / \ | : :
| / \ | : :
5|________________oo|<-4th rail target : :
start end : :
of known of known : :
track track : :

Step 2. See how far along the known track the desired target point is.
In the diagram I show three examples: on the 3rd rail, on the 4th rail
(in the corner) and somewhere between the 3rd & 4th rails. Make your
best estimate of the distance a ball would travel along the known track
from the 1st cushion to the desired target point. In this example, I
just think of the component of that distance that is perpendicular to
the 1st cushion. In other words, for a 3rd rail target, the ball
crosses the table width once after the 1st cushion, but it crosses the
table width twice after the 1st cushion for a 4th rail target. For
points in between, interpolate accordingly.

Step 3. Sight from the start of the known track into the 1st rail and
extend the line beyond the table to a point that is your best estimate
of the shot distance that was determined in step 2. This is the distant
point where you will aim the cueball to make the shot. In this
particular example, I think that it is easier to find the distant point
by erecting an imaginary 'wall' beyond and parallel to the 1st rail, and
noticing where the known track (when extended past the 1st rail)
intersects the wall. If the target is on the 3rd rail, put up the wall
one table width away from the 1st cushion. For a 4th rail target, put
the wall two table widths away. This is depicted in the diagram and
should make sense with a little thought.

Step 4. Once you have found the distant point while sighting past the
1st rail along the known track, keep looking at it while you walk over
to shoot the cueball. If you shoot the cueball at this imaginary point
using the same speed/english/etc as the known track, you will either
make the shot or else have the sweaters leaning in their chairs as you
miss by hair. The system players will wonder how you calculated the
shot so quickly and accurately. See, a typical system player will have
to worry about figuring track shifts using all kinds of approximations
and allowances. With this modified spot-on-the-wall 'system', the
allowances are built in. That's why you try to be as precise as
possible in using the correct distance from the 1st rail.

NOTE: The only point where the known track and your new ball path will
coincide is at the target point (if you make the shot, that is :) Also,
it is very instructive to physically measure the correct distance and
have a partner stand with a vertically-held cuestick at the proper
distant point. Have the partner stay in the same place while you aim at
the cuestick and try to hit the target point from several different
cueball locations. Remember to try this for all kinds of
shots...reverse, no-english, plus-2, umbrella, etc...

I hope this makes things slightly less confusing...

Rob

LMoss18701

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Jul 27, 1998, 3:00:00 AM7/27/98
to
>From: Robert Raiford

>, Linda, gotta watch those quotes :) You've got my name attached to some
>quotes from the message by Markus Funk that I was responding to. Also, the
>quote
>refers to the subject "2 PLUS

>System / Diamond system" and not the Sid and chicago
>systems, which Markus did say he found to be accurate.
>
>Rob

from linda: OOOOOOPS! SORRY!!

Bob Jewett

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Jul 28, 1998, 3:00:00 AM7/28/98
to
dst...@mediaone.net wrote:

: Could you draw an ASCII picture to help me visualize what you are
: saying?

If you want an introduction to diamond systems, I urge you to get
Byrne's "New Standard Book of Pool and Billiards" It explains several
systems including the corner-five with corrections and the plus-2,
as well as the "opposite three" which is very useful for some pool
challenge shots.

There is an ASCII drawing of the corner-five in the FAQ.

There are several other references for diamond systems in the FAQ.

Bob Jewett


Bob Jewett

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Jul 28, 1998, 3:00:00 AM7/28/98
to
Robert Raiford (erai...@fiu.edu) wrote:

: Here's why Sid and Chicago (really the same system) are so accurate.


: It uses easy to remember numbers that are extremely close to the
: 'theoretical' numbers that are calculated assuming 'angle in = angle out'.

Well, in the table, there is a 1/3 diamond error at 3/3.333. I think
it is easy enough to correct to within the nearest 0.1 diamond, and
that a third of a diamond error is worth worrying about.

: This is a valid assumption because it is a dead ball system using


: medium-soft speed. The actual numbers are a ratio as follows:

: 2nd rail # = (10*d) / (d+8)

: where d = distance in diamonds from the 1st rail to the 2nd


: rail target (measured along 2nd cushion from the corner).

To be really accurate, I think you need to include the fact that the
ball is about 1/6 of a diamond in diameter. That makes the numbers a
little more messy. A common error in the basic construction of diamond
systems is that the balls are assumed to be infinitesimally small.

Bob Jewett


Robert Raiford

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Jul 28, 1998, 3:00:00 AM7/28/98
to
Bob Jewett wrote:
>
> Well, in the table, there is a 1/3 diamond error at 3/3.333. I think
> it is easy enough to correct to within the nearest 0.1 diamond, and
> that a third of a diamond error is worth worrying about.
>

I agree, Bob, a 1/3 diamond error is significant. However, these
numbers are 1/10's of diamonds, so the actual error is reduced
accordingly. Using integers for tenths is how Walt originally published
the systems. See the link I posted if you are not familiar with the
system. In all honesty, I find the exact calculations just as easy to
use for these types of shots, so I use that instead (when I decide to
even bother with numbers). I was just showing that, as far as systems
go, this one has a more solid foundation geometrically than most, and
has easy to use numbers. Maybe my choice of significant figures was
misleading.

>
> To be really accurate, I think you need to include the fact that the
> ball is about 1/6 of a diamond in diameter. That makes the numbers a
> little more messy. A common error in the basic construction of diamond
> systems is that the balls are assumed to be infinitesimally small.
>
> Bob Jewett

I agree, and have mentioned in the past the fact that the actual playing
surface of the table is a ball short in each dimension (see dejanews
'Diamond System'). I believe, however, that the point approximation
(for the ball) is valid and useful when playing all system points
'opposite' the diamonds instead of 'thru' them. I don't mean on the
cushion nose opposite the diamonds, but the actual point of reflection
at the rail, which is a 1/2-ball width from the cushion nose opposite
the diamond. When used this way, the diamonds are as close to 1x2
dimensionally as you can get, albeit harder to use. If table
manufacturers would assume a certain ball diameter and make tables 1x2
according to the center of the 'rail track' instead of cushion nose, the
only error would come from cushion distortion due to speed (which
naturally affects all banks). Until then, maybe we should hit all banks
as hard as possible to better the approximation ;-)

Rob

Wulfe

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Jul 28, 1998, 3:00:00 AM7/28/98
to
I'll second that notion. This book is fantastic, which is
of course to be expected from Mr. Byrne.

Nathan

bp

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Jul 28, 1998, 3:00:00 AM7/28/98
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On Tue, 21 Jul 1998 19:31:09 +0200, "Markus Funk"
<Marku...@rodgau.netsurf.de> wrote:

>Hi,
>
>I have tried out both systems (referring to J. H. Koehlers Book The science
>of pocket Billiards).
>

>Both systems do work quite well but only if you alter english and force of

>the hit on almost each shot. My questions to the group: does anyone has made


>the same experience ? If anybody else uses this system...How do you alter
>english and speed??
>

You need to know how the table is playing ie. short or long, and
simply adjust accordingly. You also need to develop a consistent
stroke with these systems for them to work.


>The Chicago End Rail System by Wal Harris by the way is the most accurate
>one I have seen so far.
>

bp

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Jul 28, 1998, 3:00:00 AM7/28/98
to
On 25 Jul 1998 10:30:22 EDT, Patrick Johnson <pjm...@concentric.net>
wrote:

I wouldn't use any kick or three rail system to make a ball (reliably)
but it sure does help in at least being able to make a good hit (how
many times in a 9 ball set do you need to do that ? LOTS), and if your
lucky they go in. also if the ball is laying in the hole making a hit
is as good as making the ball.
>
>Pat Johnson
>


bp

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Jul 28, 1998, 3:00:00 AM7/28/98
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On Tue, 28 Jul 1998 05:51:43 -0400, Robert Raiford <erai...@fiu.edu>
wrote:


>I agree, and have mentioned in the past the fact that the actual playing
>surface of the table is a ball short in each dimension (see dejanews
>'Diamond System').

But isn't that why you should aim at the diamond and not the spot on
the rail?

Robert Raiford

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Jul 28, 1998, 3:00:00 AM7/28/98
to
bp wrote:

> But isn't that why you should aim at the diamond and not the spot on
> the rail?

No. To be most accurate, you should be aiming at the point of
reflection of the ball. Playing into the diamonds instead of opposite
them (in the 'rail track') magnifies the error by moving the point of
reflection up the rail and shortening the cueball path even more.

To see this effect clearly, consider a simple one rail kick with both
balls equal distance from the same long rail and several diamonds
apart. The obvious banking point is halfway between the balls on the
long rail. This should be a symmetrical shot, so the aiming point
should be the same from both directions. If you aim into the diamond
(halfway btwn the balls) from either ball, the points from either
direction will not coincide and you will miss short either way. If you
aim at a point along the rail track that is opposite the midpoint
diamond and 1/2 ball width from the rail, the aiming points from either
ball will be symmetrical and you will make the shot.

Again, this is just discussing the theoretical aiming point without
accounting for other variables like speed/spin/etc. For example, on
some tables, 'follow' will tend to cancel the shortening effect of
playing into the diamonds, and will cause you to miss long by playing
opposite them. I don't think that effects like this should discourage
anyone from learning a little table geometry, however. In fact, I feel
that it is important to know the theoretical paths to truly understand
how each variable is affecting them. Otherwise, how can you be sure?

Rob

George Rutherford

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Jul 28, 1998, 3:00:00 AM7/28/98
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In article <35BA604A...@fiu.edu>, erai...@fiu.edu wrote:

Substantial snippage

> This skill is easily acquired with a little practice.
> For example, if you are converging on a 3rd rail point going
long-short-long (like
> typical corner-5 natural), the shot path crosses 1 table width from the
1st to the 3rd
> cushion. Therefore, a handy way to find the correct imaginary point
beyond the 1st
> rail is to erect your own imaginary 'wall' exactly one table width

beyond and parallel


> to the 1st rail, and notice where it intersects the aim line of the
known track that
> you want to modify. To converge on a 4th/5th rail point along this
known track, do

> the same thing, but put up the imaginary wall TWO table widths beyond
and parallel to


> the 1st rail (because the cueball travels across the table twice from
the 1st to
> 4th/5th rail). Once you understand the principle, its easy and
accurate! That's a
> nice (and rare) combination, indeed :)

More Spippage

> Rob

Interesting system. I used to use the Diamond System, but found it
innacurate and confusing. I'm going to play some tonight and I'll give
this "spot on the wall" a try. I believe that I understand your first
example, the long-short-long shot, and the one table width displacement,
and can actually visualize it, but I'm unclear as to your explanation of
4th/5th rail shots. It may simply be that I'm confused as to what you mean
by a "known track". BTW, presumably, if you were shooting
short-long-short, the wall would be at a table's length? Interesting
thread, although it is giving me a minor headache. :-)

George

bp

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Jul 29, 1998, 3:00:00 AM7/29/98
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On 28 Jul 1998 21:14:11 GMT, gru...@bilbo.bio.purdue.edu (George
Rutherford) wrote:

Lets see if I can explain it.
A known track is ...hmmm ok this is probably the best known 3 rail
track. If you put the cue ball near the corn pocket and shoot to the
third diamond the cue will go 3 rails into the other corner. (usually)
so if you extent that track ,(stand behind the shot and visualize the
line from the cue ball through the third diamond and keep going until
you find something that you can easily pick out ie a spot on the
wall). Now remember that spot. now you can move the cue ball just
about anywhere and as long as you aim at that spot you can still go
three rails into the corner pocket. It's kind of neat really.

This is of course subject to spin, speed and other factors but it will
give you a good point of reference that you can easily adjust.

Robert Raiford

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Jul 29, 1998, 3:00:00 AM7/29/98
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George Rutherford wrote:
>
> [SNIP]

> I believe that I understand your first
> example, the long-short-long shot, and the one table width displacement,
> and can actually visualize it, but I'm unclear as to your explanation of
> 4th/5th rail shots. It may simply be that I'm confused as to what you mean
> by a "known track". BTW, presumably, if you were shooting

> short-long-short, the wall would be at a table's length? Interesting
> thread, although it is giving me a minor headache. :-)

By the looks of your quoted message (and a note from Bob Jewett), part
of the headache might be my column settings in my mail program, which I
have hopefully fixed. If its not too mangled, I drew an ASCII picture
describing this somewhere in this thread with the new title 'Distant
Point Method', which might be helpful.

What I mean by a known track is this: Any path (or 'track') that you
know the entire path the cueball takes around the table, including rail
hit points. The type of english doesn't matter, just a good knowledge
of the ball path is important. Obviously, the more tracks you know, the
better. The idea this method is based on is finding a way to hit points
along a known path when the cueball is not on the path you know. You are
creating what I will call the 'modified' track that goes from the
cueball's current position, through a similar sequence around the
rail(s) as the known shot, and through the target point on the 'known
track'. If you shot exactly parallel to the known path, which is a
common but incorrect way of modifying known tracks, you would miss the
shot by the exact distance (in theory) that your modified path was from
the known path. Parallel lines never meet, by definition. Obviously
you need to aim your modified path so it converges with the known path
somewhere (hopefully at the target point :) How much of an inclination
'toward' the known path do you aim? That's what the distant point
method helps you find. If you understood the LSL (long-short-long)
example with the 3rd rail target requiring a one table width
displacement of the imaginary wall beyond the 1st rail, then it should
make sense that a two table width displacement is required for targets
farther along the known track that cross the table twice and come back
to the 1st rail (now really called the 4th or 5th or even 3rd rail,
depending on the shot). The 4th/5th rail ambiguity stems from the fact
that for LSL shots, the long rail could be either, depending on the
particular path, LSLL or LSLSL. Does this make sense?

To answer your question: Yes, if you were shooting SLS and the desired
target point is on the 3rd (short) rail, then the proper distance for
the 'wall' beyond the 1st rail is one table length.

Please let me know how the practicing goes, and email me if you have any
more questions. BTW, this method inherently assumes that a fixed amount
of speed and spin have an constant effect off the rails regardless of
incidence angle. Playing without knowing this will give decent
accuracy, but knowledge of this assumption and how to compensate
slightly for different positions makes it incredibly accurate. Using
this kind of judgement is important to using this and any other method
properly. I find this to be a valuable method even with these
assumptions. YMMV

Rob

"Woe to those who know not the assumptions of their methods!"
- Bon Shepett

Patrick Johnson

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Jul 29, 1998, 3:00:00 AM7/29/98
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Robert Raiford wrote:

> If you shot exactly parallel to the known path, which is a
> common but incorrect way of modifying known tracks, you would miss the
> shot by the exact distance (in theory) that your modified path was from
> the known path. Parallel lines never meet, by definition.

You can simplify this concept by imagining shooting a simple one-rail kick shot
with the aid of a mirror. Say your cueball is jawed in the corner pocket and
you want to kick directly into the side pocket on the same side where your
object ball is also jawed. You hang a mirror (from your handy skyhook) so that
it's directly over the edge of the cushion you want to rebound from, then stand
behind your cueball and look into the mirror. You'll see the object ball in the
mirror as if it's on a line extended straight through the rail at a distance one
table width beyond (just like the "distant point" of Rob's method). If you move
your cueball one diamond down the near side rail, stand behind it again and look
at the object ball in the mirror, you'll see it again as if it's on another
extended line, once again one table width beyond the far rail. In fact, you'll
be looking at the same "distant point," and you'll be sighting along a line
which converges with the original line at that distant point.

Actually, you can see this quite clearly at home without a pool table, using any
mirror on the wall. Just pick an object reflected in the mirror, then move a
little to either side and you'll see that the object remains at the same
apparent position, though the point you're looking at on the mirror moves (the
new rebound point on your imaginary rail). Doing this, you can readily see that
the object remains at the end of the original line and is also at the end of
your new line. They quite obviously converge at the "distant point."

To imagine how this works with more than one rail involved, pretend you've hung
mirrors over all the rails. The resulting multiple reflections would look like
you'd pushed lots of pool tables together to fill the room, and to kick three
rails into the opposite corner you'd site at the far corner pocket two tables
over and one up, along a line that looks perfectly straight in the mirrors,
extending out two table widths past the first rail. In reality, hitting more
than one rail magnifies the effects of spin, etc., which is why your "corrected
track" for that shot starts at the 3rd diamond rather than the theoretically
correct point at 2.67 diamonds (you add running english to further correct). To
site this common "known track" using the mirrors, you'd site toward the first
diamond on the long rail near that distant corner pocket in the mirrors (it's
Rob's furthest "distant point" at the end of the extended line, two table widths
away), and that line of sight will cross the first rail directly over the 3rd
diamond. Anywhere you stand, you can shoot toward that same reflected point in
the mirror, hit the correct new first rail point (just like the one-rail kick
example) and, with the right speed and spin, kick three rails to the pocket.

Pat Johnson
Chicago


Robert Raiford

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Jul 30, 1998, 3:00:00 AM7/30/98
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Patrick Johnson wrote:

> [SNIPideedoodah]


> Actually, you can see this quite clearly at home without a pool table, using any
> mirror on the wall. Just pick an object reflected in the mirror, then move a
> little to either side and you'll see that the object remains at the same
> apparent position, though the point you're looking at on the mirror moves (the
> new rebound point on your imaginary rail). Doing this, you can readily see that
> the object remains at the end of the original line and is also at the end of
> your new line. They quite obviously converge at the "distant point."

> [SNIPideeay]

Pat, that's a good description for shots that in theory require no
english. Using the mirrors helps to understand the theory behind the
method, and on relatively new cloth the angles are as close to perfect
as you can find. The method as I described it, however, is more general
than that. I'm saying that ANY english used on a known path will work,
and this necessarily means that the target point on the real table will
be different than where it is on the image table. The two locations
will have a predictable difference, though. To help understand why,
I'll give you an idea of how I quantify spin on the cueball. In
3-cushion, my game of choice, it is very important to know just how much
spin to put on the cueball. The ideas naturally transfer to pool, of
course, and can be very handy. Anyway, here goes...

To a first approximation, assume that a given amount of sidespin has a
constant effect off of a cushion, independent of incidence angle. To
find out how much, shoot perpendicular to the long rail and calibrate
your english so that you can predictably hit 1/2 diamond to the left or
right of your starting position on the opposite long rail. Do the same
for 1, 1-1/2, 2, etc, until you hit your maximum. For me on a billiard
table with new slippery cloth, my maximum is 1-1/2 diamonds, but on a
pool table with dirty/old cloth you might get 2-1/2+ diamonds with
maximum english (BTW, the newer/cleaner the cloth, the more consistently
the table will play according to this method). I personally think in
terms of clock hands, but any consistent way of finding the same spot on
the cueball will work. For me, 1, 2, & 3 o'clock (11, 10, & 9 o'clock)
correspond to 1/2, 1, & 1-1/2 diamonds 'worth of english' across the
width of a table from the 1st rail. With this new quantification of
your english in terms of diamonds across the width of the table,
interesting things are possible.

For example, I'll use your one rail kick example with the mirrors and
assume a 2-diamond maximum, which is typical on a pool table. Kick one
rail from the jaws of a corner pocket into the side pocket on the same
long rail. You know that with no english and medium speed, the proper
aim point is the middle diamond on the opposite rail halfway btwn the
opposite corner and side pockets. If you shoot this with 1-diamond of
running english, you will miss the pocket long by one diamond. This
also means that if you shift your aim point short by 1/2-diamond and
still use the 1-diamond english, you will make the kick. To make the
kick with maximum english, move the 1st rail point over 1-diamond from
the no english aim point. Notice you no longer see the pocket in the
mirror when you place it at a point where english is involved. The
mirror is still useful, however. With 1-diamond of english, you will
see a point that is one diamond short of the pocket in the mirror. In
the same way as you described aiming at the image of the pocket from
anywhere on the table to make the kick, I'm saying that you can aim at
the image of one diamond short of the pocket with 1-diamond running
english and make the kick (assuming you are on the side of the pocket
where running english is applicable).

Now reverse the shot by shooting from the jaws of the side pocket to the
corner with no english. To go one diamond longer than the corner (like
a 3-rail diamond system shot to diamond '1') just add 1-diamond worth of
running english. To go two diamonds longer, add 2-diamonds worth which
is maximum english in this example. You could of course move the aim
point down 1/2-diamond and use only 1-diamond worth of english to go two
diamonds longer than the corner, or any appropriate blend of the
variables. The important thing is that you are calibrating your stroke
in its application of spin...sort of quantifying your 'feel' a little
more precisely. If this all seems too good to be true, please go play
with this idea on a table to see what a decent approximation this is. I
take a small amount of pride in the fact that I've lost due to the
3-foul rule only *one* time in the 10+ years I have played 9-ball, and I
attribute this mild success to using this kind of 'quantification of
feel' for english/speed/etc in my banking and kicking. Please let me
know if you find this to be helpful in your game. :-)

BTW, using this approximation helps one to understand the need to alter
english in the corner-5 diamond system. Forgetting the short rail
cueball numbers, which are garbage, the long rail cueball numbers and
1st rail numbers actually converge properly on 3rd rail points when
english is also a controlled variable. For fun, try shooting shots to
the corner, 1st and 2nd diamonds with no english whatsoever and notice
where you hit the 3rd (now sometimes 2nd) rail. Then, using your newly
quantified stroke, try shooting all shots to the corner (diamond '0')
with 2-diamonds english, all shots to diamond '1' with 1-diamond
english, and all shots to diamond '2' with no-english. Using 'opposite'
points may help. This of course isn't perfect, but is a first step to
understanding some of the ambiguities of this popular system. As you
move above diamond '2' on the 3rd rail, notice that additional running
english starts to make the ball go shorter instead of longer when
compared to the no-english path. This english is having more of an
effect from the 2nd cushion. Warning: some tables are so dirty/worn
that the rails will tend to 'normalize' the amount of spin on the ball
so that multiple rail banks are fairly insensitive to changes in applied
english. I think this is one reason that many claim a certain amount of
success using the diamond system. Nicely maintained equipment, however,
responds to slight variations in spin, which I feel gives the
knowledgeable player more options to choose from.

Rob

Patrick Johnson

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Jul 30, 1998, 3:00:00 AM7/30/98
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Rob,

If I'm not mistaken, you're saying that, once you've found the rail
contact point that works with a given amount of spin, the "distant
point" is located on the line extending through that "adjusted" rail
point and that becomes the distant point for all shots to that point
using the same spin (from whatever new beginning point). This is
exactly what I'm saying the mirror example also illustrates.

For instance, notice that I described the distant point of aim for the
three-rail kick to the opposite corner as being one diamond off the
theoretical distant point represented by the mirror image of that corner
pocket. This gives the adjusted distant point to be used with the same
spin for that three-rail kick from other starting points (through
diamond 3).

It's actually the same principle even for one-rail kicks. Using your
example of adding spin to adjust for longer or shorter one-rail kicks:
let's say you're applying enough spin to require a hit on the rebound
rail a half diamond shorter than the theoretical midpoint. If you sight
into the mirror through that point on the rebound rail, you'll see a
"target" which is one diamond shorter than the pocket you're trying to
hit. That is your distant point for the shot with that spin, and will
also be the distant point for hitting the same target with that same
spin from other beginning points. Once you've found the correct first
rail rebound point for any shot, with or without spin, then the mirror
will show you the distant point for replicating the shot from all other
starting points with the same spin (or the same lack of it).

Are we describing the same thing? I think so.

I like your clock image calibration method for applying replicable
spin. I'm going to give that a try.

Pat Johnson

Robert Raiford

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Jul 30, 1998, 3:00:00 AM7/30/98
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Robert Raiford wrote:
> [SNIP]

> I'm saying that you can aim at
> the image of one diamond short of the pocket with 1-diamond running
> english and make the kick (assuming you are on the side of the pocket
> where running english is applicable).

Now that I read this again it is a little unclear. I mean't that you
can aim at the distant point from anywhere, but that the spin won't be
considered 'running english' when you are on the other side of
perpendicular from the banking point. This, of course, becomes reverse
english (relative to the rail) even though the amount and 'direction' of
spin hasn't changed. Try aiming at the image point from the side pocket
jaws to watch it come back into the side pocket because of reverse spin.

Rob

Tim Hurson

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Jul 30, 1998, 3:00:00 AM7/30/98
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You guys are making my head hurt!!! Doesn't this book have any pictures? ;-)

--
Tim Hurson
Livermore, Ca. USA

thurs...@home.com
To e-mail: remove the knot


Patrick Johnson wrote in message <35C0C57F...@concentric.net>...

Robert Raiford

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Jul 30, 1998, 3:00:00 AM7/30/98
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Patrick Johnson wrote:
>
> Are we describing the same thing? I think so.
>

Yes we are. Somehow I missed the part in your post about the image in
the mirror and the actual hitpoint being different. It was very clear
after a second reading.

>
> I like your clock image calibration method for applying replicable
> spin. I'm going to give that a try.
>
> Pat Johnson

You also might want to try calibrating masse through cue elevation angle
to reach longer points than possible with just english. Pay careful
attention to keeping the same speed, though. Also, if you know the
Coriolis method for aiming masse shots, you can aim to curve into the
distant point using your know amount of english and use the method to
choose elevation and speed for the shot. Just make sure all masse
action happens before the first rail. Very cool :-)

Rob

Robert Raiford

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Jul 30, 1998, 3:00:00 AM7/30/98
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Tim Hurson wrote:
>
> You guys are making my head hurt!!! Doesn't this book have any pictures? ;-)
>

Sorry Tim, but I tried an ASCII picture of this not too long ago, and my
head is still hurting ;-) I have a scanner but no webspace to put up
drawings, which would certainly make this a little easier. I think,
however, that much can be gleaned by a careful (re)reading of the thread
combined with actually trying it on a table. Also, you might want to
peek through Eddie Robin's first one-pocket book as it touches on this
subject a little in the chapter on banking (which was written by Robin,
a former US national champ in 3-cushion).

Rob

Tim Hurson

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Jul 31, 1998, 3:00:00 AM7/31/98
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Robert Raiford wrote in message <35C113D0...@fiu.edu>...


Sorry Rob, I was trying to inject a little humor in this thread. Being a 3 C
player, I am familiar with the 2 Plus System. Trying to discuss/explain, to
the degree as seen in this thread, without diagrams is next to futile IMHO.
I think a reference to Eddie Robin's book would do more for the
understanding of this system than this thread. Bob Byrne in his Standard
Book Of Pool & Billiards book also has a brief explanation of it on page
243. He calls it the "dreaded" plus system because it is so sensitive to
speed and English.

Robert Raiford

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Jul 31, 1998, 3:00:00 AM7/31/98
to
Tim Hurson wrote:
>
> Sorry Rob, I was trying to inject a little humor in this thread. Being a 3 C
> player, I am familiar with the 2 Plus System. Trying to discuss/explain, to
> the degree as seen in this thread, without diagrams is next to futile IMHO.
> I think a reference to Eddie Robin's book would do more for the
> understanding of this system than this thread. Bob Byrne in his Standard
> Book Of Pool & Billiards book also has a brief explanation of it on page
> 243. He calls it the "dreaded" plus system because it is so sensitive to
> speed and English.
>

Sorry for holding a virtual gun to your head and forcing you to read the
thread, Tim. We are not discussing only the plus-2 system. If the
general ideas we have been talking about have appeared in a book then we
could simply tell the page and forget it. The fact is, no book exists
that I know of, including Byrne's and Robin's, that discuss the aspects
of the techniques that we are discussing here. I have made reference to
Robin's and Byrne's books before and have mentioned my enjoyment of
Byrne's characterization of the plus-2 as 'dreaded' in particular, but
this thread still exists because IMO these authors' presentations have
been lacking in certain respects. For example, part of the
'sensitivity' of the plus system can easily be attributed to forcing a
relationship between the short and long rail diamonds that simply
doesn't exist. The only way to make it sort of work is to constantly
fudge english and speed. We are discussing other alternatives that
don't seem to exist in print, so if this bothers you, maybe ignoring us
would be best.

Rob

dst...@mediaone.net

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Aug 2, 1998, 3:00:00 AM8/2/98
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On Fri, 24 Jul 1998 00:38:23 -0400, Robert Raiford <erai...@fiu.edu>
wrote:

>For those interested, the Sid system can be viewed here:
>
>http://www.billiardsatlas.com/sid.html
>

On the above link, the diagram indicates numbers across the top rail:
1.0 2.0 2.5 3.0 3.5, etc.

Do you see a problem here? It goes from 1.0 directly to 2.0, and then
by increments of 0.5. Is this really correct? Or is it a typo in the
diagram?

Just Curious

Thanks - Dave

Gordon Matheson

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Aug 2, 1998, 3:00:00 AM8/2/98
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dst...@mediaone.net wrote in article
<35c31075...@news.jacksonville.net>...


From a non physics point of view: try it, works. You don't have to
understand everything in order to enjoy or use it. Do you really
understand how your T V works. How about your Wife and/or girlfriend??
G.

dst...@mediaone.net

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Aug 2, 1998, 3:00:00 AM8/2/98
to
Ok thanks. Now my next questions...

This was called a "three cushion" solution, but it seems to only
address two cushions. Can you clear that up for me?

Also, is this system somehow applicable to a side-rail-first shot?

Thanks! (I love this group)

Dave

Canpacks

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Aug 2, 1998, 3:00:00 AM8/2/98
to
>"Gordon Matheson"

Wrote>From a non physics point of view: try it, works. You don't have to


>understand everything in order to enjoy or use it. Do you really
>understand how your T V works. How about your Wife and/or girlfriend??
>G.

I have yet to have a tv slap me .Maybe I`m pushing the wrong button???????
It does work ,I tried it.How often do I need it, is another story..
Thanks D Crosby

Gordon Matheson

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Aug 3, 1998, 3:00:00 AM8/3/98
to
I learned about the Sid System on one of The Preacher's tapes. Everything
mentioned concerned end rail first, then side rail then object ball.
Perhaps "three cushion" solution was a reference to three cushion
billiards. Ask Deno.

G.

dst...@mediaone.net wrote in article
<35c38108...@news.jacksonville.net>...

Markus Funk

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Aug 3, 1998, 3:00:00 AM8/3/98
to
Hi There,

sorry to disagree. Ther are at least two books I know abou which have both
systems, the Diamond system and the PLUS system, explained quite well. The
first is by J.H.Koehler and titled The Science of Pocket Billiards and the
second book is the Billiard Atlas on Systems and Techniques.
The Plus system is a dread becuase you always have to alter speed and
english at you own personal preference to make the white go where it is
supposed to go.

regards,
Markus

Robert Raiford schrieb in Nachricht <35C1561E...@fiu.edu>...


>Tim Hurson wrote:
The fact is, no book exists
>that I know of, including Byrne's and Robin's, that discuss the aspects
>of the techniques that we are discussing here>

>Rob

Bob Jewett

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Aug 3, 1998, 3:00:00 AM8/3/98
to
dst...@mediaone.net wrote:
: Robert Raiford <erai...@fiu.edu> wrote:

: >For those interested, the Sid system can be viewed here:
: >http://www.billiardsatlas.com/sid.html

: On the above link, the diagram indicates numbers across the top rail:
: 1.0 2.0 2.5 3.0 3.5, etc.

: Do you see a problem here? It goes from 1.0 directly to 2.0, and then
: by increments of 0.5. Is this really correct? Or is it a typo in the
: diagram?

As Rob pointed out before, the numbers used in the system are
approximations, not the exact numbers. Walt Harris mentions in his
book that the exact numbers would be much harder to deal with, and I
believe him, having calculated some of the exact numbers. There is a
choice between having exact calculations and having do-able
calculations. I think you need to do a division to get the exact
number.

Bob Jewett


Bob Jewett

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Aug 3, 1998, 3:00:00 AM8/3/98
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Markus Funk (Marku...@rodgau.netsurf.de) wrote:

> sorry to disagree. There are at least two books I know about which


> have both systems, the Diamond system and the PLUS system, explained
> quite well. The first is by J.H.Koehler and titled The Science of
> Pocket Billiards and the second book is the Billiard Atlas on Systems
> and Techniques. The Plus system is a dread becuase you always have to
> alter speed and english at you own personal preference to make the
> white go where it is supposed to go.

Well, I think neither book explains how you are supposed to alter the
spin to "make the white go where it is supposed to go." In my view, no
explanation of a system is complete unless it discusses such little
details -- details that are certain to make you miss most of your shots
unless you compensate for them consciously or subconsciously.

Bob Jewett


Markus Funk

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Aug 3, 1998, 3:00:00 AM8/3/98
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Hi Bob,

well in this matter you are right, but in walt harris book for instance,he
discribes what kind of english you have to apply to the ball to achieve your
goal. A freind of mine and very good pool player here in my area altered the
plus system in that way, that he is using always full running english and
medium stroke with a good follow through. I like that way becaus once you
know how english works on your shot, the complete system becomes more
usable.


Bob Jewett schrieb in Nachricht ...

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