Evernotice those little dots around the rails of a pool table? They're called diamonds and most people think they are decorative, but good players actually use these strategically placed gems to kick at balls when they are in a tight spot. The methods used to calculate these kicks are called 'diamond systems'. For people who play 3-Cushion Billiards, these systems are absolutely essential, but they also apply on any table where the the width (short rail) is half the length (long rail). There are many different diamond systems, but the one that I use most frequently is also known as the Plus System. It involves a little math, but don't worry! It's easy.
The Plus System is very useful for 2 rail kicks that first go into the short rail, then hit the long rail. Each diamond on the long rail and short rail are assigned a value, as shown:
The value on the short rail is half the value of the long rail, and adding those values results in a destination. If your object ball is sitting in the pocket (80), then you find the line that the cue ball is on. For simplicity, I have the cue ball originating out of 30 and going through 50. 30+50=80. You'll want to use a medium speed and hit this shot with about one tip of english, so make sure you grab your favorite chalk and apply some to your cue before trying this one. The number one cause of miscues is not enough chalk, so don't forget!
A more difficult example is with the object ball at 65. The cue ball is originating out of 27 and going through 38. Add those numbers and you will hit your destination. To save time, I always start by finding rounded numbers that are close to the cue ball (like 30+35) then adjust until I find the exact line.
People often say, "Why learn kicking systems if you can only hit it at a certain speed?", but the answer is that once you learn the system you can also start learning the adjustments to make when you have to hit it soft, or when a ball is in the way. It will also give people who kick by feel some backup when they're not feeling it. Most people aren't willing to put in the time and effort to learn these systems, but if you do, you will never regret it. Diamond Systems will help you win in seemingly hopeless situations, and that alone makes it worth it.
One fascinating aspect of mathematical billiards is that it gives us a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers. Have a look at the Geogebra animation below (the play button is in the bottom left corner) and try to figure out how the construction works. If you would like to play the animation again, double click the refresh button in the top right corner. The two natural numbers are 40 and 15 in this case. The least common multiple of 40 and 15 equals 120, and the greatest common divisor is 5. [1]
The diamonds on a pool table consist of nine diamonds and eight segments length-wise. Along with five diamonds and four segments width-wise. Yes, the pockets are included in the count. Having that two-to-one relationship is very important for geometric accuracy. Connecting the diamonds lead to learning the proper angles, this will helps you understand how the cue ball will bounce off the cushions in order to produce the desired impact. [2]
The Tangent Line is one of the most important things to know regarding position play. Simply defined, the tangent line is the natural direction a sliding cue ball takes after contacting an object ball. If a cue ball is rolling when it contacts an object ball (Topspin), or spinning backwards (Draw), when it contacts an object ball, the cue ball will roll forward or behind the tangent line.
The tangent line is perpendicular to a line drawn through the object ball and cue ball at the point of contact. This is a 90 degree angle from the path of the object ball to the pocket. On all shots the cue ball will travel this path unless it is shot with follow or draw.
Depending on the circumstances you may want to have the cue ball follow this line. If that is the case you need to have the cue ball sliding, not rolling or spinning when it makes contact with the object ball. Depending on the distance between the object and cue ball, you have to adjust your contact point on the cue ball or the hardness of the hit. This takes a lot of trial and error to find the best combination of speed and cue tip location.
In some cases you simply need to hit harder to keep the cue ball sliding over a longer distance. In some shots you need to hit lower on the cue ball so it starts out spinning backwards but has stopped spinning at the moment of contact with the cue ball.
Identifying and understanding the tangent line on each and every shot will become a guide to your controlling the cue ball and becoming successful at position play. You can use forward roll or topspin to have the cue ball roll forward of the tangent line, or use a draw stroke to have the cue ball move behind the tangent line.
The tangent line is is the natural line that the cue ball will travel down after impact with the object ball when hit with stun (no top or bottom spin). This is the natural line that the cue ball wants to travel down and spin is the only thing that will take it off of that line. The tangent line is drawn at 90 degrees to the line that the object ball will travel, but starts from the center of the cue ball at impact with the object ball. This is the single most important concept of cue ball control. [6]
To train and become better at pool and cue sports, players need a training cue ball that helps them know where to hit the cue ball to pocket the object ball. The billiard training ball allows players to find the right areas to hit on both the object ball and the cue ball for a cut shot. By using a geometric design, the practice cue ball and object balls allow players to easily see the spots that need to be hit to sink a pool or snooker ball into the pocket.
The two plus system uses the diamonds on the table as markers where each diamond has a numerical value to it. With simple subtraction you can take the numbers from the diamonds to find the exact spot on the table you need to kick at to hit your target.
The other factor to keep in mind is the lower the number on the short rail the more your running English you need to use because the cue ball tends to slide at such steep angles so you need add a little more side English to keep the cue ball on course.
The billiard table diamond system always sparks debate over whether it is a legitimate aiming system. Most billiard tables have diamond spots, and many beginners wonder what they are for. There are many different versions of the diamond aiming system. Here you will learn about the common elements of all billiard diamond aiming systems. You will also learn the basic fundamentals of using the diamond aiming system and we'll describe how the diamond system can help improve your aiming accuracy and your overall pool game.
Use of the diamond system varies. The players, professional or not, who do learn how to use the diamond system swear by its effectiveness. On the other hand, most professional billiard players don't use it, with one exception: that the majority 3-cushion players use a diamond system of some sort. It can be said that most players generally learn the angles without any assistance from the diamond system whatsoever. This ability is beneficial as your "table layout" at the time may not be in a position where you can benefit from the diamond system.
There are "invisible lines" going across the pool table from diamond to diamond, forming a grid e.g. the lines go from each diamond on the left side across the table to the corresponding diamond on the right side. (see the diagram below; the dotted lines illustrate the invisible lines.) You can use the diamonds along with the invisible grid as the base of the diamond aiming system.
The Diamond System can be learned by practicing with simple geometry in mind. The general principle is that if you hit the cue ball (or any ball) perfectly straight at one diamond, it will travel completely straight back toward the diamond at the opposite end of the table. If you hit it from ten degrees either way, and it should rebound ten degrees out in the opposite direction. If you find yourself playing a situation where a diamond is not in the appropriate spot, you will have to envision "imaginary diamonds" in the appropriate spot, and the corresponding imaginary grid lines.
It may sound complicated, but you can worked out the general feel with a few hours at the pool table using only the cue ball. By the end of the session, you should have a good feel for how to use the pool table diamonds to estimate rebound angles.
As mentioned earlier, most three-cushion players use a diamond aiming system. Below is a very basic system (with no English used) that some find helpful as a primer to the more complicated diamond aiming systems. Note that the "System" is a personal thing, and diamond systems vary from player to player.
Other than the above, there is not much more you can "learn" without first logging some hours at the table practicing the basics. Once you have done that, you can read some more. Check out the following works, which go in more deep detail on various uses and systems for the pool table diamonds:
This covers the very bare minimum basics of the billiard diamond system. As mentioned earlier, there is no substitute for hours logged at the table. Read the basics to get a feel for the general idea, and then get off the internet, and hit the table. Once you have mastered the basics, come on back here and get some more advanced information on the diamond system.
To me the pool table diamonds are used for a reference only. They are a starting point and you adjust from there depending on what English is on the ball and the angle. But there are far to many combinations of English and angle and they vary too much for there to be "a system" that works consistently.
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