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The Diamond System This section is the result of a partnership with Billard Club Sottevillais. We realy hope this information will help improve your mathematical thinking of billiard. Although this information is specific to the game of Carom Billiards, it is clear it will help you figure out (1) how the rails can be calculated and (2) how to efficiently use the diamonds situated around the table. Follow each step… one at a time. 1. The Basic Diamond System 2. Efficiency Limits 3. Step 1 : Finding the Finish Point 4. Step 2 : Finding the Start Point 5. Step 3 : Visualize the cue ball position numbers 6. Ball No 1 is not along the rail 7. Other examples of the Diamond System 8. Extend this method to the "Natural Points" 9. Extend this method for 4 or 5 rails 

The Basic Diamond System Basics setting Height on cue ball : Center Spin : Maximum Cue stick position : Parallele to the floor This system is considered to be the universal method for carom billiard. It’s a common fact that in a game of Carom Billiard more than 1/3 of the points will be made with the help of this technique. The shots shown below are just a few examples of the points that can be accomplish with this method. Although the formula is quite simple to memorize, the position markers are much harder to remember, the values carried over on the table being different for the 3 parameters (A, S, F). To remember : Aim = Start  Finish If you have difficulties remembering all the diamond system parameters, for now I suggest you use this method for shots where the Finish point is between 0 and 40 and the start point between 35 and 60. When you feel comfortable with these parameters, go on with the entire set of numbers. 
Efficiency Limits This method is efficient for shots played “Long rail Short rail” when the Start value is higher than the finish value. It’s not possible to apply this method when the player’s ball is below the 20 marker (2nd diamond on the long rail). Be patient… there is another method for shots below the 20 marker. In the diagram below, Start is at 30 and finish is at 50, which means it’s impossible to accomplish this shot with this method. At best, one could reach the finish point 30 while using the aiming point 0. 
Step 1 : Finding the Finish Point You must keep in mind the finish lines as they are described in the table below. The markers are located on the rail in front of the corresponding diamond. Note: between the 40 and 90 marker on the long rail, each set of 10 corresponds to ˝ a diamond. 

In this diagram, the finish value is 20. It must come to the attention that each point located on this line is the equivalent of a 20 finish point. There is no difference in calculation between the diagram above and the one below. 
Step 2 : Finding the Start Point When the player’s ball is on the long rail, the start value is given in the table below. 

In this diagram the start value is 50. 
Step 3 : Visualize the cue ball position numbers It’s now time to apply the magic formula: Aim = Start  Finish. Aim = 50 – 20 Aim = 30 The point of aim 30 is given according to the table below. Note : between the 50 and 90 marker on the long rail, each set of 10 corresponds to ˝ a diamond. 

Note : If the starting point is on the short rail (equal or higher than 50), aim must be done through the rail (aim at the diamond). If it starts on the long rail (lower than 50), aim must be in front of the rail (facing the diamond). In both cases below, the aiming point value is 20. 
Ball No 1 is not along the rail If ball number 1 is not along the rail, pivot your cue while using your ball’s axis as pivot point until you reach the right application of the formula : Aim= Start  Finish. 
Other examples of the Diamond System 
Extend this method to the "Natural Points" This system can be applied to those points called "natural". In order to find the point of aim (or the point of impact on the first rail), one must use the pivot method to find the right pair Aim/Start corresponding to the formula. This time, the pivot will be ball number 2 and the pivot line will be the ball’s tangent and not its axis. You will then need to find the corresponding ball in order to reach the aiming point obtained. The two examples below show how to obtain the same aiming point with different number 1 ball positions. 
Extend this method for 4 or 5 rails The diagram below gives the path of ball number 1 after the 4th and 5th rail with a 30, 40 and 50 start point. 

Extend formula to realize this shots. 
That’s it ! And to show you that this method is valid for various points, here’s how to calculate the famous "umbrella" point (but be careful it’s still a hard shot to accomplish). 
All rights reserved / Copyright © 19982011 by Eric Perreault 