I am a Mexican amateur intermediate player and I think that this is a game that you never finish to learn; I consider that we all are students, some more advanced than others. Lately I have been dedicated to study the 3 cushion carom variant of billiards.
I was looking for some websites about three cushion systems and came across this forum, I did some reading and decided to register and make this post.
I spent some time learning how to use the wonderful software here and now I am ready to post about something that keeps troubling my game.
The first book I found about billiards was “Billiards as it should be played”, the classic work of Willie Hoppe published in 1941.
Some billiard’s historians consider this as the book that settled the bar as far as divulging a consistent system for 3 cushions. In his precious work Hoppe also reviews caroms, the American series, and cushion caroms. It is a very complete work indeed.
Different versions of his Diamond System for three cushions are available now in a lot of books and websites, in Spanish and in English as far as I know. Different numbers are assigned to the diamonds but the simple principle remains the same:
Point of Aim = Departure Point – Arrival Point
I am sure that most of you, if not all, are familiar with this system. If you are not you might want to go to this site:
The system shown in the site above is what I will call the S-L-S (Short-Long-Short) part of the system. I call it this way to emphasize that we are shooting from the Short rail to the Long rail and we hit the opposite Short rail as the second cushion. It’s been said, in sites like the one of the French Federation of Billiards, that at least one third of the problems arising in a regular match can be solved with this S-L-S. I believe so.
However, Hoppe includes in his great book another part of the Diamond System, the one that I will refer as L-L-S. A typical member of the family of positions that can be solved using this subsystem is this:
The above formula remains the same. The only remark made by Hoppe, copied and pasted by many people, is that in order to solve problems like this one you must aim to the point of the cushion “in front” of the diamond instead of aiming “thru” the mark as prescribed for the S-L-S system. Other features like English, cue level and speed remain the same: Running English, holding horizontal cue level, and medium speed. Well, as some of you must know by experience this remark is not enough.
I have been looking around the web for a consistent theory to solve this issue but so far I have failed. There are several sites, like some Spaniard Federations websites, the French Federation and many others that for some reason do not even consider this subsystem.
I know two different ways to assign numbers to the diamonds in the departing long rail in the sketch above:
1. Starting from left to right the first diamond takes the number 15, then 20, 25, 30, 35, 40, 45 (diamond seven) and the corner gets 50.
2. Starting from left to right the first diamond takes the 10, then 15, 20, 25, 30, 35, 40 (diamond seven), 45 (spot at the end of the rail) and the corner gets 47.5. See figure below.
The first way is the one suggested by Hoppe and it fails without certain empirical compensations. In my experience the second one has proved to be more accurate since it takes into account those compensations in a more systematic way..
I would very much appreciate your comments on this subject.
Best regards and greetings from Mexico.