Conti system
The Conti is a calculation system for three-cushion billiards. It's mainly used for "long cushion – short cushion – long cushion" cushion-first shots: ball 1 touches a long cushion, then a short one, then a long one, before going on to reach ball 3. It can also be used for turned or reversed shots.
It doesn't play the same role as System 4. System 4 predicts where a ball arrives. The Conti does the opposite: you decide where the ball must arrive, and a subtraction tells you where to send it.
⎙ Printable A4 sheet The diagram, the scales and the formula on one page.
The path, cushion by cushion
The diagram shows the table seen from above, with the long cushions at the top and bottom. The start is at the bottom left of ball 1. Ball 1 touches four cushions, in the order of the gold markers: the 1st, the long cushion at the top; the 2nd, the short cushion on the right; the 3rd, the long cushion at the bottom; the 4th, the short cushion on the left (or the corner, or the long cushion at the top), when the shot continues on.
Example shown: start 50, arrival 20 on the 3rd cushion, so aim 30, then arrival 20 on the 4th cushion, in the corner where ball 3 is waiting. The blue dotted line is the aim line: it runs from the start (bottom-left corner) to the aim (at the top) passing through the center of ball 1. The white marks on the rail are the diamonds: these are the reference points. On the 1st cushion, the ball doesn't leave at an equal angle: the system counts using the side spin given to the shot, not a perfect bounce. Numbers boxed in yellow: those of the example.
Where to read the numbers
Four scales, one per role. The white marks on the rail are the diamonds: they serve as reference points. The start and aim numbers are written on the outside, opposite their diamond. The arrivals are read on the nose of the cushion (the rubber), in the orange bands, where dotted lines extend the diamonds. The intervals aren't the same from one scale to another.
- The aim (1st cushion, long cushion at the top, in blue). 0 is in the right-hand corner. Going left: 10 at the first diamond, 20 at the second, up to 50 at the fifth. After that each diamond adds 20: 70 at the sixth, 90 at the seventh.
- The start (long cushion at the bottom, then short cushion on the left, in gray). 15 at the first diamond starting from the right, then 5 more per diamond going left: 20, 25, 30, 35, 40, 45. 50 is in the left-hand corner. The count continues on the short cushion, going up: 60 at the first diamond, 70 at the second, 90 at the third, with 80 between the second and third.
- The arrival on the 3rd cushion (long cushion at the bottom, orange band). From 0 on the right to 100 on the left, with irregular intervals: 0 is 0.6 diamond from the short cushion on the right, 10 is at 1.6, 20 at 2.3, 30 at the third diamond, 40 at 3.7, 50 at 4.4. Then 60 is at the fifth diamond, 80 at the sixth, 100 at the seventh, with 70 and 90 in between.
- The arrival on the 4th cushion (light orange band). It has its own scale, with the same numbers. It starts on the long cushion at the top (−10 at the fifth diamond starting from the right, 0 at the sixth, 10 at the seventh), passes through 20 in the top-left corner, then goes down the short cushion on the left from 30 to 100: 30 is at the first diamond starting from the top, 50 at the second, 80 at the third, and the numbers bunch closer together toward the bottom.
1. Choose the arrival
Look at where ball 3 is waiting, and decide at what point on the 3rd cushion (the long cushion at the bottom) your ball 1 needs to pass to reach it. The corresponding number, read on the orange band, is the arrival. In the diagram: 20.
2. Choose a start
Several starting points give the same gap with the arrival. You need the one whose line, drawn to the aim, passes through the center of your ball 1. You try one, calculate, and check. In the diagram: 50, in the bottom-left corner.
3. Subtract: the aim
start − arrival on the 3rd cushion = aim on the 1st cushion
In the diagram: 50 − 20 = 30, you aim for 30 on the 1st cushion, on the long cushion at the top. Then check that the line from the start to the aim really does pass through your ball 1. If not, change your start and start over.
4. Going on to the 4th cushion: the correction
Up to the 3rd cushion, the subtraction is enough. If the shot continues on to the 4th, you add a correction, because the path between the 3rd and 4th depends a little on the start chosen. The result is read on the 4th-cushion scale:
arrival on the 4th cushion = arrival on the 3rd cushion + correction
The correction is never applied to the 3rd cushion, only to the 4th. The known corrections here:
| Start | 30 | 40 | 50 | 70 |
|---|---|---|---|---|
| Correction | −5 | −1 | 0 | +5 |
A start of 50 adds nothing: 20 on the 3rd cushion, 20 on the 4th, as in the diagram above.
The calculation in 6 steps (click)
Step 1. You decide where the ball must touch the 3rd cushion to reach ball 3: here 20 (boxed). Ball 3 is waiting in the corner.
Step 2. You try a start: 50, in the bottom-left corner.
Step 3. You subtract: 50 − 20 = 30. The aim is 30 on the 1st cushion, on the long cushion at the top.
Step 4. You check: the line from 50 to 30 passes through the center of ball 1. If it passed to the side, you'd change the start.
Step 5. You play toward 30. The ball touches the 1st cushion, the short cushion on the right (2nd), then the 3rd cushion at 20, as expected.
Step 6. To go on to the 4th cushion, you add the start's correction: 0 for 50, so 20 + 0 = 20. The ball ends up in the corner and touches ball 3.
Where is ball 3? Three examples
The same calculation works no matter where ball 3 is. What changes is the cushion where you want to arrive. In each diagram, only the numbers used in the calculation stay legible and boxed, the rest are faded.
1. Ball 3 is against the 3rd cushion
It's waiting near the 20 on the long cushion at the bottom. The shot stops there: ball 1 touches the 1st, 2nd, 3rd cushion, then ball 3. So we want to arrive at 20 on the 3rd cushion. Your ball 1 is on the line for start 40: 40 − 20 = 20, aim for 20 on the 1st cushion.
2. Ball 3 is against the 4th cushion, on the long cushion at the top
It's waiting around 15 on the 4th-cushion scale, between 10 and 20. The shot goes all the way to the 4th. Your ball 1 is on the line for start 30, and we choose to arrive at 20 on the 3rd cushion: 30 − 20 = 10, aim for 10 on the 1st cushion. Correction for start 30: −5, so 20 − 5 = 15 on the 4th cushion. That's where ball 3 is waiting.
3. Ball 1 starts from the side: start on the short cushion
Start 70 is on the short cushion on the left: ball 1 is on the side of the table. Ball 3 is waiting against that same short cushion, around 45 on the 4th-cushion scale. We want to arrive at 40 on the 3rd cushion: 70 − 40 = 30, aim for 30 on the 1st cushion. Correction for start 70: +5, so 40 + 5 = 45 on the 4th cushion.
📐 These paths are drawn by hand from the reference figure: they show the order of the cushions and the numbers to read, not the exact geometry of the trajectory. On a real table, side spin and the cloth shift it a little.
The stroke: always the same one
The system only holds up if the shot is repeated identically. Ball 1 is hit high, that is above the ball's center, with the maximum "good" side spin. The speed is that of an ordinary shot, neither soft nor hard: enough for the balls touched to travel at least 40 cm.
Setting up the system for your table
Not all tables return the ball the same way. Before relying on the values, play the four test shots below and note where the ball actually arrives on the 4th cushion:
| Start | Aim (1st cushion) | 3rd arrival | Expected 4th arrival |
|---|---|---|---|
| 50 | 30 | 20 | 20 |
| 40 | 20 | 20 | 19 |
| 30 | 10 | 20 | 15 |
| 70 | 30 | 40 | 45 |
If the first shot arrives at 22 instead of 20, your table adds 2: keep that +2 in your following calculations.
The full step-by-step guide, with a tool that calculates your setting from the four shots, is in Testing your table.
Calculator
Enter the start and the intended arrival on the 3rd cushion. The calculator gives you the aim, and the 4th cushion once your table's correction is known.
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Practicing the Conti
A start and an arrival drawn at random: it's up to you to subtract. The first exercise asks for the aim, to click on the cushion at the top. The second goes all the way to the 4th cushion, with the start's correction. Chain them together: that's how the subtraction becomes automatic at the table.
⚠️ These values are theoretical. The side spin given, the cloth's condition and the speed change the actual trajectory. The Conti demands serious study: setting it up for your own table and repeating the same shots are what bring precision.