Diamond system
A second calculation system for three-cushion billiards, alongside the Conti system already explained on this site. The principle is the same — a start and an arrival give, by subtraction, the point to aim for — but the reference marks and the formula are different. It comes in handy when a ball happens to sit right on the aim line the Conti system would need.
Sometimes called the "+ system" or diamond system, it is only confirmed here for a start between the 2nd and 7th diamond of the long cushion: outside that range, the method described on this page does not apply.
⎙ Printable A4 sheet The formula, the reference marks and the cue stroke on one page.
The principle
Ball 1 starts from the bottom long cushion, at a numbered position: the start. You choose where you want it to come back, the arrival — on that same bottom cushion if it's close, or further on the left short cushion if it goes past the 7th diamond. A subtraction between the two gives the aim: the diamond to look at, on the right short cushion, for the ball to go touch there before coming back.
Bottom cushion: start and arrival, numbered 0 to 7 from the right corner — the confirmed domain for the start (2 to 7) is in gold. Right cushion: the bounce numbering, fixed, from 0 (top-right corner) to 4 (middle diamond) — it only goes halfway along the cushion, not all the way to the opposite corner. Left cushion: the arrival continued beyond the 7th diamond, from 8 (bottom-left corner) to 11 (middle diamond) — it too only covers half the cushion.
Where to read the reference marks
Everything is counted in diamonds, those white markers set into the cushions.
- Start: the position of ball 1 on the bottom long cushion, counted from the right corner, 0 to 7. The system, as confirmed here, only covers starts from 2 to 7.
- Arrival: the spot aimed for on the ball's return. If it's 7 diamonds or less from the right corner, it's read on the same bottom cushion as the start. Beyond that, it continues on the left short cushion, from 8 (just past the corner) to 11 (at the middle diamond).
- Aim: the result of the subtraction, read on the right short cushion — a fixed scale, always the same, from 0 (top-right corner) to 4 (middle diamond), whatever the start.
The formula
Aim = Arrival − Start
You choose the arrival you want, you know the start (the position of ball 1), and the subtraction gives you directly the diamond to aim for on the right short cushion.
The calculation in 6 steps (click)
Step 1. You locate the start: the position of ball 1 on the bottom long cushion. Here, start = 6.
Step 2. You choose the arrival you want. Here, arrival = 9: past the 7th diamond, it's read on the left short cushion.
Step 3. You subtract: aim = arrival − start = 9 − 6 = 3.
Step 4. You aim for this point, 3, on the right short cushion — that's where the ball must touch before coming back toward the arrival.
Step 5. After touching the right cushion at diamond 3, the ball bounces — true reflection, angle of incidence = angle of reflection — toward the top cushion.
Step 6. The last segment, dashed, joins the arrival announced by the calculation: here 9, on the left cushion. A visual adjustment, owned up to — pure reflection doesn't always land exactly right (see the note at the bottom of the page).
Five examples, from the tightest to the widest
Five cases, in order of the aim's angle (the aim diamond): from the tightest (1) to the widest (4), to see how the path changes depending on the start and arrival chosen.
Start 2, aim 1, arrival 3: the tightest angle in range
Aim = 3 − 2 = 1. Start at the 2nd diamond, the low end of the confirmed range: the ball aims right next to the corner of the right cushion, the tightest return angle this system covers.
Solid line: the two real bounces, calculated by reflection (angle of incidence = angle of reflection) — right cushion, then top cushion. Blue dashes: the last segment, adjusted to land exactly on the arrival announced by the calculation — pure reflection doesn't always land exactly right (see the note at the bottom of the page).
Start 5, aim 2, arrival 7: the last diamond still counted on the bottom cushion
Aim = 7 − 5 = 2. The arrival (7) is the last value still read on the bottom cushion: one diamond further, it would switch to the left cushion, as in the example further down.
Same logic: solid line for the two real bounces, blue dashes for the adjusted return to the arrival.
Start 3, aim 3, arrival 6: everything on the bottom cushion
Aim = 6 − 3 = 3. The arrival (6) doesn't go past the 7th diamond: it stays on the same bottom cushion as the start. The ball touches diamond 3 on the right, bounces off the top cushion, then comes back to touch the bottom cushion at the arrival.
Solid line: the two real bounces, calculated by reflection (angle of incidence = angle of reflection) — right cushion, then top cushion. Blue dashes: the last segment, adjusted to land exactly on the arrival announced by the calculation — pure reflection doesn't always land exactly right (see the note at the bottom of the page).
Start 6, aim 3, arrival 9: the arrival continues on the left
Aim = 9 − 6 = 3. The arrival (9) goes past the 7th diamond: it's read on the left short cushion, at the 2nd position on that scale (8, then 9). Same aim diamond (3) as the previous example, but a different start and arrival.
Same logic: solid line for the two real bounces, blue dashes for the adjusted return to the arrival, this time on the left cushion.
Start 7, aim 4, arrival 11: the widest angle in range
Aim = 11 − 7 = 4. Start at the top of the confirmed range (7) and aim at the top of its scale (4, the middle diamond of the right cushion): the widest return angle this system allows, with an arrival that lands far down the left cushion.
Same logic, at the other end of the range: solid line for the two real bounces, blue dashes for the adjusted return to the arrival.
The cue stroke
The system only holds if the stroke is repeated identically every time:
- Ball struck in the center, at center height (no pique, no elevated cue).
- 2 tips of good side spin, always the same.
- Cue held as horizontal as possible.
- You aim right at the heart of the diamond — the marker itself, not its shadow or its reflection.
- A measured stroke, neither pushed nor held back: the speed of an ordinary shot.
Calculator
Enter the start (bottom long cushion) and the arrival you want (bottom cushion if ≤ 7, otherwise left cushion).
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⚠️ System reconstructed from several public sources and back-and-forth exchanges over the diagrams, in our own words. The two bounces traced on the examples (right cushion, then top cushion) are calculated by true reflection (angle of incidence = angle of reflection); we checked that this pure reflection doesn't always land exactly on the arrival announced by the calculation (the gap runs up to about 0.7 diamond depending on the start and aim chosen) — which is why the last segment of the path is adjusted rather than purely calculated, and shown dashed to flag it. As with any calculation system: the side spin given, the condition of the cloth and the speed change the real trajectory.