One-cushion system
A small calculation rule for guessing where ball 1 will go on to touch the opposite cushion after grazing ball 2, when the shot crosses the table along its width. It's played with no side spin and fits in one line:
CD = 4 − AB
Here AB is measured from the starting cushion to ball 2, where the collision happens: it's this distance that sets the path left for ball 1 after contact.
The shot
These are the conditions of the natural shot: ball 1 aims at half of ball 2, it's hit high and with absolutely no side spin. On contact, ball 2 moves off to the right and ball 1 is sent off to the left of its path. The rule gives the number of diamonds separating where ball 1 arrives from where it would have touched the opposite cushion had it kept going straight.
The three reference points
Everything is measured with the diamonds, those white markers set into the cushions. In the diagrams, the starting cushion is the long cushion at the bottom and the opposite cushion the one at the top. Across the width, there are 4 diamonds: the scale on the left numbers them from 0 (starting cushion) to 4 (opposite cushion).
- AB: how far ball 2 is from the starting cushion, in diamonds. You read it on the left-hand scale, level with ball 2; ball 1 can be anywhere behind it, on the aiming line. In the diagram, AB = 2.
- The aimed point: where the aiming line, if extended, would end up on the opposite cushion (this is the 0 of the count, at the top).
- CD: the gap, in diamonds, between this aimed point and where ball 1 actually touches the cushion, measured to the left when looking at the opposite cushion from the starting one.
AB = 2, so CD = 4 − 2 = 2: ball 1 (white line) arrives 2 diamonds to the left of the aimed point. Blue dotted line: the extended aiming line. Dotted circle: ball 1 at the moment of impact, at half-ball. Yellow dotted line: ball 2 is pushed to the right.
The formula
CD = 4 − AB
The reasoning: after the collision, ball 1 leaves at a rejection angle of about 40 to 45°, so it shifts by as many diamonds as it has left to travel to the opposite cushion. What's left for it is the width (4) minus how far along ball 2 is: the closer ball 2 is to the starting cushion, the more path ball 1 has ahead of it and the more it drifts. The rule is given for three positions:
| AB (diamonds) | CD (shift) | Direction |
|---|---|---|
| 3 | 1 | Left of the aimed point |
| 2 | 2 | Left of the aimed point |
| 1 | 3 | Left of the aimed point |
The calculation in 5 steps (click)
Step 1. Measure AB: ball 2 is 2 diamonds from the starting cushion. You read it level with ball 2 on the left-hand scale (yellow dotted line).
Step 2. Calculate: CD = 4 − AB = 4 − 2 = 2.
Step 3. Aim at half of ball 2 and extend the aiming line (blue dotted line) to the opposite cushion: this is the aimed point, the 0 of the count.
Step 4. Count CD = 2 diamonds to the left from the aimed point: that's where ball 1 must arrive.
Step 5. Play it high, with no side spin. Ball 1 touches ball 2 at half-ball, deflects left and arrives on the opposite cushion at the expected point; ball 2 moves off to the right.
Three positions
AB = 3: shift of 1 diamond
Ball 2 is almost against the opposite cushion: only a single diamond of path is left after the collision. CD = 4 − 3 = 1: ball 1 ends up 1 diamond to the left of the aimed point, even coming from far away.
AB = 2: shift of 2 diamonds
Ball 2 is at mid-width. CD = 4 − 2 = 2: ball 1 ends up 2 diamonds to the left of the aimed point. Chain a few attempts, noting the arrival each time: you'll quickly see whether your table and your stroke match the rule.
AB = 1: shift of 3 diamonds
Ball 2 is right next to the starting cushion, ball 1 just behind it. CD = 4 − 1 = 3: this is where the shift is largest, and so where the slightest irregularity in the hit shows up most at the arrival. Take extra care with the high hit.
Adding side spin
Each dose of side spin adds one diamond to the shift: CD = 4 + doses − AB. The sum AB + CD is then 4 with no side spin, 5 with one dose, 6 with two. For the same position, the arrival moves further from the aimed point by one diamond per dose.
| Side spin | AB + CD | CD for AB = 2 |
|---|---|---|
| None | 4 | 2 |
| 1 dose | 5 | 3 |
| 2 doses | 6 | 4 |
Same position (AB = 2), three arrivals: 2, 3 or 4 diamonds to the left of the aimed point depending on the dose of side spin.
When the shot isn't straight
On a real table, ball 1 and ball 2 are rarely lined up exactly perpendicular to the cushion. The counting stays the same in three moves: AB is always read level with ball 2 on the left-hand scale (not along the diagonal), the aimed point is the extension of the aiming line, and you count CD to the left on the opposite cushion. What changes is the value of CD: it's no longer the one from the table. Our approximate calculation gives this trend:
| Aim | Rejection | CD relative to the table |
|---|---|---|
| 20° to the right | tighter | × 0.85 |
| 10° to the right | tighter | × 0.9 |
| Straight | — | × 1 |
| 10° to the left | wider | × 1.2 |
| 20° to the left | wider | × 1.7 (danger, see below) |
To the right: little difference
Ball 2 is up and to the right of ball 1. Here, AB = 2 and the aim goes off 15° to the right: ball 1 arrives a little less far from the aimed point than in the straight case, around 1.7 diamond instead of 2. The table remains a good baseline.
Aim 15° to the right, AB = 2: CD ≈ 1.7. AB is always read level with ball 2.
To the left: the shift grows
Ball 2 is up and to the left of ball 1: ball 1 is sent even further left, and the shift grows fast. With 15° to the left and AB = 2, you end up closer to 3 diamonds than 2.
Aim 15° to the left, AB = 2: CD ≈ 2.9.
Near the corner: the counting no longer works
The further left you aim, the flatter ball 1 leaves. If the count takes you past the first diamond of the opposite cushion, toward the corner, the ball touches the short cushion before reaching the opposite cushion: the formula no longer applies, you need to change shot or system.
Aim 25° to the left: ball 1 leaves almost flat and touches the short cushion.
These diagonal corrections are our own approximate calculation, not a published rule: they combine the formula with a rejection angle of about 42° and should be checked at the table.
When the formula breaks down
Two setups fall outside the scope of the formula:
- Ball 2 against the opposite cushion: almost no path is left after the collision, and ball 1 must be hit one notch lower than usual for the arrival to stay the one predicted.
- Balls 1 and 2 almost touching: ball 1 is sent off harder than expected, so it arrives further left than the formula says.
The rule gives an order of magnitude to fine-tune at your table: it's by regularly playing the same positions that you'll learn to correct these small gaps.
Calculator
Enter the distance AB (from the starting cushion to ball 2, in diamonds), the direction of your aim and the number of doses of side spin.
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⚠️ Theoretical values: the table, the cloth, the speed and the condition of the cushions change the actual trajectory. Check every position at your own table before relying on it.