Half System Half / Mirror
A no-English aiming reference that uses the midpoint at equal distances and a mirror construction when distances differ. It also applies to the 3-cushion half reference line that goes around the corner.
Written and edited by TTBoys · How we write and check sources · Report an error
Sources and diagrams reviewed: 2026-10-04. Rules of thumb are practice references for a specific diamond scale and stroke. Geometric constructions are kept separate from real trajectories, and nothing was measured on a real table. On mobile, the table stays in landscape so the directions in the text match the diagrams.
Presets are comparison examples from a physics model; they do not guarantee the formula's real-world accuracy or a point.
What do you read from the layout?
- Cue ball 6: its position along the long axis.
- Target 2: the target position for this one-cushion drill.
- Aim 4: (6 + 2) ÷ 2 when the distances are equal.
Slope and correction: If the two balls sit at different distances from the cushion, drop the average and find the point again with the mirror construction. It does not work by adding an arbitrary angle correction.
New to this? Start here
“Half” means half. First check whether the two balls are the same distance from the cushion you will aim at. If you miss this condition, the path changes even if you aim at the midpoint. Here the red ball shows the target position.
- Compare the lengths of the dashed lines dropped straight from each ball to the cushion you will aim at. Use the simple average only if the two lengths are equal.
- In the example the horizontal positions are 6 and 2. Add them to get 8, divide by 2, and aim at the midpoint 4. This is a geometric reference for a single rebound.
- If the distances differ, stop halving and look at the mirror construction below. Imagine the target moved the same distance outside the cushion, then connect it to the cue ball with a straight line.
Check yourself: Cue ball at 6 and target at 2, but their distances to the cushion differ. Do you still always aim at 4?
No. The equal-distance condition is broken, so you need the mirror construction. As in the example below, the aim point can shift toward the nearer target.
6 → 3 · 3C
When both are the same distance from the cushion
It isn't just a matter of averaging the two balls' long-rail coordinates. In real play you also consider the target point for the cue ball center that matches the ball radius and the contact thickness you want.
When distances differ, mirror the target
If the perpendicular distances to the reflecting line are d₁ for the cue ball and d₂ for the target, and their horizontal coordinates are x₁ and x₂, the aim coordinate is (x₁d₂ + x₂d₁) ÷ (d₁ + d₂). This follows directly from the ideal model in which the angle of incidence equals the angle of reflection.
The half reference line applied to 3-cushion
- INPROD's half is a practical reference line that goes around the corner by aiming at half the departure, such as long-rail departure 8→4 or 6→3. How the ball meets the two cushions at the corner is sensitive to ball size and spin, so don't predict a score from an ideal point-particle corner collision.
- If you hit the first object ball first, read the departure number from the line after the collision. Practice from a reference stroke with no left-right spin and no excessive follow or draw.
- The mirror value is a first aiming reference. Tendencies such as playing short when hit hard depend on speed, roll and cushion condition, so adjust on the real table.
Practice with the example layout
Back to the worked example and layout ↑The red ball in the picture is the target of a one-cushion drill. This picture alone does not complete a 3-cushion point that hits all three balls. In play, plan the ball to hit first, the remaining cushions and the last ball separately.
- Point to the cue ball and the cushion target where the calculation ends. Then think separately about the cushions and the order of the two object balls after this partial route.
- Repeat the same layout 5 times and record where the first cushion and the calculated target actually land.
- If the first cushion is already off, check your aim and thickness; if the first cushion is right but later ones drift, check spin and speed. Change only one thing for the next 5.
Sources and verification
- Dr. Dave · Mirror Kick and Bank Shot Aiming System — The mirror construction and why real shots need corrections.
- INPROD · 당구 3쿠션 하프시스템 — The 8→4 and 6→3 reference lines, the departure line after the object-ball collision, no left-right spin.
- Dr. Dave · Bank and Kick Physics Effects — Effects of power, spin, cloth and cushions. Pool experiments, not a verification of 3-cushion number tables.
Sources may use different diamond scales and conditions. The text notes which scale it uses and the limits of what was checked; the diagrams are our own concept drawings.