Corner-5 gives you a starting line for a running-side-spin, multi-cushion route. Its numbers belong to three different scales. A correct subtraction is useful only when you have read the departure and arrival on the matching diagram.
What the letters mean
D is the originating direction: extend the aiming line back through the cue ball to the departure scale. F is the aiming number on the first cushion. T is the intended third-cushion arrival. With the traditional scale, T = D − F; if you choose D and T first, solve F = D − T.
Do not number the whole table as one circular scale. The departure scale and the first/third-cushion scales are different. Multiplying every value by ten is a consistent change of units; mixing a 5-scale departure with a 20-scale arrival is not.
Read one Corner-5 route in three steps
The drawn route starts immediately after contact with the first object ball; the cue-ball marker is the departure reference.
- Project the cue ball onto the departure scale: 5.
- Choose the required third-cushion arrival: 2.
- Subtract arrival from departure: 5 − 2 = 3, so aim at 3 on the first cushion.
This is a reference route, not a promised result. Recheck it on the table and adjust for cloth, cushions, speed and running english.
Check the arithmetic before aiming
These are number-reading exercises, not recorded scoring shots. The drawn reference explains the contact order; it is not a physics-generated trajectory.
| D · departure | T · third cushion | F = D − T · first cushion |
|---|---|---|
| 5 | 2 | 3 |
| 4.5 | 2.5 | 2 |
| 6 | 3 | 3 |
A useful table check
- Choose one reproducible starting position and mark the intended third-cushion arrival in your notes.
- Read D along the actual aiming line, not simply from the diamond nearest the ball. Changing F can also change that projected departure.
- Keep cue elevation, running side spin and pace consistent while checking the line. Record whether the third-cushion arrival is short or long.
- Change one variable, repeat the same layout and compare the arrival. Keep separate notes for a different table or markedly different cloth conditions.
When the number does not fit
If the subtraction sends the aim outside the diagram’s supported first-cushion range, recheck the chosen route, orientation and scale. Do not add 180 or wrap around the table to force a target. A different starting direction or another route family may be needed.
For a ball-first carom, the useful departure is the cue ball’s direction after contact with the first object ball. Ball thickness and remaining spin affect that direction. The formula alone does not specify the cut, speed or a successful carom.
Use 3Ball as a comparison tool
Open a position in the simulator, identify the first object ball and follow the cushion sequence in the replay. Keep the layout fixed while comparing one aiming or spin change. A simulated result describes the model; check the reference again on the physical table before using it in a match.
The linked Alciatore explanation and technical proof show the numbering convention used here. His illustrated examples include pool tables; pocket geometry and table response should not be transferred to a carom table without checking the actual reference points.