Tips / Systems

Five & Half Five & Half System

A rule of thumb that finds the third-cushion arrival from the difference between the departure number and the first-cushion number on a long → short → long path. This page uses INPROD's scale system.

Formula / route reference

Third-cushion number = cue ball number − first-cushion number

When to use it

Side-around shots and bank shots that hit the far long rail first and come through the short rail to the opposite long rail. If you hit an object ball first, read the departure number from the path after the collision.

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.

Compare in the simulator

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?

Start 50: read it by extending the cue ball’s path backward.
Target 30: the arrival number at the third cushion.
Aim 20: the first-cushion number from 50 − 30.

Slope and correction: Don’t add a separate angle correction. If the cue ball moves, read the aiming line and the start number on its extension again. The path after the third cushion depends on the starting position.

See the worked example and layout See related practice

New to this? Start here

You don't need to memorize every number at first. Start with one example: finding arrival 30 from departure 50. The cue ball is the white ball you strike, and the first cushion is the cushion it touches first.

First aim only: red departure 50 − white arrival 30 = yellow first cushion 20. The dashed line is the extension used to read the departure number. This is a concept diagram that ignores the offset between the frame and the ball size.

First decide on the white arrival 30. Then extend the cue ball's aiming line backward to read the red departure 50.
What you want is the first aim point, so rearrange the formula: 50−30=20. Aim at yellow 20. 50−20=30 is the same calculation used to check the arrival.
In the full path diagram below, follow long rail ① → short rail ② → long rail ③. Learn up to the third cushion first; you can read the fourth-cushion correction afterward.

Check yourself: Starting from 50, what is the first aim number if you want to arrive at 20?

50−20=30, so the first cushion is 30. Find yellow 30 on the scale below. It is a different scale from red departure 30 or white arrival 30.

Departure, aim and arrival use different scales

Cue ball number: 15–50 on the long rail, 60 and 70 on the short rail, then 10 per half diamond
First-cushion number: 10 per diamond from 0 to 50, then 10 per half diamond
Third-cushion number: 10 per diamond from 0 to 40, then 10 per half diamond

First-cushion 50 and third-cushion 50 are in different places. Other materials may differ from the point where the first-cushion spacing changes, so use one source's table, tip position and corrections together. Long paths with high numbers need more separate correction than the basic range.

Frame points and rail points

Aim at a frame point and the ball touches the cushion short of it, toward the cue ball (by the red section). The more oblique the shot, the larger this gap.

This page reads the cue ball number and the first-cushion aim at frame points (the diamonds on the rail) and the third-cushion arrival at rail points (the cushion nose). The lines in the diagrams are path concepts and don't precisely reproduce the offset between the ball center and the frame.
If the cue ball is inside the table, extend the line joining the first-cushion candidate and the cue ball backward to read the departure number. Adjust while checking that departure number − target arrival number matches the candidate.
When you hit the first object ball first, extend the cue ball's line after the object-ball collision, not the original cue ball position.

Reference shot: 50 − 20 = 30

A layout example for 50−20=30: long ① → short ② → long ③ at 30, then the red object ball 1 and the yellow object ball 2. The yellow path is the part you still plan after the third cushion.

Red dashed line: extend the first aim line backward to read the start number
White line: the order in which the cue ball travels around three cushions
Yellow line: an example of meeting the two object balls after the third cushion

A sketch of the worked example's ball layout and travel order. Where the ball actually lands depends on thickness, spin and speed.

The reference is about 2 tips of running English. Tip units and tip height vary with the material and the cue tip, so repeat the reference shot with the same tip position and power.
Start with enough power for the ball to keep going after the third cushion, but don't apply a speed figure to every table. Change spin, power and roll one at a time and record the arrival differences.
You can't say new cloth always plays short or humidity always plays long. Cushion rebound, ball cleanliness, speed and spin act together.

Read the fourth-cushion correction separately

The path from departure 50 through third cushion 20 to the opposite corner is taken as the reference for fourth cushion 20. If the departure number changes, the path after that changes even when you hit the same third-cushion number. It is not a rule that always adds a correction to the third-cushion arrival number.

INPROD (4) example: from departure 30, aiming at first cushion 10 goes through third cushion 20 toward fourth cushion 10. To reach the fourth-cushion corner, adjust the third-cushion target toward 30.
MANUAL FACTORY presents a separate correction of about 2.5 per 10 of departure number for a fourth-cushion target. Don't average the two sources' coefficients or mix them into one third-cushion correction.

Practice with the example layout

Back to the worked example and layout ↑

50 − 20 = 30 is the reference up to the third cushion. When you hit the cushion first, as in the worked example picture, also check the path that meets the two object balls in turn after the third cushion. In a side-around shot that hits the first object ball first, read the start number from the cue ball’s line after the collision.

Point to the cue ball, the ball you hit first and the last ball, and say the cushion order.
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

INPROD · 파이브앤하프 (1) — The three scales adopted on this page, the subtraction formula and 2 tips.
INPROD · 파이브앤하프 (4) — Examples of the fourth-cushion path after the third cushion changing with the departure position.
MANUAL FACTORY · 파이브 앤 하프 — The frame/rail distinction and a different fourth-cushion correction convention.
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.