Tips / Systems

No English System No English

An aiming method with no left-right spin. Even without side spin the ball still rolls forward, and it doesn't mean a real cushion reflects like a perfect mirror.

Formula / route reference

Ideal corner departure: third-cushion distance counted from the departure corner = 2n (0 < n < 4)

When to use it

When setting the geometric reference for a no-English bank shot. The formula below applies only to a specific corner departure traveling long → short → long in an 8×4 rectangle.

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: the bottom-right corner of an ideal table.
First aim n = 2: two diamonds from the left on the opposite long rail.
Arrival distance 4: 2 × 2 diamonds counted from the starting corner.

Slope and correction: If you change the starting corner or hit in a different direction from a ball farther in, don’t apply 2n as is. Also keep no sidespin and no forward roll apart.

See the worked example and layout See related practice

New to this? Start here

No English means “no side spin.” It does not mean the ball has no forward rolling spin. The numbers here are ideal coordinates for understanding the principle of the path, before any practical diamond scale.

Follow one path first: corner start → n=2 → short rail → 4 diamonds from the departure corner. The short yellow dashed line is the arrival distance, not the ball's path. Ideal construction that ignores ball size.

Fix the departure at one corner in the diagram. Count the first aim n from the end of the opposite long rail marked 0. Read n and the arrival distance from different ends.
With n=2, the ball comes back 2×2=4 diamonds from the departure corner. It is also 4 from the opposite end where you read coordinates, so check your reference point first to avoid confusion.
In real practice keep the left-right tip position at center and use the same power. Moving these coordinates straight onto the frame diamonds introduces errors from ball size and cushion rebound.

Check yourself: With n=1, how many diamonds from the departure corner is the third-cushion arrival?

2×1=2 diamonds. Counted from the opposite end, the coordinate is 8−2=6. “Distance 2” and “coordinate 6” are two readings of the same arrival point.

Separate an ideal mirror reflection from a real ball

An 8×4 reflecting rectangle ignoring ball size. (8,4)→(2,0)→(0,4/3)→(4,4). The dashed n=1 arrives at (6,4). The numbers are ideal coordinates, not frame diamonds.

The cue ball is placed on the ideal corner start line. Follow the order long ① → short ② → long ③, then on to the two object balls. The 0 and 4 boundary lines are point-particle reflection lines, not where the center of a real ball meets the cushion.

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.

Counting n from the left end of the top long rail, the arrival x is 8−2n and the distance counted from the departure corner is 2n. n=4 is a corner hit, so it is excluded from this path. A real ball center travels one radius away from the cushion nose, and the frame diamonds are farther out still, so you can't use this formula directly as a practical point table.

Practice conditions

Keep the left-right tip position at center, and keep the roll and slide as the ball enters the cushion consistent. No English doesn't mean zero spin on every axis.
Cushion friction can create side spin even on a ball that started with no English. A single coefficient of restitution can't decide the direction or size of the arrival error.
Distinguish the ball-center reflection line, the cushion nose and the frame diamonds. Don't use an aiming method that adds or subtracts a fixed 3 cm at every angle of incidence.
Simulator results are the output of a particular physics model. Don't use them as measured corrections for a real table; use them to compare spin and power changes in the same layout.

Practice with the example layout

Back to the worked example and layout ↑

First read the construction that starts from the corner point, then see what it means in the worked example picture to place a real cue ball on that first line. A real ball cannot have its center on the corner, so 2n is a geometric reference for understanding position and direction.

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

Dr. Dave · Mirror Kick and Bank Shot Aiming System — The mirror construction and why real shots need corrections.
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.