The rule: T = D − F. Origin direction D, 1st-rail diamond F, 3rd-rail arrival T. Running english, aiming through the diamonds.
Plus System (Joe's "3-5-7"): number the right short rail 1 at the far corner, +1 per
half diamond, so the diamonds read 3, 5, 7. Count the diamonds from the target up
the long rail to the cue ball; aim through that number with running english and a
rolling ball. Cue ball off the rail: pivot the cue about the nearest on-rail reference
line (butt moves 2 diamonds per 1 the tip moves) until it passes through the ball, and read
the fractional number. Joe's parallel shift is a close approximation of the same thing.
Low numbers run long (add english); 6 and 7 run short (less english or more speed).
4-to-10 bank system (Mika Immonen, via Dr. Dave's "4d-to-10d"). Two rails get counted.
Rail you bank off (orange): zero is the pocket straight across from the target, then
10 per diamond, pockets included. Rail you bank from (blue): zero is the target
pocket, then 4 per diamond to 20, 5 per diamond to 40, then 10 per diamond
up the short rail. Put the object ball on the line that joins matching numbers, aim
through the rail at the diamond, and shoot a medium-speed stun shot with no side spin.
Works for cuts too: just send the object ball down the matching line.
Speed: 10 to 30 tolerate slow to medium; 40 and up need a firmer hit or the angle opens up.
Bigger or faster tables bank longer, so a 60 may need a 62. Calibrate on your table.
Mismatched numbers: bank number above the from number comes up short; below it overbanks.
Fix with a different line, or with side spin (see the note above the table).
Reverse-cut banks (cue ball crossing the line) throw the object ball short: overbank a bit
or use outside english.
Sid System (Sid Banner, from 3-cushion billiards). Multiply the red target number
(1 at the top-right pocket to 5 at the bottom-right) by the blue origin number (where the
cue ball's line crosses the bottom rail: 0 at the left corner, 1 per diamond). Aim
through the rail directly at the product on the orange scale (10 per diamond from the
right corner), center-ball hit, no spin, medium speed. The cue ball just lies somewhere on
the line; the origin is read where the line behind it meets the blue scale. In-between
products: estimate the spot between diamonds — it stays accurate.
Every table kicks a little long or short, so calibrate yours. Pocket hanger? Aim half a
number short of it so the cue ball cuts it in instead of following it into the pocket.
3-rail side-pocket bank. Count the bottom rail by 2s and the top (bank) rail
by 8s (by 7s on a 9 ft table), both from the left corner pocket. Send the
object ball down the line joining matching numbers with medium stun and no side spin: bank
rail → short rail → bottom rail, into the top side pocket. Reliable up to about
10 = 10; past that the ball catches the corner pocket.
Cut shots put spin on the object ball. Cutting toward the corner adds check spin (banks
short): overcut about one diamond near the corner, about half a diamond by 10–10, or
use gearing (outside) english and shoot the counted line. Cutting the other way adds
running spin (banks long): overcut into the rail, or again outside english. Object ball far
off the bank rail? The induced spin dies before the rail — no adjustment needed.
Blue = origin direction numbers (D) · Orange = 1st-rail numbers (F) · Red = 3rd-rail numbers (T).
Along the long rail D changes 0.5 per diamond; up the short rail, 1 per diamond.
Aim through the circled diamond, not at the cushion spot opposite it —
the diamonds sit behind the cushion nose, so the ball actually bounces a hair
short of the diamond (the white dot). The 3rd-rail T numbers read the same way.
The cue ball just lies somewhere on the track: D is read where the dashed line
behind the ball crosses the blue scale.
Path is schematic: the system assumes medium speed with natural running english.
Real tables run a bit long or short, so calibrate a half-diamond on yours.