A full frame on a 12 ft table, at the WPBSA's real dimensions
You0high break 0
Opponent0high break 0
break 0levelreds 15remaining 147
redSNOOKERED
Nominate a colour S3 R3(h)(i)
Free ball S3 R12
You were snookered after a foul. Nominate any ball as the ball on — it
acquires the value of the ball on, and if potted it is spotted.
After the foul S3 R10(h)(ii)
In hand — place the cue ball in the D S3 R5
The stroke
1.0 m/s at the cue ball · aim 0°
Tip position — top
side 0.00 R, height 0.20 R
Opponent
frame 1 · frames played on this device 0
Values S3 R1(a)
Referee
Frame over
0 – 0
Snooker — the rules this app implements, and where they come from
Every rule below is quoted by its number from the WPBSA Official Rules of the Games of
Snooker and English Billiards, Official World Rules revised September 2024, published by
the World Professional Billiards and Snooker Association. "S3 R11(b)" means Section 3,
Rule 11, paragraph (b) of that document.
The table and the balls
Playing area, within the cushion faces: 11 ft 8½ in × 5 ft 10 in (3569 × 1778 mm),
tolerance ±½ in — S1 R1(a). The engine works at the exact imperial figures in metres.
Baulk line 29 in from the face of the bottom cushion, and the "D" a
semicircle of radius 11½ in centred on the middle of it — S1 R1(d), R1(e).
Only the Black spot is given as an absolute distance, 12¾ in from a point
perpendicularly below the face of the top cushion — S1 R1(f)(iv). The other five are
defined by construction and are derived here, not hard-coded.
Balls 52.5 mm in diameter, ±0.05 mm — S1 R2(b). Note this is the rulebook's own
metric figure; the older "2 1/16 in" is 52.39 mm and falls outside that tolerance.
The pockets are the one thing no governing body publishes. S1 R1(g) of the 2024
rulebook says, in its entirety, that there shall be a pocket at each corner and one at the
middle of each long side. Earlier editions referred to physical templates "owned and
authorised by" the WPBSA, whose dimensions have never been printed. This app uses the
WPBSA's own 2005/6 rationalised template drawings, measured from the published artwork:
a corner opening of 3 5/16 in with a 3.000 in jaw arc, a middle opening of
3.906 in with a 3.125 in jaw arc, and 1.875 in from the cushion nose
line to the slate edge. The middle pockets are 17.9% wider than the corners, and
there is no cut angle anywhere on the drawings — the jaws are pure arcs.
Those three numbers do not quite fit together: a knuckle of the drawing's radius,
tangent to the cushion face, has its narrowest point deeper than the drawing's slate edge,
and no inset brings the two together. This app keeps the opening and the
radii as measured — so a corner leaves 31.64 mm of clearance around a 52.5 mm ball
and a middle leaves 46.72 mm — and measures the 1.875 in fall from the narrowest line
rather than from the nose line. That datum is the app's own choice and the one assumption
in the pocket the drawings do not support; the credits explain why.
Playing a frame
Red 1, Yellow 2, Green 3, Brown 4, Blue 5, Pink 6, Black 7 — S3 R1(a).
Reds and colours alternately until the Reds are gone, then the colours in ascending
order — S3 R1(b), R3(h). Every Red potted in one stroke is scored — S3 R3(g).
A colour potted while Reds remain is spotted; in the ascending sequence it stays
off — S3 R3(h)(i), (iii).
In hand, the cue ball is played from on or within the lines of the D, and may be
played in any direction — S3 R5.
Fouls, and what they are worth
Every foul is four points unless a higher value applies — S3 R11 header.
Missing every ball, potting the cue ball, or playing improperly from in hand is worth
the value of the ball on — S3 R11(a).
Hitting a ball not on first, or pocketing one, is worth the value of the ball on or
of the ball concerned, whichever is higher — S3 R11(b).
Hitting two balls simultaneously is worth the ball on or the higher of the two —
S3 R11(c).
Playing at Reds in successive strokes is seven — S3 R11(d)(iii).
More than one foul in a stroke incurs the highest value — S3 R10(g). Points made
before the foul count; nothing potted in the foul stroke does — S3 R10(e).
Free ball, snookered, and the touching ball
You are snookered when a straight stroke to every ball on is wholly or partly
obstructed by a ball not on; if any ball on can be hit at both extreme edges, you
are not — S2 R17. A cushion cannot snooker you — S2 R17(e). This app computes that
exactly, from the two tangent lines, not by sampling.
Snookered after a foul, you may nominate any ball except the ball on as a free
ball; it takes the value of the ball on, and if potted it is spotted — S3 R12.
Free ball and a Red both potted: both score, because the ball on was a Red. With
a colour on, only the ball on scores — S3 R12(e).
With the cue ball touching a ball that is on, playing away from it without moving it
counts as the contact — S3 R8(c). Playing into it is a push stroke — S3 R8(b).
Spotting a colour, and the endgame
Own spot occupied → the highest value spot available, which is why a Yellow can
end up on the Black spot — S3 R7(e).
Several to spot → the highest value ball first — S3 R7(f).
All spots occupied → as near its own spot as possible, between that spot and the
nearest part of the top cushion — S3 R7(g); and for Pink and Black, if there is no
room there, on the centre longitudinal line — S3 R7(h).
With only the Black left, the first pot or foul ends the frame — unless the scores are
then level, when the Black is re-spotted, lots are drawn and the next player plays
from in hand — S3 R4. More than seven points ahead with only the Black left ends it —
S2 R1(b).
A frame may not be conceded until a player requires penalty points — S4 R2(b).
The physics, and what is not from the rulebook
The rules specify no coefficient of anything, and no ball mass. What this app models, and
where each number came from:
Where the tip strikes the ball is the whole game. A tip offset of b radii
gives angular velocity ω = (5/2)·b·v/R, so a ball struck exactly two fifths of a radius
above centre rolls immediately — that is where "natural roll" comes from, and it falls
out of the model rather than being set. The tip cannot grip past half a radius off
centre; past that it is a miscue.
A sliding ball's contact point loses speed at 7/2·μg while its centre loses it at
μg, so rolling begins at exactly 5/7 of the striking speed. Both are asserted
against the closed form.
Throw. Friction at the ball-ball contact drags the object ball off the line of
centres by up to 3.4°, which over a metre is wider than the pocket — so the aiming line
and the opponent both compensate for it. The impact model reproduces Alciatore's published
table for the 90-degree rule with inelasticity and friction to three decimal places.
Ball–cloth sliding friction 0.212 and rolling resistance 0.0128, ball–cushion
restitution 0.818 and friction 0.14, and a cushion nose 1.4 ball radii
above the cloth — all measured on real snooker equipment with high-speed cameras by
Mathavan, Jackson and Parkin (Proc. IMechE Part C, 2010; Am. J. Phys., 2009). The cushion
touching the ball 0.4 R above its centre is why a cushion puts topspin on a ball.
Ball–ball restitution 0.94 and the speed-dependent ball–ball friction fit are Alciatore's
published pool figures, applied to snooker for want of a snooker measurement. Squirt is
2.0° at the miscue limit, from measurements on real cues. Ball mass 0.1406 kg, from the
balls the Mathavan group weighed.
RECONSTRUCTED, with no source: vertical-axis spin decay; the cloth's nap has a
specified direction (S1 R1(c)) but no published dynamical effect, so this app models it as
having none rather than inventing one; every colour of the table itself; and the opponent
entirely — no governing body specifies one.
What this is, and what it is not
This is an independent reimplementation of the sport of snooker, written from the
published rules. Snooker was created in 1875 by Sir Neville Chamberlain, an officer of the
Devonshire Regiment stationed at Jabalpur, India; the modern rules are owned and published
by the World Professional Billiards and Snooker Association, whose rulebook is the source
for everything above. This app is not affiliated with, endorsed by or connected to the
WPBSA, World Snooker Tour, or any other body, and it reproduces no artwork, branding or
text of theirs.
What differs from the real game: there is no referee to judge intent, so the miss
rule is applied mechanically from the geometry; jump shots and push strokes can be committed
but a ball can never leave the cloth, so "forced off the table" (S3 R11(b)(x)) cannot occur;
the stalemate re-rack (S3 R17) is not implemented; Four-handed snooker (S3 R18) and
six-red snooker (S3 R19) are not implemented; and the aiming line is an aid the real game does not have — you can
switch it off.