The rules provide for "matches or legs of a fixed odd number, such as 501, 701,
or 1001" [WDF 3.01]. Every one of them is straight in and double out.
"The number of legs in a set must be odd" and "the number of sets in a match
must be odd" [WDF, definitions]. The winner of the bull throw starts the match and every
odd-numbered set, and the throw alternates leg by leg [WDF 12.02].
Nobody repeats a throw exactly. The wobble comes from the match's own seeded
stream, so a match is still reproducible from its seed.
Under WDF 2.05 a bust puts the score back to what it was at the start of the
whole visit and the rest of the visit is forfeited. The "Northern bust", which Wikipedia
records as a London name for a regional variant, puts it back only to before the dart that
busted, and the visit continues. It is not a WDF rule; it is offered because it is played.
Darts - how this works
An independent implementation of darts, built to the published specification rather than to
a guess. It runs entirely in your browser: no account, no model, no credits, and nothing is
sent anywhere.
The board, to the millimetre
Every figure below is from the World Darts Federation Playing and Tournament Rules,
20th revised edition, clause 4.01 - and they are the app's constants, not a description of
them.
Overall diameter 451.0 mm, of which the scoring area is
340.0 mm across, outside-of-double-wire to outside-of-double-wire.
Outside edge of the double wire to the centre of the bull, 170.0 mm;
outside edge of the treble wire, 107.4 mm. Not 107 - the WDF's own
tolerance on that figure is 0.2 mm, so the rounding every popular chart uses is
outside it.
The double and the treble band are both 8.0 mm wide on a wire board,
measured inside wire to inside wire, and 10.00 mm apex to apex on a
board made with strip material.
The bull is 12.7 mm across inside its ring and the 25 ring is
31.8 mm. The bull scores 50 and counts as double 25 [WDF 2.03, 2.04].
The wires are between 1.27 and 1.85 mm in section. This app models
them as lines of zero width at the published radii, which keeps every published
number exact and the bands exactly 8 mm; a real board's wire takes up to one thickness of
that, putting its double band nearer 160.15 - 168.15 mm. On a real
board the rule that settles the case is 4.01's companion: "the score is counted from the
side of the segment wire in which the point of the dart enters" [WDF 3.03].
The board is hung so the centre of the bull is 1.73 m from the floor
[WDF 6.01] and the back of the oche is 2.37 m from the face of the board
[WDF 6.02]. The published diagonal from bull to oche is 2.93 m
[WDF 6.03] - and , so the three published figures check each other.
The 20 is at top centre and is the darker of the two segment colours [WDF 4.02]. The
order clockwise from it is .
The rules name the layout only as the "1 - 20 clock pattern" and do not print
the order. The order this app uses is read off the segment-label coordinates of the Wikimedia
Commons drawing Dartboard.svg, and the harness re-derives it from those coordinates
rather than trusting the list.
Why the numbers are in that order
The arrangement punishes inaccuracy: every large number is flanked by small ones, so a dart
that drifts off the treble twenty lands in a 1 or a 5. On this board every number of 17 or
more has neighbours summing to no more than 10. The usual attribution is
to a Lancashire carpenter, Brian Gamlin, in 1896 - but that attribution is disputed, and the
darts historian Patrick Chaplin, whom Wikipedia's own source cites, holds that Gamlin never
existed. A better-evidenced alternative is Thomas William Buckle of Dewsbury, who set out a
board in 1913. Neither claim traces to a contemporary document.
The throw
A dart is a projectile. Given where you aim, the app solves the launch elevation that
would put a dart through that point at your natural release speed, then flies it under
gravity. From the oche that is a flight of about 0.35 s launched at
about 18 degrees, arcing 146 mm above the straight
line from your hand to the target - a real dart really does arc that much.
Power is therefore not a fudge. The elevation is solved for the nominal speed, so
throwing harder sends the dart long and high and throwing softer drops it: one per cent of
release speed is 11.5 mm up or down on the board.
Line is the sideways error at release. Ten milliradians of it is
21.7 mm across the board.
A dart cannot weigh more than 50 g or be longer than
30.5 cm [WDF 1.01].
Darts already in the board
Darts here are solid. A dart already in the board is a real obstacle along its own axis, and
an arriving dart is tested against it in three dimensions. Strike the barrel dead on and the
dart bounces out: under WDF 1.05 it "shall not be thrown again", and under WDF 3.02 it
scores nothing, so you lose the dart. Graze it, or clip a flight, and the point is deflected
a few millimetres - which is why the second and third darts of a visit hit the treble less
often than the first, and why a good player slides along the band rather than throwing at the
same point three times.
The game, from the rulebook
Straight in: "to begin scoring the player need only land a dart in the dartboard
inside the outer Doubles wire" [WDF 2.01]. No double to start.
Double out: "to finish, and win, the player must land a dart in the double (Double
Ring or Bull) of the number equal to one half of the remaining score" [WDF 2.02].
The bust rule, all three of its cases: "if a player in a throw scores more points
than remain in the leg or match, or the same points as remain without finishing on a
double, or leaves a score of one, then that throw shall not count and the score shall
remain as it was prior to that throw" [WDF 2.05]. The rest of the visit is forfeited.
A throw is at most three darts [WDF 1.03], and "a dart thrown by a player after finishing
shall not count" [WDF 2.09].
A dart scores only if its point "remains in or touches the face of the dartboard, within
the outer double wire" [WDF 3.02]. A dart that misses the board entirely, or bounces out,
is still a dart thrown.
The order of play is decided by a throw at the bull, nearer the centre throws first, and
a tie is re-thrown [WDF 12.01-12.03].
Checkouts, enumerated rather than copied
The suggested finish is computed, not looked up. The app enumerates every ordered one-, two-
and three-dart finish the board allows - 82,047 of them - and keeps the
shortest route to each score.
The highest score with three darts is 180; the highest three-dart
checkout is 170, T20 T20 bull, and the highest with two is
110.
162 of the scores from 2 to 170 can be checked out in three
darts. The seven that cannot are - derived from
the enumeration, not typed in. 161 is not among them: it is
T20 T17 bull.
Diffed against a published checkout chart, the two agree on which scores are checkable,
all 169 of them. They disagree at five scores, and always the same way: the chart avoids
the bull as a finishing dart, so it quotes three darts for
110, 107, 104 and 101, and two for 50, where the app finds shorter
routes that are perfectly legal. The chart itself uses the bull at 170 and 161, where
nothing else works - so the omission is a preference, not arithmetic.
A leg of 501 cannot be won in fewer than nine darts, and the harness
makes a near-perfect thrower prove it.
The computer, measured rather than claimed
Its accuracy is one number: the standard deviation, in millimetres, of where its darts land
around the point it aims at. That is the model Tibshirani, Price and Taylor use in "A
statistician plays darts", which also supplies the one published calibration point available:
at a scatter of 16.4 mm the best place to aim stops being the treble twenty and becomes the
treble nineteen. The four levels below are not claims - they are what 1,500 simulated legs
each actually produced, and the harness fails if they drift:
For scale, the mean three-dart average of the seventeen players in the 2017 PDC
World Matchplay was 97.3 with a mean checkout success of 39.6%, and a retailer's often-quoted
guide puts 35-45 at beginner, 46-55 at pub level and 56-70 at county level.
What is reconstructed, and said so
The board, the setup and the rules above are all published. These are not published by any
governing body and are the app's own:
Where the hand is at the moment of release, and how fast a dart leaves it. The app
releases from 2.17 m in front of the board at 1.72 m, at 6.6 m/s.
The thickness of the board (38 mm here) and the colours of the segments beyond
WDF 4.02's "the 20 is the darker of the two".
The collision model for darts already in the board: the bounce and deflection
radii, and how far a clipped dart is pushed. The rules say what a bounce-out scores; they
say nothing about how often one happens.
The scatter figures for each computer level. Only the shape of the model is
published; the four sigmas were chosen by measuring what came out.
The numerals in the outer ring are drawn from a stroke font written for this app.
Sources
World Darts Federation, Playing and Tournament Rules, 20th revised edition,
28 February 2018 - the board specification (4.01), the colours and position (4.02), the
setup and oche (6.01-6.03), the throw (1.01-1.07), starting and finishing (2.01-2.11),
scoring (3.01-3.08) and the order of play (12.01-12.05).
Darts Regulation Authority, Rule Book - the 451 mm diameter and the flush-spider
rule, and the rules the PDC plays under.
Wikipedia, Darts - the bust rule in plain words, the Northern bust variant, the
nine-dart minimum, the Gamlin attribution and its dispute, and the Quadro 240 board.
Ryan J. Tibshirani, Andrew Price and Jonathan Taylor, "A statistician plays darts",
Journal of the Royal Statistical Society A 174(1), 2011 - the scatter model and the
16.4 mm crossover.
darts501.com, William Hill and The Dart Scout - the published checkout chart the app's
own enumeration is diffed against.
Wikimedia Commons, Dartboard.svg - the segment order, derived from its label
coordinates.
This is an independent implementation. It is not affiliated with, endorsed by
or connected to the World Darts Federation, the Professional Darts Corporation, the Darts
Regulation Authority or any manufacturer. CREDITS.txt carries the full list of sources and
every reconstruction.
Controls
Move the pointer over the board, or use the arrow keys, to aim. Then
space, Enter or the Throw button three times: once to start, once to set the
line as the marker crosses the middle, and once to release as the power bar crosses its mark.
H suggests a dart. N starts a new match. P is practice.
Escape closes a panel.