9Darts

The nine-dart finish

How many ways can 501 be finished in nine darts? Every one, counted by the app’s own rules: the doubles they end on, the visits and the sets of darts.

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From 501, there are 3,944 ways to win a leg in nine darts, and 2,296 of them end on the bull.

A nine-dart finish, or nine-darter, is a leg of 501 won in nine darts: three visits, and not one dart wasted. No leg can take fewer, so it is the perfect leg.

Why nine is the fewest

No dart scores more than 60, the treble 20. Eight of them make 480 and leave 21, and a leg has to end on a double, which 21 can never be. So eight darts are never enough, and nine are — but only just.

Nine treble 20s would make 540. A nine-darter can fall short of that by 39 and no more, and the double at the end takes at least 10 of the 39 on its own: the bull, the best of them, is worth 50. Its three-dart average is 167, the highest a leg of 501 can have.

How every one is counted

The count above and the tables below come from the code that scores a game in the app. It starts at 501, tries each of the 62 scoring darts, and sends every dart through the rule that decides a bust and a finish. It keeps each leg that ends with the ninth dart on a double.

Two finishes are different when any dart differs at any point, so T20 T20 T19 and T19 T20 T20 are two ways, though they score the same. No nine-darter holds a bust, since a bust scores nothing, and none can finish before its ninth dart. So each one is three full visits.

The game is the usual one: 501, straight in, double out. The bull counts as a double, worth 50.

Where they end

Only six doubles can end a nine-darter: the bull, D20, D18, D17, D15 and D12. The eight darts before the last have to leave one of them, and no eight darts can leave any other.

More than half of all the ways end on the bull. With the bull to finish, the eight darts before it must make 451, which is 29 short of eight treble 20s, and there are many ways to be 29 short. D12 is the other end: it needs seven treble 20s and one treble 19, so the only choice is where the 19 goes.

The visits

The second table lists every way three visits can add up to 501 in nine darts, with how many finishes each one has. The best known is 180, 180 and then 141 — T20, T19, D12. As a pattern, though, it has the fewest ways of all, 20, because a 180 can be thrown only one way. The most, 162, belong to 177, 174, 150, and to the same visits with the first two swapped.

The last visit is always a checkout of 141 to 170, and 170 is T20, T20, bull — the biggest checkout there is. So the first two visits make 331 to 360 between them.

The sets of darts

Put the order aside, and a nine-darter is a set: eight darts, and the double they end on. The third table gives each set with the number of orders its eight darts can come in. The biggest, with 840 orders, is four treble 20s, a treble 19, a treble 18 and two bulls, with the bull to finish.

Practising for one

No drill throws a nine-darter, but its parts can be practised. The first six darts are trebles, mostly the 20. The last visit is a big checkout, and five of the twenty in the app’s Checkout practice can end a nine-darter: 170, 167, 161, 160 and 141.

Every checkout from 170 down →

How to finish a leg of 501 →

All 3,944 nine-darters, by the double that ends them.
DoubleWaysShare
BULL2,29658.2%
D1879220.1%
D2067217.0%
D151203.0%
D17561.4%
D1280.2%
The 71 ways three visits can make 501 in nine darts, the most ways first.
First visitSecond visitThird visitWays
177174150162
174177150162
174167160108
167174160108
18017115090
17717714790
17118015090
17117016090
17017116090
17716416081
16417716081
17716715772
17417415372
17417015772
17416016772
17017415772
16717715772
16716716772
16017416772
18017414760
17717115360
17418014760
17417115660
17117715360
17117415660
17116017060
16017117060
17717015454
17716016454
17715716754
17415717054
17017715454
17016716454
17016416754
16717016454
16716417054
16417016754
16416717054
16017716454
15717716754
15717417054
18017714451
17718014451
17716815645
17715417045
16817715645
15417717045
18016715436
18016415736
18016116036
17017016136
17016117036
16718015436
16418015736
16118016036
16117017036
18016815330
18015416730
16818015330
15418016730
18015716427
15718016427
18017015124
18016016124
17018015124
16018016124
18016515621
18015117021
16518015621
15118017021
18018014120
The 22 sets of nine darts: the first eight, which can come in any order, the double that ends them, and how many orders there are.
First eight dartsDoubleOrders
4 × T20, T19, T18, 2 × BULLBULL840
3 × T20, 3 × T19, 2 × BULLBULL560
5 × T20, T19, T18, D20BULL336
5 × T20, T19, T18, BULLD20336
4 × T20, 3 × T19, D20BULL280
4 × T20, 3 × T19, T18D18280
4 × T20, 3 × T19, BULLD20280
5 × T20, T17, 2 × BULLBULL168
5 × T20, T19, 2 × T18D18168
5 × T20, 2 × T19, T17D18168
6 × T20, T17, D20BULL56
6 × T20, T19, D17BULL56
5 × T20, 3 × T19D1556
6 × T20, T19, T18D1556
6 × T20, T19, BULLD1756
3 × T20, 5 × T19D1856
6 × T20, T18, T17D1856
6 × T20, T19, T16D1856
6 × T20, T17, BULLD2056
7 × T20, T19D128
7 × T20, T17D158
7 × T20, T15D188

Common questions

Why can 501 not be finished in eight darts?

Eight treble 20s are the most eight darts can score, and they make 480. That leaves 21, and a leg has to end on a double, which 21 is not. So nine darts is the fewest.

Which double do most nine-darters end on?

The bull: more than half of all the ways finish on it. Only six doubles can end one at all — the bull, D20, D18, D17, D15 and D12.

Is 180, 180, 141 the most common nine-darter?

It is the best known, because its first six darts are all treble 20s, which is where a player aims anyway. As a pattern, though, it has the fewest ways: 20. The patterns with the most are 177, 174, 150 and 174, 177, 150, with 162 each.

Does the order of the darts matter?

Yes. Two nine-darters are different when any dart differs at any point, so T20 T20 T19 and T19 T20 T20 are two ways. That is how the total on this page is counted.