According to Wikipedia there are 22 different ways of scoring 501 with nine darts. If you take into account the different order in which you can make the scores, there are 5,944 different sequences.
If you have to start on a double, there are only 11 different ways and 574 different sequences.
Wikipedia spells out the four most common ways of doing it – assuming you don't have to start on a double. Three of them involve scoring a maximum 180 with your first and second three–dart throws. This leaves you needing 141 to check out. The three options for your last three–dart throw are:
| • | treble 20, treble 19, double 12 (60 + 57 + 24) |
| • | treble 20, treble 15, double 18 (60 + 45 + 36) |
| • | treble 17, treble 18, double 18 (51 + 54 + 36) |
Obviously you can do the unique treble (19, 15 or 18) with any one of the first eight darts; hence there are eight different sequences for each of these methods.
The fourth method involves three identical scores of 167 with each of your three three–dart throws, which are:
| • | treble 20, treble 19, bullseye (60 + 57 + 50) |
This is more spectacular, not only because of its perfect symmetry but because of the three bullseyes. But it's also more risky – because it relies less on treble 20s, which are the professional player's stock in trade, and also because each dart is aimed at a different part of the board from the previous one. Consequently it's more likely to be attempted in exhibitions than in match play.
© Haydn Thompson 2021