Each round the DM rolls an extra d6 in addition to everyone participating rolling one. Initiative is then grouped like this:
Pseudo-Holmes Initiative Groups per round
d6 | Inish Groups |
1-2 | 18-17-16, 15-14-13, 12-11-10, 9-8-7, 6-5-4, 3 |
3-4 | 18-17, 16-15-14, 13-12-11, 10-9-8, 7-6-5, 4-3 |
5-6 | 18, 17-16-15, 14-13-12, 11-10-9, 8-7-6, 5-4-3 |
So if you have a Dex 16 initiative some rounds you will automatically lose to anyone with a Dex 17 or 18 while rolling off against Dex 15 or 14. Other rounds you automatically beat Dex 15 or lower and roll off against higher Dexterity.
I developed this method for the Brawl at the Tanglebones Tavern.
What if you tie on the die roll with people in your peer group? Hell if I know.