One way to almost do Holmes initiative

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.