Old School AD&D group initiative for PbP?
I use a system of initiative that uses a roll of 2d6 in one of my games (Not D&D). The higher roll goes first, as the segments of a combat round are counted down from 12. Outcomes higher than 12 go in round 12 in order, highest to lowest.
There are die modifiers for DEX, weapons proficiencies, special equipment, etc., that apply to these initiative throws. These are all done "in the background" by the referee if the player does not know or does not supply them.
Time scale is one segment = 5 seconds, one round = 1 minute.
The way it works is that I have all participants roll for initiative and declare their intended actions in individual posts. When everyone has posted, I look at all declarations, stack them in order of initiative, then adjudicate and describe the scene to declare the results in my reply for that round. Damage in this game is done in cinematic fashion, so no one ever sees "XX hit points of damage", rather they see what their character is capable of evaluating.
It's a bit of work for me, but it seems to work well enough.