Fighters Get Better Initiative

I have come around over time to the system of initiative Courtney Campbell uses in Numenhalla as simple and effective. Briefly, the system is that each side (PCs and monsters) rolls a d6, with the higher roll going first. Even ties are resolved in favour of the player acting first, odd ties result in the monsters going first. I used to be more of a proponent of individual initiative, and still use it in some games, but for Swords and Wizardry, and other old school D&D versions I play, I tend towards using this method.

I have a proposed alterations to this system which I will be experimenting with in the next Necrocarcerus campaign:

If a fighter is the highest level character in the party (or all characters are of equivalent level), then the group may roll a d8 for initiative.

The idea is that the fighter is tactically acute in a way other characters aren't, and helps coordinate not just their own actions, but the actions of others, allowing them an operational edge. You can continue to roll surprise on a d6.