|Guess who's got the higher Dex? By Trampier, from the Monster Manual|
In the oft-overlooked back of the 1E Player's Handbook (1978), Gygax ends a section titled "First Strike" with "When important single combats occur, then dexterities and weapon factors will be used to determine the order and number of strikes in a round" (pg 105). This, plus the reference in the Monster Manual (1977), makes me think that for a time Gygax considered including a Holmes Basic (1977) type dexterity-based initiative for certain combats in AD&D. However, by the time of the Dungeon Master's Guide (1979) there's no trace of using the dexterities of opponents to determine first strike other than a reaction bonus for missile weapon fire. Perhaps Gygax dropped this in a (futile?) attempt to keep the complexity of the DMG combat rules for initiative under control. The PHB reference does suggest a way to adapt Holmes-initiative if moving on to AD&D: subtract the AD&D weapon speed factor (e.g., fist = 1, dagger = 2, two-handed sword = 10) from dexterity to determine an adjusted dexterity for each melee combatant, and use this to determine strike order. Number of strikes per round is more difficult to determine/integrate, particularly when monsters are also considered, so I'm not going to consider it today.
(I was inspired to write this after reading a post in this thread on Dragonsfoot)