It may not be the definitive interpretation of ADnD combat but is certainly one of the most complete. For me personally after reading it I finally got what Gygax was getting at in the 1st edition DMG. The two key points are
- The initiative number is the segment when the OPPOSING side gets to act. So if Side A rolls a 5 and Side B rolls a 2; Side A starts their combat round on segment 2 and Side B starts their combat round on segment 5. Thus for side A any spell that takes 2 segments or less can be cast safely. Three segments spells will be simultaneous with melee combat. Any longer casting time spells run the risk of being disrupted by Side B.
- Weapon speed, and all the rules about multiple attacks with weapon speed only come into play when initiative is tied. So when Side A and B both roll a 4 then weapon speeds are compared and it may be possible that if the weapon speed is low enough the wielder of that weapon will get multiple attacks.