Claytonian JP put up an interesting link yesterday which explains the mechanics pretty well. If the combat round and in particular the combat roll represents the average of a set of swings, moves and evasions. Then yes to win initiative is to place the first killer blow. But in OD&D characters don't wear out during combat. A character is just as fresh defending from one opponent in a round as from three. Even if that means dealing with two more attacks.
Working from a less abstracted fatigue mechanism in which there is no single roll representing a set of actions, but rather a roll by roll definition of attacks and parries, taking the initiative isn't always such a good thing. With fatigue rules you have to pay to parry and pay to dodge. If you're facing many opponents you may run out of breath before dodging them all. So holding your attack may be a good strategy. That is if you survive.
Using fatigue rules you can defeat a big monster because monsters wear out too. A ravaging giant may blitz you and attack and attack and attack. If your character is good he keeps his strength and attacks. Counter striking when fatigue kicks in and the giant is tired and beginning to endure penalties for it. Slower dodges and parries on the giant's part make your attacks more effective. These type of strategies are not really possible in OD&D in part due to the highly abstracted combat and in part due to the fact that combatants don't fatigue!!
As D&D rules progressed combat abstraction seemed to fade. Feats, movements, attacks of opportunity, etc, make it seem like there is one main attack and many others options. If you move half the round and then attack, isn't that attack taking place in the second half and thus in a more compact period than the "abstracted model" of OD&D. Think about it, you could attack anything on the move during that round, but it's not really allowed in 1st and 2nd. Third allows for feats to do this, but it's an add on contrary to the original OD&D abstraction. So the abstraction seems to break up the more elaborate and decorated the combat mechanism becomes.
Moving away from an un-abstracted mechanism has its drawback. Namely : complexity. You have to keep tabs on a lot of things. Unless you can simplify the system greatly, and even then it is nowhere near as simple as OD&D. Players nonetheless demand these details, these actions that spice up the narrative. The character moves, swings, falls back, rolls and jumps up again. Using a non abstracted mechanic allows greater access to these details as they're not abstracted to a single die roll. More so it seems that putting all that detail back onto the combat mechanics, like a coating of detail rules, is more complex than starting from an un-abstracted mechanism to begin with. On top of this it doesn't wear the combatants out, which leads to min-maxing and optimization, as I'll address in a future post.
Working from an un-abstracted mechanism breaks down combat into individual actions. You attack, parry and dodge individually. If such a mechanism has a cost per action instead of a fixed set of actions per round then it becomes even more interesting. You can wage on your opponents actions. Hold back on attacks. Use lighter weapons and armor, ones less "expensive" to use. It also gives more directions in which to improve your character. Speed and agility really kick in and more importantly the choice of initiative. You are committed to defend. It's not like you'll let your opponent take a clean swing at your neck. So holding back, parrying, measuring your opponent is a good strategy now. Making an all out attack that leaves you out of breath to endure the counter attack can become suicidal. As more and more attacks come in you raise your shield once, twice, thrice, and your arm begins to burn. It becomes harder, and as your rolls become worse, as you run out of breath you realize it wasn't such a good thing to strike this round and to do so with such vehemence.