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Out of all the concepts I have learnt in AD&D 1e, I find initiative to be the most difficult to wrap my head around in a realistic way.

I understand thus far that combat is divided into rounds of one minute. Then, it is further divided into ten segments of six seconds. First, the two parties decide what they are going to do. Then two parties roll for initiative. Say party A rolls a 4, and party B rolls a 5, that means that party A will have their actions resolved on segment 5, while party B will have their actions resolved on segment on 4. I don't really understand what this means, however.

I certainly do not know how to deal with contradictions. Say for example, a fighter wants to attack an Orc leader, but he lost initiative, and a slew of subordinate orcs surround him. During the fighter's segment, he is now unable to reach the Orc leader, and I don't know what he does now in accordance with the rules.

Another example would have to deal with movement and segments themselves. I do not understand exactly what can be accomplished by a party in one round. It only makes sense to me that both parties would begin moving towards (or away) the other by the time segment one started, as it would be ridiculous if a dice roll decided that one party stayed standing in one spot for 30 seconds while the other party is beating them to death.

And if a combat round ends, I don't know why those still performing an action (such as preparing a spell) would have to roll initiative again to see when they can resume.

I know that I am misunderstanding these concepts, so if somebody could help me decipher this system of initiative it would be greatly appreciated.

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dragonsfoot.org/php4/… - It's a 20 page read (with the citations), but every post I've found similar to yours has this included somewhere in the first answers. –  JohnP Apr 9 at 21:46
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Try to ignore segments. They're a concept that was mostly introduced to keep track of how long it takes to cast a spell (more on that below), and aren't helpful for the rest of combat.

Instead, concentrate in the actual initiative results. Treat the action of a round as mostly simultaneous, but with the winners of the initiative getting the advantage. So it's not really that the losing side stands still for 30s, it's that they both maneuver, but the side with the initiative simply maneuvered better and got the battle line they wanted.

So in general, just use initiative to decide what order to resolve actions in. You can layer on house rules on this to make it work more how you think it should, but it's not necessary. (One house rule you'll see sometimes is resolving all combatants' movement in initiative order first, and then resolving actions in initiative order, to make the feeling of everyone just standing around go away.)

As for spells, a spellcaster already in mid-spell from an earlier round doesn't act on the initiative number of their side. Segments are counted to find out when the spell finishes, and until it does they are occupied. This often won't matter, as many spells are fast enough to begin and finish before the enemy acts or the round ends, but when the initiative rolls are close, then it matters, and when the spell takes a lot of segments to cast, it matters more. The most important thing segments tell you is: does the magic-user get hit before the spell finishes, disrupting it? and, does the spell take up their next round as well? Segments exist almost entirely as a tool to determine the answer to those two questions.

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Back in the day, I used initiative to determine what order things happened, and that included movement. (I did individual initiative each round, since I wanted a little more tactical feel.) I did a simple d10 roll, modified for Dex (Reaction/Attacking Adjustment, with the sign flipped) and for weapon speed (Speed Factor from PHB p. 38, divided by 3, rounded to nearest integer). Negative numbers were possible (and such results were handled in sequence low to high), as were numbers over 10 (slow weapons could actually result in an attack being delayed into the next round at segment roll-10, which gave people an incentive to use lighter weapons that might not do as much damage). Spells were d10 + Dex mod, and began on the roll result and ended after a number of extra segments for casting time; long spells likewise could delay the final result into the next round.

As I recall, I used movement as a delay. When the number with your initiative came up, if you wanted to move and then attack, you could...it was a simple enough thing to figure out how far someone moved, and what fraction of a round that would take (based on racial movement speed, straight from the Monster Manual), and then tack that on to the initial number to represent the segment they'd attack on. (And if the movement took them into the next round, it was done just as noted above.) This allowed for some tactical situations to develop on the battlefield, with people moving to try to take advantage of positions to allow multiple-on-one or flanking maneuvers, though the monsters could do the same. The battlefield became a bit of a chessboard, and players actively looked for ways to anchor a position to prevent flanking (or take advantage of badly positioned opponents).

And yes, if you try to think of it as people "just standing around" then it doesn't work, but it isn't people "just standing around". If you read any books that describe a fight, you'll note feints, posturing, feeling out an opponent...all things which contribute to the final initiative result in game terms. The guy who got the better roll is the one who was first able to create an opportunity to make a meaningful attack. He wasn't just standing around, he was trying to make something happen. That's also a reason why you can consider Dex as an initiative modifier: faster reflexes means being able to take advantage of smaller windows of opportunity, and thus force a result more quickly.

Depending how much detail you want, you can add concepts from wargames (which in fact did get added in later versions of the game) such as zones of control and attacks of opportunity, so that someone can't just decide to waltz by a bunch of people without consequence. Or you can leave them out...which can make combat quite chaotic and fluid indeed, as people take advantage of any possible opening. The thing is, at this point we're branching deeply into house rules, and any answer becomes less authoritative and more a matter of the opinions and preferences of the people running the game.

If you do want a more theater-of-the-mind type of combat, then Seven's answer is pretty much the way to think of this, however. Discard the board-wargame tactics mindset, let the numbers dictate general order of action without getting all bothered about the detail, and concentrate instead on using description and improvisation to make things more interesting. If, on the other hand, you want a more tactical way of doing things that takes the game closer to later editions...well, then welcome to house-rules land, and be prepared to do a lot of tinkering to find the answers you like. What I outlined above is only a fraction of how complex you can make things if you really want to.

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Re zones of control: they're in the rules already, but most people overlook them. Look at "retreat" and "flee" movement options: they're the only ones you can take once you're in melee range of an opponent, and they are only permitted directly away from the opponent. (And if you choose "flee", they get a free hit at you just like an AoO, but better because you can't use it to bypass them.) You can't just waltz by armed opponents. –  SevenSidedDie Apr 10 at 4:19
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