I will admit right now that I do not use the initiative rules as written in my own campaign. However I do understand these rules and how they function, and I have used them in my AD&D dogma trial adventure (when I remembered that they applied).
As written, the rules for armed opponents vs. spellcasters is somewhat confusing and doesn't follow the normal flow of initiative as presented in the book. Many of us have taken that to mean that the rules are broken or don't make sense as written. This may be the case, or they were left overly simplistic to make the game run smoother. You decide which is right.
Here are some examples I just whipped up. I will attempt to explain each in as much detail as possible:
EXAMPLE 1
A melee between party A and party B has erupted in a dungeon chamber. The combatants had all engaged their opponents when a fighter from party B saw an opening and headed off to take on the magic-user in party A. They begin within melee range. Before initiative the magic-user declares he is casting a magic missile spell (casting time: 1 segment) at the offending fighter. The fighter is armed with a short sword (Speed Factor 3). Initiative is rolled and party A gets a 2, while party B gets a 1. According to the rules as written, we compare the casting time (1 segment) with the speed factor of the weapon minus the losing die roll (3-1 = 2) to get the segment when the attack occurs. Proceed from lowest number to highest. Thus the spell would come off first!
EXAMPLE 2
A magic-user is casting a slow spell (casting time: 3 segments) upon an evil cleric and his undead minions. The cleric is within melee distance of the magic-user (less than 10') and will strike at him using a footman's mace (Speed Factor 7). Initiative is rolled and the magic-user's party gets a 3 while the cleric's side gets a 5. Comparing the casting time (3 segments) to the weapon speed factor minus the losing die (7-3 = 4) we can see that the slow spell will indeed occur first.
EXAMPLE 3
An evil cleric player character is casting bestow curse (casting time: 6 segments) upon a fighter attacking him with a battle axe (Speed Factor 7). The initiative roll for the cleric's party is 1; the fighter's party rolls a 2. Comparing the casting time (6 segments) to the weapon speed factor minus the losing die roll (7-1 = 6) shows that the action is simultaneous. Thus the spell will occur at the same time as the weapon strike. Both attacks will take effect and neither will be disrupted.
EXAMPLE 4
A druid encounters a small group of goblins in the forest chopping down trees in a sacred grove. The druid engages the goblins and is able to dispatch all but one which is armed with a hand axe (Speed Factor 4). The druid begins casting his heat metal spell on the goblin (casting time: 4 segments). They roll for initiative and the druid gets a 5 while the goblin rolls a 2. Comparing the casting time (4 segments) with the weapon speed factor minus the losing die (4-2 = 2) indicates that the goblin will strike the druid BEFORE his spell comes off, despite having lost initiative. If the goblin hits, he can disrupt and spoil the spell.
EXAMPLE 5
An illusionist is casting color spray (casting time: 1 segment) at a hobgoblin armed with a longsword (Speed Factor 5). Initiative rolled results in a 3 for the illusionist and 4 for the hobgoblin. Comparing casting time (1 segment) to the weapon speed factor minus the losing die roll (5-3 = 2) indicates that the spell will go off before the hobgoblin can strike despite the hobgoblin winning the initiative.
EXAMPLE 6
A magic-user casts hold monster (casting time: 5 segments) at a frost giant wielding a huge battle axe (Speed Factor 7). Initiative is rolled with the magic-user scoring a 3 and the giant scoring a 3. Since initiative is tied, attacks are resolved in order of speed factors/casting times without adjustment by the losing die roll. In this case the spell occurs first (CT 5) and the axe after (SF 7).
Interestingly enough, this works also with activated magic items in melee, like potions, wands, scrolls, rods, staves, some rings and some miscellaneous magic items. Basically anything that lists how many segments it takes to use or activate. It doesn't work well with missile weapons or clerical turning, however, since no speed factor is listed. In such a case, use the general rule "you go on your opponent's die roll" to determine when the attack occurs. Remember though that, by the rules as written, weapons with multiple attacks in a round go FIRST and LAST. Thus, if the missile were a bow (Fire Rate 2), it would go before a spell caster and after the spell caster. This must be why magic-users cower behind their party (to gain a cover bonus, or at least concealment). It also explains the existence of spells like shield (which is better against missile weapons) and protection from normal missiles. If darts are being used, the thrower goes FIRST, on initiative, and LAST. If more than one combatant goes FIRST and LAST, use initiative to see which gets the jump on the other.
The next example showcases increased number of attacks based on speed factor. Note that this ONLY occurs on a TIED initiative, when both combatants are using weapons in melee, and only after having closed/charged; so this rule will only come up on rare occasions.
EXAMPLE 7
A thief armed with a dagger (SF 2) has been caught infiltrating an orc lair ahead of her party. She was discovered by an orc guard armed with a bastard sword (SF 6). They have traded a few blows and now find themselves tied for initiative. Since the orc's weapon is more than twice the speed factor of the thief's dagger, the thief will get two dagger strikes BEFORE the orc gets to swing his blade. This only occurred because of the tied initiative (or whenever speed factor becomes a determinant in who strikes first).
This next example indicates the use of Dex bonuses when engaged in missile fire.
EXAMPLE 8
A party of adventurers comes across a band of gnolls in the wilderness. The elf fighter/magic-user has his short bow at the ready and wants to fire at the gnolls before they close. His Dexterity score is 16, granting him a Reaction bonus of +1. Some of the gnolls are also firing arrows from long bows at the party. The gnolls have no Reaction adjustment (the DM decides they all have average scores). When initiative is rolled, the elf gets to adjust the party's roll by +1 for himself only. The party rolls a 4 and the gnolls roll a 5, so the elf also goes on 5. The elf and gnolls fire their first arrows simultaneously before he rest of the party and/or gnolls get to do anything.
Now, let's look at an example that defies rolled initiative -- charging. When charging, weapon length dictates who strikes first.
EXAMPLE 9
Assume a warrior with a spear is being charged by an angry giant boar (DM declares the charge before initiative). The warrior states he is setting his spear for the charge. Initiative is rolled with the boar scoring a 6 and the warrior a 5. Regardless, the warrior strikes first since his weapon is much longer. If the warrior hits, the boar will impale itself on the spear for double damage; otherwise the boar strikes the warrior at +2 to hit. If the warrior had only a dagger in hand, the boar would have struck first since it had an equally long weapon (tusks), but won the initiative roll.
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