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Your standard (or stereotypical) initiative rules do far more damage than good.
The good of these rules is to represent the characters' abilities and skills - some people get the drop on others faster. It makes sense that a skilled warrior can smack a lumbering zombie before the zombies have a chance to strike him; attacking first in the round will always (at some point) mean killing someone, and therefore avoiding the attack an enemy would have otherwise made.
At this point, rolling Initiative was pointless - whether the fighter misses first, and the goblins misses second makes no difference. So the Initiative rolls affected nothing but narrative (and that's not nothing, but we have easier ways to construct narrative).
Initiative has once again changed nothing in the outcome.
Theoretically, someone may change their plans - seeing an ally wounded, they decide not to attack the goblin in front of them, but to move next to their ally, and attack that goblin, in order to help their ally.
Of course in this case Initiative functions as a penalty rather than a bonus - players who take their turn later have access to more information, while players going at the start of the turn lose the ability to react to anything.
Once again, Initiative has done nothing.
Finally, we have an example of meaningful initiative...although we'll never find out if that example was meaningful. If the goblin didn't roll to hit, then they might have missed, making Initiative pointless post mortem.
With enough time, someone could doubtless construct a couple of other examples of Initiative providing meaningful results, which represent a character's speed well. However, I think it's clear at this point that these rare pay-offs cannot justify the persistent price.
A lot of people discard the Initiative system and allow people to attack whenever, as narrative or volume dictates. I dislike this approach to combat, but I can see exactly why people do it.
A related method from A,D&D involves each side rolling 1D10, and the side with the highest roll goes first - either all players, or all monsters.
I've never seen this approach, but for a slight improvement on the existing system, we could simply read the attack result twice.
In D&D-style Initiative, this would mean rolling 1D20, and using it for both attack and Initiative. Add any Initiative bonus to this roll, then whoever goes first also finds out if they have hit at the same time by adding their attack score. We don't need to stop to record Initiative, because the dice on the table keep the record.
Players could let themselves mix turn order between themselves - all that matters is the initiative score in relation to the monsters.
Returning to the A,D&D rule of 'both sides roll 1D10', we could let each individual character add their own Initiative Bonus. If the group rolls an '8', and your Initiative Bonus is '+2', you get a '10'.
This significantly cuts down on the rolls, and lets everyone know who's going first immediately - it's just whoever has the highest Initiative.
Under the standard Initiative, when 5 players attack one monster, that monster will almost never attack first. However, if both sides just roll one dice, the monster still has a chance, which feels like a better result to me.
All previous alternatives relied on reducing Initiative rolls, but we might tip the scales another way - instead of reducing the initiative mechanics, we can make them more valuable.
D&D currently has rules for making multiple attacks in a single round - these require referencing some chart concerning a character's level, which is a bit of a hassle for a GM with 5 NPCs to govern. Instead of the chart, we could just say that attacking 'costs' some amount of Initiative. That way, the Initiative bonus also servers to allow characters to attack lots.
Imagine a table where 'Hargor the Mighty' rolls Initiative 13. If he spends 8 Initiative to attack, he could attack twice.
13: Hargor the Mighty 12: 11: 10 Goblins! 10: 9: Faelon the archer 8: 7: 6: Goblin shaman 5: 4: 3: 2: 1:
Those who don't have enough Initiative to complete 1 action can simply act at the end of the round (at Initiative 0).
We could add different costs for movement, spell-casting, firing arrows, using Feats, et c. and let people spend Initiative as a resource. We have more work than the standard Initiative system, but by adding options we can allow players to make real decisions with their Initiative.
Since Initiative only applies at times, people could just declare their actions in any order, and we reference Initiative rules only when disagreements arise.
I go for the skeleton - that's an '18', so I smash him with my axe for 10 Damage.
The skeleton tries to stab you before you destroy it. It hits you too, so roll for Initiative! The skeleton rolls '11'.
I want to smash the skeleton, before it stabs Rognar...okay, I rolled '5', so I can't?
Rognar rolls a '10', so I guess I'm getting hit.
...it's a little circumlocutious, and would probably have to resolve like Magic: The Gathering's rules for Instant spells on the stack. But it has the advantage of meaningful decisions; notice that when Rognar's companion went to attack the skeleton, they already knew the skeleton's Initiative was high, making the counter-attack a rather bad decision.
We now have a full resolution:
1. The skeleton stabs Rognar. 2. Rognar destroys the skeleton. 3. Rognar's companion stabs at the (already obliterated) skeleton.
Various sub-rounds could occur as different people choose to react or not react, and Initiative rolls can be discarded once someone misses.
For BIND, I went with a mix of most of the above systems. Players don't start by rolling Initiative - they just declare attacks, then spend Action Points (AP) to attack.
If disputes arise about who goes first, we resolve them by looking at who has the most AP (no rolling required).