Nail said:
Interesting.
Let's say your Wiz has Improved Init. With a moderate Dex, that's an Init +5. And let's say he's in a party that's attacked by 4 orcs (Init +0).
The Wiz's chance of beating any one orc in initiative is 74%.
The Wiz's chance of beating all four orcs (assuming they all roll initiative individually -- and how many DM's really do that?) is 30%.
..........Now, let's remove the feat Improved Initiative. The chances go down to 57% (for any 1 orc) and 11% (to beat all the orcs). Is the feat worth it?
Well, I'm glad you fixed your math. I had written a correction post earlier, but while at a meeting, my PC rebooted for updates and lost the post.
Course, your math is still incorrect. Even though it is 57.25% chance to beat one orc, it is not that to the fourth power (10.74%) to beat all 4.
In fact, you have a 10% chance to beat all 4 just by rolling a 19 or a 20 (you win ties with +1 init over +0 init).
If you roll an 18 (5% chance), the odds of none of them beating you is .95^4 (all of them rolling 19 or lower) * 5% ~= 4%.
So, this is a 14% chance to beat all of them just with rolling 18 through 20.
The chance to beat them with a 17 is 5% * .9^4 = 3.3%, etc.
The overall chance to beat all of them is actually 27.58% chance without Improved Initiative. I'll do the odds later with Improved Initiative.
Nail said:
And: How does your analysis change if the DM regularly rolls initiative for groups of opponents?
Ok, I have to go see Superman Returns. So, I'll just note that this is typically a poor idea (with one basic exception). If you have 4 opponents, you should roll all 4. If you have 20 opponents, you should roll them either individually, or in groups of say 3 to 5, depending. The basic problem is that DND balance and tactics go out the window if all opponents consistently go on the same init. I'll explain more later.