Stuntman
First Post
But if you get a low roll, say a 1, then II makes that 5. If you have DS and you roll a one then you get another go, 75% chance of beating that 5. So there is a 25% chance you'll not win that tie.
Like everyone says, DS is reduscing the chance of a low roll. II is boosting your low roll, but that's no guarantee it will be high (granted 75% isn't a guarantee, but it's good!).
Roll a ten, and you get a 14, with DS you get a ten and then re roll, 35% chance to win.
Say you now roll a twenty, Woo! You now have a score of 24. Wow, Roll a twenty with DS and you don't win.
As you can see, II relies on you getting a good roll, you have to roll well for it to pay off. Not as well as without it, but still well, i.e rolling a 5 is still as likely as rolling a 10, or ten. Granted you'll never roll a one... DS on the other hand gives you consistently better rolls, regardless of the first one, a 20 is 4 times more likely than a 5. And with DS a roll of 5 or less is 6.25% likely, which is negligible.
The results I provides takes into account all of this. The way I did the calculation, I first assumed that both you and your opponent has the same initiative modifier. If the opponent rolled a 1, what's the chance you win initiative. If the opponent rolled a 2, what's the chance you win. I did this all the way to 20. The calculations pretty much emulated every possible combination of initiative rolls between you with each feat and your opponent. The results show that Improved Initiative has a slight edge over Danger Sense.