I know, it's a noobie question, but I am curious to find out what good it does for the char. Improved initiative gives you a bonus on your initiative roll.

First part of any combat is the initiative roll. The person that gets initiative gets to attack first.

Fighter A has initiative bonus of +10 and 4 attacks per round.

Fighter B has initiative bonus of +2 and 3 attacks per round.

Fighter A rolls 1d20 and gets 15(+10)=25. Fighter B rolls 1d20 and gets 10(+2)=12.

Each round is divided into 3 flurries. Fighter A (4 attacks) gets 2 in the first flurry, 1 in the 2nd and 1 in the 3rd. Fighter B gets 1 attack in each.

Now the order of events.

Flurry 1 Fighter A gets his 2 attacks before Fighter B gets his 1 attack. Fighter is B is considered flatfooted.

Flurry 2 Fighter A gets 1 attack. Fighter B gets 1 attack.

Flurry 3 Fighter A gets 1 attack. Fighter B gets 1 attack.

In a close and tight fighter the person attacking first has the clear advantage. If that fighter also has sneak attack he gets to land 2 sneak attacks before the second fighter can react.

Syrath
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It's SHADOWDANCER, dammit, shadowdancer!!! So it is something I should consider adding to my char. Thanks Syrath