After 520 days playing, I finally got my first rainbow from a daily summon. I am sure that I did way more than 400 daily summons.
I know that I may be an extreme case, but I think that it shows how important a pitty timer is. The only reason I didn't give up on dailies is stubbornness.
Before the 3% rate I had only 2 rainbows, Ramza (of course, useless for a looong time) as the anniversary free one and Olive as the free compensation.
Nowadays I have a good number of rainbows and it is way more fun to play.
I'm not sure what rainbows are, I'm assuming it's part of the badge system that other users have mentioned? I have yet to do any research on it.