EDIT - NB: My sim might be overcounting pulls due to a gacha rule that we don't fully understand. See here.

2nd EDIT - Since the time of this sim we've had plenty of samples to look at and from empircal evidence the rules don't seem as simple as what is outlined here. Bunloagus has a theory that seems to fit pretty well.

TLDR: On average you get a Featured 5* every 104.5 pulls.

That doesn't mean you only need to save 105 pulls. You still want to save till 180, because this average is including the pity safety net. But you can 'expect' in the Really Long Run^tm to spend 104.5 pulls on every chase, as long as you always save back to 180 before trying again.

Hey guys.

I'm sure it's... possible... to math it, but I did a quick sim for the average number of pulls to get the Featured 5 instead. I used the rules from here, please sanity check my understanding:

• 0.6% chance to get a 5* on a featured banner roll. Once you hit this roll, there's another 50% chance for it to be a Featured 5*. Effectively a 0.3% chance to get a banner 5*. Only for the first 5* you pull at the start/after a feature 5* pity reset, every pull after getting a non-featured 5* is effectively 0.6% chance for a featured 5*, till you get it.
• You're guaranteed a 5* by the 90th pull, so if you luck out on a 5* on your 20th pull, that counter is reset, and you're pulling up to (20 90=) 110 total.
• The guaranteed Featured 5* part of the pity is a separate rule that doesn't care about total pulls, if you miss a Featured on a 5* pull the next 5*(from pity or lucking out) will be a banner 5*.
• A Guaranteed 4* pull can be 5*s (ingame help says 4* or above). But the rate isn't any higher (99.4% chance to be 4*). An assumption since I would have expected in-game text to mention if it had a higher 5* rate.
• Not related to the Sim itself since it stops on the first featured, but if you do get the featured character on your first 5* pull, the 2nd is no longer guaranteed to be the featured (but if your 2nd 5* is off-banner, the 3rd is).

Code here if anyone doesn't mind double checking my logic. Fiddle will time out if you try to do huge number of sims, 1 million is fine but you'd have to run it on your own PC for bigger (I got the above results from 1 billion sims).

P.S. the average pulls to get the 5* if there wasn't any pity is about 235 pulls. So... save for pity.