Worth pointing out, with the way the RNG code works, it rolls a 101 sided dice. Meaning effective probabilities come in multiples of 1/101. KOS-MOS's probability is so low that you can only get her by rolling a perfect 0, no matter what you do you cannot improve her odds.
I have some C++ code I wrote to simulate the gacha and give odds of each individual Blade popping up. It's... messy and runs in the command line so it's really not user friendly, but if somebody wants to it'd be neat to see it adapted to a web app or something. Code's here.
EDIT: Code link is updated, I caught a bug in the booster calculations.
I just wanted to say that that's some goddamn nice code to look at lol. Almost makes me want to install visual studio and mess around with C++ for a bit when I get home.