Random gee-wiz information for those interested.
True percentages based on multiple pulls.
Disclaimer:
- this can apply to any gacha pulls; be it in this game or others
- this does not assume or take into account poorly-designed/rigged/weighted random engines
- randomness (math) becomes more accurate the more pulls one can make
Here is the math for pulling at least one X rarity from a multi-pull gacha.
note: the math for pulling more than one (i.e. at least 2/3/4/etc) is different and gets a bit more complicated, so we'll stick to one so people can get a feel of what the actual percentages are.
1 - ((100 - C)/100)^N
1 - ((100 - <percent chance>)/100)^<number of pulls>
example: currently a 6 star girl has a 0.5% of dropping on a single gacha pull for 5 flower gems
however, it's better to use 50 flower gems for not only 1 extra pull (10->11), but for a larger attempt as well
6 star
1 - ((100 - 0.5)/100)^11
1 - (99.5/100)^11
1 - (0.995)^11
= 0.05364542018655696690418950195313
= 5.354% for (at least) one pull out of 11 to be a 6 star
here are the remaining chances for your viewing pleasure
5 star
1 - ((100 - 6)/100)^11
1 - (0.94)^11
= 0.4937017927507942803456
= 49.37%
4 star
1 - ((100 - 30)/100)^11
1 - (0.7)^11
= 0.98022673257
= 98.02%
3 star
1 - ((100 - 63.5)/100)^11
1 - (0.365)^11
= 0.99998468131418123243611440429688
= 99.998%
as you can see, it's nearly impossible to not pull at least 1 3-star girl during an 11 pull.
it may happen 1.54 times out of 100,000 11-pulls (i.e. likely around 1.1 million girls pulled from the gacha)
final thoughts:
do know that these chances are not linear.
if you pulled 11 twice in a row, it would not double your chances for a 6-star, but because the chances are so low it very nearly would.
instead, replace the exponent with a 22 to get your answer.
the higher the chances already are, the smaller the increase will be, but regardless it will move closer to 100%
6 star (11 -> 22)
5.354% -> 10.44%
5 star (11 -> 22)
49.37% -> 74.36%
warning: the following may induce headaches, trauma, nightmare, and flashbacks.
you have been warned
sources:
https://en.wikipedia.org/wiki/Binomial_distribution
or google:
chances over multiple rolls
Triggered by raw text equations... typeset that stuff fam
にせがいじん
I found out that turning autorun off and spam clicking the next button during a mission is alot faster than setting it to on, never knew this trick before
Faster (click-spam) vs. Convenient (auto-run, you can click once and walk away, come back a few minutes later to see if SG/RB spawned)
Trade-off but it's nice to have the option.
If you for whatever reason (had to leave, fell asleep, etc.) have only a few hundred XP until level up but a lot of stamina, start a daily mission (or gift), but just before your girls reach the flag, Retreat. You'll get a small portion of the XP, but keep all the drops (I've found I usually get 48-55/160 XP for the 80 stamina Daily/Gift maps doing this), and still use the stamina without it being wasted. This lets you put that stamina to use instead of wasting it when you get the free refill from leveling up.
Flower Gem tips
1.Never ever use Flower Gems to restore raid or stamina points, those things regen on their own.
2.Expanding your knight roster will happen more often than your equipment list since dragons and fairies occupy the same space as your knights. As long as you have enough space for your equipment, you really don't need much more.
3.Wait for 50 gems for the 11 for 50 special.(Or at least wait for the limited gacha) Premium gacha doesn't look to be worth it
Given the difficulty of obtaining one from gachas, is it better for a rare knight (e.g. rainbow, gold) to get an immediate upgrade instead of being stashed while waiting for copies?