I was thinking about probability tingz and I decided to calculate some gacha probabilities for fun for anyone else who was curious like me. :O this list might make you feel better/worse depending on your luck so far :"D
These calculations are made under the assumption that the last pull is always a 3☆ (97%) or 4☆ (3%) girl, because I'm pretty sure that's how it works?
For 10-play scouts, the probability of:
A single 3☆ pull (like... nine 2☆ and one 3☆): 32.30%
A double 3☆ pull: 27.92%
A triple 3☆ pull: 10.73%
4☆ pulls: (note that the last pull must be a 4☆ in these cases)
A single 4☆ pull: 1.00%
A double 4☆ pull: 0.30%
A triple 4☆ pull: 0.04%
Mix 3☆ and 4☆ pulls:
A single 3☆ and single 4☆ pull: 10.72%
A double 3☆ and single 4☆ pull: 7.90%
A triple 3☆ and single 4☆ pull: 2.62%
Now, let's say we're in an event with a special featured 4☆ girl with the regular rate of 0.5% (1 in 200). For 10-play scouts, the probability of:
Getting the event girl in a scout: 4.89%
Getting the event girl in 10 scouts (100 girls): 39.42%
Getting the event girl in 20 scouts (200 girls): 63.30%
Getting the event girl in 40 scouts (400 girls): 86.53%
Now for some funny ones. For a single 10-play scout, the probability of:
Getting all 3☆ girls: 1 in 4,451,012,160
Getting all 4☆ girls: 1 in 1,693,508,780,843,028
You have less than a 1 in 3 chance of getting the worst pull possible (only one 3☆)
The probability of getting a triple 3☆ pull is almost equal to the probability of getting a pull with a single 3☆ and a single 4☆
It is 10 times as likely to get a pull with a single 3☆ and a single 4☆ than it is to get a pull with a single 4☆ (this is because in the latter case, the last girl must be the 4☆)
Although the probability of a single girl being the event girl is 1 in 200, the probability of 200 girls containing at least one event girl is only 127 in 200.
You have a better chance of getting into Stanford than you have getting the event girl in a single pull
The probability of getting a triple 4☆ pull is almost as likely as getting struck by lightning
You are 169,350,878 times more likely to become the president of the United States than you are to get an all 4☆ pull.
w0w I have way too much time on my hands
EDIT: Actually, on the more optimistic side, the probability of getting at least one 4☆ in a 10-play scout is 26.26%... that’s more likely than flipping a coin twice and getting two heads :O
Misaki is such a talented girl. She can compose music, she makes felt art, and she plays tennis. Plus, she can perform in the Michelle suit during the summer and not pass out. Misaki deserves a cookie.