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:

####
3☆ pulls:

- 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

####
Interesting takeaways:

- 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