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