So I've been replaying Pokemon White 2 on a whim and got nerd sniped by this random trainer line.
Immediately my first thought was "what is Alomamola's catch rate, anyway?". I took it a step further and used a catch rate calculator to get the proper odds, which turned out to be 17%.
Note that this is the worst case scenario - or for a catch failing, the best case. Full health, no chance of critical capture, etc. And still, there's a 95% chance of catching it within 16 balls. So what's the chance of taking 100? That means 99 attempts with 0 successes, so we can break out the good old binomial distribution.
n = 99 attempts (since the 100th was a success). k = 0 successes. p = 0.1752 as derived above. (n choose 0) and p^0 both simplify to "times 1", so it's just 0.8248^99. And that's... 5.23... x 10 ^ -9. Less than 1 in a billion chance.
This fisherman has some of the worst luck imaginable. If you tried to replicate the feat, to throw 99 balls in a row at Alomomola and have none of them catch, you'd on average find over 23000 shinies before you managed it. I really have to wonder if GF had any idea what they were implying when they wrote this line.
