Pokemon Go Shiny Pokemon and the Odds of Finding One in the Wild
Trainers, the very first shiny Pokemon in Pokemon Go were introduced in March, 2017, and Trainers around the world got a chance to catch Shiny Magikarp and Shiny Gyarados.
Until today, the game introduced more than 250 shiny Pokemon, and most of the players got a chance to catch more than 100. Some caught less, while some are still thinking that Niantic has something against them and that some accounts have a higher chance to find a shiny Pokemon in the wild. Well, that’s not true as it all comes down to RNG and probability.
A Pokemon Go player from Buffalo, Lvl 38 Team Mystic, made an ‘Actual probability of finding a shiny Pokemon’ research on TSR, explaining what are the chances of finding a shiny Pokemon in the wild.
“The odds of tapping a single Pokemon and encountering a shiny are debatable. Some say it’s 1/256 while others say it’s more like 1/512. I’ll discuss both and I’ll use Makuhita as a reference.
If you tap a Makuhita, the probability of it being shiny is, let’s say, 1/512. Now, this doesn’t mean that tapping 512 Makuhita guarantees a shiny. The probability of finding at least one shiny Makuhita after tapping 512 Makuhita = 1 – the probability of not finding a single shiny Makuhita.
This equals to 1 – (511/512)512 = 0.632 or 63.2% chance. That is less than two third! There is a whopping 36.8% chance you won’t see a single shiny Makuhita after tapping 512 Makuhitas. Similarly, If you tap 1000 Makuhitas, the probability of finding at least one shiny = 1 – (511/512)1000 = 0.8585
That is still a 14.15% chance of not finding a shiny Makuhita after 1000 ‘seen’.
Similarly, If we take the probability of a Pokemon being shiny as 1/256, the probability of not finding a single shiny after: 256 ‘seen’ = 36.72% 512 ‘seen’ = 13.48% 1000 ‘seen’ = 2%.”
It all comes down to random luck because the Shiny Pokemon are very rare and there is no way that one can boost the chance of finding a shiny Pokemon. With that being said, it’s all about RNG and Probability!
For last, all credit goes to ‘our math teacher’ kramer753, and big thanks for letting us use his analysis. Don’t forget to give him an upvote for his hard work!