Hey there,
Being roasted by a lot of my own team and would love to just have a GM or Dev step in to help settle a debate.
First, this post is not a "hot take" on how fair shiny rate is. It's 1/30K. This is to discuss if you can apply a binomial distribution to the approximation of outcomes over a fixed number of encounters (trials)
Based on this statement we know that the odds of getting a shiny in any encounter is INDEPENDENT from any other encounter. We also know that the odds do not improve from encounter to encounter for a majority of players (anti-cheat measures excluded here)
Thus we can use a binomial distribution to tell someone their statistical likelihood of seeing at least 1 shiny in X encounters. This does not guarantee anyone a shiny on their next encounter or mean that their ODDS in any one encounter are improving, but that their overall chances are improving.
Then we can use a calculator to express the P(shiny) = 1/30,000 and make up a number of trials = encounters as 50,000. The odds of not seeing at least one shiny over 50,000 encounters is 81.1%.
This does not mean you have an 81.1% chance of getting a shiny in 50,000 encounters.
This does not mean that you have to wait 50,000 encounters to see a shiny, or that you can't get a shiny on encounter 1, 2, 3, 4, 5
One way to interpret this is that if 1,000,000 players did 50,000 encounters each, each one would have ~81% chance to see at least 1 shiny in their 50K encounters.
I would love to hear from some other stats enthusiasts or a GM to help settle it!
https://stattrek.com/online-calculator/binomial.aspx