>>20153982No, that's not how stacking probabilities work. Since it would be overly complicated to try directly calculating the odds of any given horde member being a shiny, it'll be easier to calculate the odds of none of them being shiny.
The probability of a given wild Pokémon being shiny is 1/8192, meaning that the probability of it not being shiny is 8191/8192. Since there are five Pokémon in a horde, the probability that none of them will be shiny is that probability taken to the fifth power:
36870975646169341951/36893488147419103232
So, big fucking digits. But that's the chance that none will be shiny; to get the probability that at least one will be shiny, that fraction has to be subtracted from 1, which gives the probability of finding at least one shiny in a horde as being:
22512501249761281/36893488147419103232
Since that can't be reduced or anything, I'll bring it down to percentage: there's a 0.06102% chance that you'll run into a shiny in a horde. Not all that impressive, but it still means you're likelier to run into a shiny in a given battle when you're dealing with hordes than in single battles.
