I know this hasn't been found out for sure yet, please do not comment that it hasn't been found out! If someone does the research or finds someone who researched this I would like to know the exact percentage increase for Shinies for the Friend Safari versus the regular grass. Please do not answer if you are not giving the exact percent. Thanks!
According to The Scientist from this Smogon thread, the chance to encounter a shiny in the friend safari is most likely 1/512. We can't know if this is exact, but The Scientist's calculations seem quite accurate.
Hope I helped.
Hello , I noticed the shiny odds for Friend Safari is incorrect, but to be expected since this page haven’t been updated in years.
the 3ds hackder/Dataminers MrNbaYoh and Shinyhunter_map have found the real odds by looking into the games code. I posted my sources below.
The odds are 1-(4095/4096)^5 = 1/819.6001138 (~1/820) and with charm 1-(4095/4096)^7 = 1/585.5715635 (~1/586), as stated by MrNbayoh.
Sources - https://twitter.com/MrNbaYoh/status/760877085887987712 https://twitter.com/shinyhunter_map/status/932502961644888064 https://bulbapedia.bulbagarden.net/wiki/Friend_Safari