You both misunderstand. I am talking about theoretical probability, not experimental probability.
sumwun, obviously flipping two coins does not guarantee you get heads, but because the odds are 1/2, *theoretically* the odds are much greater.
Psyduck, I completely agree and understand what you said.
"The shiny chance of all encounters is 1/8192 pre-Gen 6, and not finding a shiny on an encounter doesn't increase the shiny chance of the next encounter to 2/8192, because both encouters are independent. This also means you aren't guaranteed a shiny every 8192 encounters, and could go for millions of encounters without finding a shiny or keep finding one every encounter, though the odds of both are extremely low."
This is obviously true when you are talking about chaining encounters, but not when we are talking about a single double encounter. Every single Pokemon you encounter has a 1/8192 chance of being shiny. So, theoretically, if you are encountering two Pokemon at once, the odds are 1/8192+1/8192. This is similar to Horde Encounters in XYORAS. If you have the shiny charm in XY, base shiny odds are 1/1365. Because you are encountering 5 Pokemon at once, you divide 1365 by 5 to get 1/273, which are the odds of encountering a shiny Pokemon in a Horde encounter.
If you follow my logic, the same principle applies to encountering two Pokemon at once in Eterna Forest. You are encountering 2 Pokemon at 1/8192 odds, so your odds become 1/4096 for any of them to be shiny.
Again, keep in mind we are talking about theoretical probability.