The probability of someone having an IQ of 155 of higher, assuming a mean of 100 and standard deviation of 15, is 1 in 8,137.
The probability per encounter of a wild Pokémon in a main series Pokémon game from Generations II to V being shiny is, with a few exceptions, 1/8,192.
Hopefully a comparison like that will help readers, especially those in a certain age bracket, to understand how exceptional such high IQs are by statistical necessity, and how skeptical you should be whenever figures like that are casually tossed around. You can easily play through all of Pokémon Emerald, Diamond, etc., without encountering a single shiny Pokémon.
I probably played those games for a total of hundreds if not thousands of hours, but that was before I was a confident Google user, so I didn’t know what shiny Pokémon were. I wonder how many I missed without knowing…