I've been looking at bulbapedia and I figured the calculation of 1/512 MM shiny odds is wrong.
Shiny charm and Masuda Method adds number of rolls. There's usually just 1 roll to get a 1/4096 value every Pokemon generated in-game. If that value matches your Shiny Value, the Pokemon generated will be shiny. Shiny Charm adds 2 extra rolls and Masuda Method adds 5 extra
rolls.So shiny Charm + Masuda Method gets you 8 rolls, each with a probability of 1/4096. This is not equal to 8/4096(1/512), as each roll is independent of each other.
If you don't understand this, think of flipping a coin. There's 1/2 chance it gets heads. So flipping a coin twice does not mean 2/2 or 100% chance that the coin will be heads at least once, it's just 75%.
According to wwwwwwzx, the dataminer on twitter, there's a maximum of 15 rolls for SOS with Shiny Charm.
I tried MM-ing Caterpie(one of the lowest egg cycle pokemon) and SOS'ing caterpie with synchronize(one of the highest call rate Pokemon, also does not learn egg moves). I could hatch 100 eggs in an hour(you can only carry 5 at a time) and you could encounter 180 caterpies in an hour with SOS.
The formula is (probability of getting a shiny)=1-[(4095/4096)^(number of pokemon encounters)(number of rolls per encounter)]
With 8 rolls per egg, You get around 20% probability of getting a shiny in an hour with MM.
With 15 rolls per encounter, you get around 48% probability of getting a shiny in an hour through SOS. However, there's 50% probability that sync won't work lol.
I would advise doing SOS only on high call rate pokemon that don't learn egg moves or don't require egg moves like beldum, magnemite, caterpie, or staryu, though. I think you could make gastly and midday lycanroc work without egg moves? Maybe trapinch and magby. Am I forgetting any others from US/UM?
