PokéBase - Pokémon Q&A
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I’m trying to hatch a shiny Magikarp... it’s not going so well.

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The odds of hatching a shiny Pokémon as of US/UM:

NO boosters: 1/4096
Using ONLY the Shiny Charm: 1/1365
Using ONLY the Masuda Method: 1/683
Using the Masuda Method AND Shiny Charm: 1/512

Shiny Charm - The Key Item reward you get for completing the National Dex

Masuda Method - A Shiny Hunting method involving breeding two different Pokémon from two different nationalities; only language tag matters for this, not system regionality.

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What is the masuda meathod?
The Masuda Method is a shiny hunting method that increases your odds of hatching a shiny when breeding two Pokémon of different languages.
I'm going to be pedantic and quickly add that *technically*, the odds for only Shiny Charm and only Masuda method are 3/4096 and 6/4096 respectively.
The fractions with a numerator of 1 are 'near enough is good enough' approximations of the actual probabilities. Websites use them because they're nicer to look at and compare, but they're ever-so-slightly inaccurate.
Well if Fizz is going to get technical like that then *technically* the odds for only Shiny Charm are 1-(4095/4096)^3, only MM is 1-(4095/4096)^6, and both are 1-(4095/4096)^8 (with the final result multiplied by 100 if you want them as a percentage). But at the end of the day, it still turns out to be basically the exact same number as if you had just started out with 1/1365, 1/683, and 1/512, respectively.
I've never seen the probabilities represented that way before -- what's the logic behind it?
The difference between 3/4096 and 1-(4095/4096)^3 is even more negligible than between 1/1365 and 3/4096, but obviously I want my numbers to be precise. :P
Yeah, the way that the Shiny Charm and MM work is by rolling the shiny chance extra times and seeing if any of them are shiny, so it’s functionality equivalent to encountering several Pokémon at once. The miniscule chance that you get the same non-shiny value twice during those rerolls is what causes the difference between x/4096 and 1-(4095/4096)^x (where x = number of rolls / encounters). The difference between the two formulas is more drastic the higher x is, and it’s pretty negligible when it’s less than around 500.