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Without shiny charm.

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Are you asking for the chance of getting a shiny Pokemon as the 255th Pokemon called, or the chances of getting a shiny Pokemon on any encounter, assuming that the chain has 255 total Pokemon called?
any encounter in the entire chain.
After 70 encounters, I think, the Shiny multiplier doesn't grow anymore. So any Pokémon after number 70 will have the same Shiny chance.
but like what would be the chances before it resets by 255?

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SHINY CHANCE
A chain length of 70 to 255 gives you a 1/1024 chance of encountering a shiny (normally 1/4096). If you have obtained the Shiny Charm, the chance becomes 1/683.
Source


After a chain of 70 the game rolls the shiny chance an extra three times, meaning the normal chance of 1/4096 gets increased to 4/4096, effectively giving a chance of 1/1024.
With a shiny charm, this chance is originally 3/4096 (two extra rolls for shiny spawn), and so gets boosted to 6/4096 after a chain of 70, effectively giving about a 1/683 chance of a shiny until the chain counter rolls over to 0.
Source


After 70 chains, the Shiny chance is 1/1024 (0.097%) or 1/683 (0.146%) with the Shiny Charm.

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I think he was asking for the chance of at least one shiny in 255 calls and not the chance of a shiny in one call.
He said any encounter in the entire chain.
Thanks! I was asking for what sum said, but I did some quick math, and its around 25% without charm and 37% with the charm.