PokéBase - Pokémon Q&A
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So, after a chain of 3, what are the chances of the next one being a shiny? After a chain of 17, what are the chances of the next one being a shiny? After a chain of 52, what are the chances of the next one being a shiny, and so on for every number. Is there any formula for it?

Finally, if you have no luck with your shinies, will it get to a point where the next one in the chain must be a shiny?

I know this is a lot to answer, so thanks in advance. :D

FrenzyTorterra out - shiny style!

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It turns out that if you manage to get a chain of consecuctive fishing hooks, it will gradually increase the likelihood of finding a Shiny Pokémon, with the exact figures still to come. The higher the amount of Pokémon hooked, the more likely you get a shiny Pokémon, but as with PokéRadar, this is not a guarantee.

To improve your chances of chain fishing success, put a pokémon that has the Suction Cups ability or the Sticky Hold ability in the first slot of your party. This increases your chance of getting a bite from a wild pokémon while fishing

But after 25 the chance is the highest it can be.

Source Serebii

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I upvoted :P