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I have seen videos and they both say different odds?

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Base odds are 1/4096.
Methods like Dex Nav and the Masuda Method increase your odds.
Getting the shiny charm increases your odds to like what 1/1365 or something? I don't know the odds off the top of my head.

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Some of the simplified odds are rounded to the nearest whole number.

Base odds: 1/4096
With Shiny Charm: 3/4096 (~1/1365)

Masuda Method: 6/4096 (~1/683)
With Shiny Charm: 8/4096 (1/512)

Consecutive fishing (max chain): 41/4096 (~1/100)
With Shiny Charm: 43/4096 (~1/95)

DexNav: Complex mechanics; see Bulbapedia's table

Shiny Pokemon (Bulbapedia)

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Where applicable, I think it's better to give the exact fraction as well (e.g. 3/4096 for Shiny Charm not just ~1/1365), since it's more reflective of how the odds boost actually works.