PokéBase - Pokémon Q&A
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Now I'm sure everyone knows that Synchronize provides a 50% chance for a wild Pokémon to have the nature that matches your Sync Pokémon. But is this really true? As far as I know, there is a 50% chance for the nature to match. But what happens if the ability doesn't proc? Now we have a 1/25 chance to have any of the 25 natures. This means that there is still a 1 in 25 chance for the nature to match. Doesn't this mean there is a (1/25 + 1/2) = (27/50) or 54% chance? Or does Synchronize raise the chance of the specific nature to 50%, leaving the other 24 natures at a 2.083333% (etc) chance each?

Thanks in advance for any insight!

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50% of the time, Synchronize exerts its effect, which ensures the right nature. The other 50% of the time, the nature is up to a random roll, so the odds of not getting the Sync but randomly fluking into the right nature anyway is 1/25 of that remaining 50%, which is 2%. Overall, you have a 52% chance of the desired nature.

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Ahh, that makes more sense actually. Thank you! What's your source, btw?
Simple math, and if you want a verifiable secondary source to look at, try getting a breakdown from something like 3DSRNGTool.