PokéBase - Pokémon Q&A
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I just wondered, what is the chance of getting a shiny salazzle since shinnies are rare and that there's 12.5% chance of getting female, what exactly is the chance to get them?

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Salazzle are 100% female. If you're talking about Salandit, then (I'm pretty sure) it would simply be the gender ratio times the shiny chance, or 1/8 times 1/4096, or 1/32768.
Why would the gender change the shiny chance?

EDIT: Nevermind I didn't realize you couldn't get a Salazzle from the wild.

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If you have the shiny charm and you are chaining above 70 Sos calls, the chance of getting a shiny salandit is 12/4096. The calculation is as follows: standard in sun/moon you have a 1/4096 chance of encountering a shiny Pokemon. Shiny charm multiplies that by 3. So that gives 1/1356.3. However if you chain above 70 sos encounters the number is again multiplied by 4, giving a grand total of 12/4096 = 1/341. Now that is for a regular salandit.
To get rid of the 1/8 gender rate it appears in you can use a Pokemon with the cute charm ability. Which gives you a 2/3 chance of encountering a Pokemon of the opposite gender. Now if you find a shiny salandit instead of 1/8 there is a 2/3 chance of finding a female. '
The chances of finding a shiny female salandit are thus 1/512. Not too bad I guess.
Watch this video for more info on how to do the trick: https://www.youtube.com/watch?v=TxV7VEVc_rY

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That's not exactly how SOS chaining works. After 70 calls, the game starts rolling the shiny generator 4 times instead of once, and the Pokemon is shiny if any of those rolls succeed. The chance of each roll failing is about 1355/1356. The chance of the roll failing twice is 1355/1356 of 1355/1356, or 1355/1356 squared. Since it's being rolled 4 times, the chance that it's not shiny is (1355/1356)^4. Therefore, the chance that it is shiny is 1-(1355/1356)^4, which is much closer to 1/339 than it is to 1/341.