PokéBase - Pokémon Q&A
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Like, since there's three of them, and you see them all at once, so per encounter since there's 3 and the odds are 8192.

Like, would that mean my odds are like 0.03% per reset or am I really bad at math

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I've calculated and recalculated these values in particular, so here they are:
The chance of finding a shiny starter is A + B + C, where A is the chance of one Pokemon being shiny, B is the chance of two starters being shiny, and C is the chance of all three starters being shiny.
The chances of B and C happening are almost negligible, but for the sake of accuracy (and lowering the estimated amount of time), I will incorporate these values. (for the records, the chance of finding one shiny Pokemon is 1/8192.

A = 0.00000000018189894
B = 0.00000148993422000
C = 0.01220405120000000
(these are all probabilities)

Therefore, the probability of finding one shiny starter is 0.01220554131611894%.

Each soft reset gives you that chance of finding one. Now, with a bit more calculations, we can determine the approximate number of tries it'll take to find a shiny starter.
To do this simply, just enter XX/0.01220554131611894 into google, where XX is the percent you want.

For example..

After your 4,096th reset, you're more likely than not to have found a starter by this point.
After 7,373 resets, there's a 90% chance that you'll have found a shiny starter.
Just 800 more, and you have a 99% chance..you're basically guaranteed to find one by this point.

Source

I hope this was what you're asking, lol. Hope this helps :P

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Is this the same for resetting 5 pokemon at the same time at the game corner for example?
I feel like Coco is genius
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Yes, it would be. Since the odds of getting a shiny Pokemon in gen IV is a 1/8192, or a .01220703%; .012% rounded. So, it's not a lot. Since you are encountering 3 Pokemon at the same time, each has that 1/8192 chance, so It'd be a 3/8192, or a .0366% for each soft reset. And sadly, no, percentages and probabilities are different. Say you have 1/8192 for a shiny. You could SR 10,000 times and still not have it shiny, because each encounter has the 1/8192. I did Lugia in SS, didn't, get it until 12,777 SR's.

Good luck on your hunt!
I'm on 700 for starter in HG.
Happy Shiny hunting,

~Freezee

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It is a little different for legendaries in my experience legends seem to need more than regular pokemon and starters it took me about 50k sr to get a shiny registeel before and iv done starters getting them in about 2-8k sr and mesudo takes me about 300+ eggs