What are the odds that you will find a Shiny Pokemon by its listed odds?

Question

I think I saw this somewhere on the site at one time but I don't know where.

Some people may not understand what this means, but I believe you have to use binomial probability to know this? Idk, basically I'm asking what the chance of you going over odds for a shiny hunt is. And is the chance different for methods with different odds?

Answer 1

In general, you have about a 63% chance to find a shiny before reaching odds, though it goes down slightly the worse the odds are. You're right that you need to use the binomial probability formula, which is 1 - (inverse odds)^attempts.

For example, Masuda+Charm odds in Gen 6+ is about 1/512, so the odds of finding a shiny before reaching odds are:
1 - (511/512)^512 = 0.632480109 or 63.2480109%

Full odds Gen 6+:
1 - (4095/4096)^4096 = 0.632165471 or 63.2165471%

Full odds Gen 2-5:
1 - (8191/8192)^8192 = 0.632143014 or 63.2143014%

Yeah, when I said the chance goes down slightly, I meant very slightly.

Comments

Thank you, that was exactly what I was looking for

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Is that 1 - (1 / e)?

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Yes, it seems to approach 1 - (1 / e) as the inverse odds and attempts approach infinity.