Under these circumstances, what is the percentage of me (already) finding a shiny?

Question

So I know my odds are 1/8192 in Platinum.

I'm doing an Oak Challenge, as per usual, and I'm quite surprised that I have not found a shiny. I have 80 hours. Hypothetically, if I encountered 1 Pokemon per 2.5 minutes (to make up for travel/idle time), what is the potential percentage of me already/could've found a shiny?

Answer 1

Expanding on Mega-Blade X’s answer, using “number of attempts / denominator of odds” is an okay shorthand formula for calculating the cumulative chance if the number of attempts is way less than the odds, but starts getting further from the truth the more attempts you do. The actual formula is (1 - (inverse odds)^(number of attempts)). So, for Gen 4 full odds, that’s (1 - (8191/8192)^(attempts)). Then if you want it as a percentage, you’d multiply it by 100%.
Using the actual formula and plugging Mega-Blade’s calculated attempts of 1920, we get (1-(8191/8192)^1920), which gives us a final true chance of 20.8946% chance of having found a shiny.

Comments

I have never wanted to BA more than one answer in my life. What do i do? I guess if yours is more accurate i should BA yours. Thank you uwu

Answer 2

Let's see if I'm doing my math correctly:

80 hours is 4800 minutes. Divide that by 2.5 to get 1920. 1920/8192 is 0.234375. In percentage form, that's about a 23.44% chance of you already finding a shiny.

I'm not entirely sure I did that math correctly, so please say if I made errors. Hope I helped!

Comments

Hmmm so hypothetically, if i multiplied that number by 4,  i would have close to a 95ish% chance ive already foumd a shiny. 80 x 4 is 3600 i think. So that means id need 3600 hours of encounters to be guaranteed a shiny? Lol

Edit no i was wrong, 320. Not bad. Right spirit wrong idea, lol. This is why i asked

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Well, it wouldn't be guaranteed, seeing as that's not how odds work. But yes, that's quite a long time.

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Krlw gave a more accurate answer so ill ba's hers instead, but ill give an upvote for effort. Thank you uwu