What were the odds of me getting two full odds gen 4 starters in less than 10 resets apart?

Question

Hahahahahahahahahahahahaha self explanatory

• HeartGold SoulSilver specifically, so I found three starters per reset
• odds are 1/8192 (3/8192 since hgss?)
• I don’t know the exact number. I found the starter in one game, played a bit, booted up another save and almost instantly found another shiny Cyndaquil. I personally believe it was only three.
• Bonus points if you can calculate the odds for me finding cyndaquil both times instead of the others

Comments

This is for your krlw

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Seriously, you should ask me these on Discord, instead. At this point, it almost feels like point-coordination...

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I’ll just lose them on discord :weary: and it’s my way to flex my epic hunts

I just know you’re the one who’s likely going to answer since you’re the mathematician no one else does math on the site

Answer 1

Okay, the formula for finding the probability of getting 2 shinies within a certain number of encounters is this: (1 - (inverse odds)^(total attempts - 1))^2. If you really want me to explain why it's this formula, I can explain it in a comment, otherwise just trust me on this one.

Odds within three resets (nine Pokemon seen):
(1 - (8191/8192)^8)^2 = 9.52859782e-5% or 1/1,049,472.

Odds within ten resets (thirty Pokemon seen):
(1 - (8191/8192)^29)^2 = 0.00124891265% or 1/80,070.

Bonus! Odds of Cyndaquil specifically within three resets (three Cyndaquil seen):
(1 - (8191/8192)^2)^2 = 5.9597369e-6% or 1/16,779,264.

Edit: Just double-checked my math and it looks like my formula was slightly off. Fixed.

Comments

wow, you are very smart

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Daaaaaaaamn ty got lucky