What are the chances of finding this Pokemon in dynamax adventures?

Question

Several years ago, for my birthday, my sister gave me a shiny gigantimax toxtricity, one of my favorite Pokemon! It was from a dynamax adventure in Pokemon shield, and she wasn't playing with anybody online, just npcs. I know she hadn't hacked or purchased it, because she showed me a video on her switch of her catching it. (also she was like 7 yo)

It is naturally gigantimax, shiny, and also has perfect spatk ivs, maybe more perfects if I remembered.
What's the combined chance of toxtricity spawning, it being gigantimax, shiny, and perfect spatk?
Thanks in advance!!

Comments

The shiny odds in the Max Lair (Dynamax Adventures) are 1/300 without the shiny charm and 1/100 with the shiny charm.

All Pokemon in the Max Lair are guaranteed 4 perfect IVs.

Toxtricity always has gigantamax factor in the Max Lair if I'm not mistaken.

Now I don't know which raids gigantamax toxtricity normally spawns in but it should always have 4 perfect IVs. The chances of your sister randomly stumbling upon a rare pool dynamax raid with a 1/4096 shiny odds perfect special attack IVs gigantamax toxtricity inside are probably a lot lower than the chances of your sister stumbling upon a Dynamax Adventure toxtricity in one of the three out of the 10 battles before the legendary and that toxtricity having perfect special attack IVs and it happening to hit the 1/300 or 1/100 odds of being shiny.

All this to say that some of these factors aren't influencing the odds like you think they are, and this event is likely a lot less lucky than you initially imagined. I imagine the odds are more like [the DA shiny odds] times [the odds of toxtricity being in one of the 10 slots out of the 226? possible Pokemon before the legendary]. However, I am not a math guy, so that's someone else's problem.

Either way much congrats and a couple years later Happy Birthday!

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Thanks Ditto!

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Did your sister have the shiny charm?

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no, she didn't have the charm.

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So the chance of toxtricity alone being shiny is 1/300.

A factor I forgot to consider is accounting for the Pokemon you get at the start, since Toxtricity couldn't have been one of those Pokemon. I'm not exactly sure how many Pokemon are at the start and how it works with the Pokemon you/npcs/other players can pick so that's likely something for someone to figure out if they want to do the deep probability calculations for this questions.

Answer 1

From what I can tell there are 236 possible non-Legendaries in Dynamax Adventures. Correct me if I'm wrong. If there is no shiny Charm:

1/300 (shiny odds) x 1/(236/10) (chance of Toxtricity appearing in one of ten slots) x 3/10 (rough chance of you getting Toxtricity out of all 10 Pokemon) x 4/6 (Perfect Sp.Atk)

= 1/35,400

Taking out the IV factor, it is a 1/23,600 chance to find a specific shiny Pokemon in Dynamax Adventures without the shiny charm.

Comments

Does this account for toxtricity not being one of the available Pokemon at the start or does that have no effect on the math?

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thanks MonkeyBusiness!!!! exactly what i was looking for :)