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Iirc they are limited like 2 you can capture per game, but what are the encounter rates while they are still present for you to catch?

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I thought it was 3 a game
Me too and that's what I originally had, but I saw 2 in another question so I changed it. It's either 2 or 3 but I don't know if the amount left influences anything.
If you have a Repel active and a leading Pokemon between level 55 and 59, they will amount to 100% of eligible encounters.
I'm not trying to get a 100% encounter rate, I want to know the rate of a non guaranteed encounter.
I did 100 encounters (during the day), and out of those, I got 80 Stakataka, 2 Heracross, 8 Buneary, 6 Trumbeak, and 4 Zoroark. Based on this, Stakataka's encounter rate is around 80%, but this of course could change if I were to do more attempts. Around 80% seems accurate to me, as it's high enough that you're getting stakataka/blacephalon nearly every time, but it's low enough that other encounters feel possible. This isn't an answer, just an observation, and it wouldn't surprise me if the encounter rate were even higher or slightly lower.

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So here is the rundown


Stakataka and Blacephalon are limited to two of them, not each, two of the same kind depending on what game you have Stakataka for Ultra moon and Blacephalon for Ultra Sun. Now your first encounter is guarenteed for both but they will not be shiny. This is due to it being part of the post story after becoming champion. You may catch them but if you flee or defeat them, they will respawn. If you do defeat them or flee they are now static encounters meaning that they can only spawn in Poni Grove. They have a 15% chance to appear before you. According to one source I have, they are an endless respawn.

Sources
https://www.serebii.net/ultrasunultramoon/ultrabeasts.shtml
https://www.dittobase.com/ultra-sun-ultra-moon/pokedex/blacephalon Stakataka has same rates due to them being cross game opposites
https://www.pokeos.com/q/capture/usum/stakataka/where-to-find
https://noseclub.bluwiikoon.art/usumubs.shtml: This should help you shiny Hunt

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edited ago by
https://bulbapedia.bulbagarden.net/wiki/Poni_Grove
https://www.serebii.net/ultrasunultramoon/ultrabeasts.shtml
Bulbapedia and Serebii disagree with your second source's encounter levels, so I'm inclined to believe that it's incorrect. Do any other sources back up that 15% encounter rate?
Don't know what kind of info you got. For one, I know there's two of the same UB for each game, that's irrelevant. The first encounter isn't a guaranteed Ultra Beast, as you can get other encounters. The first encounter can very much also be shiny, I got a shiny Stakataka during the part with the Ultra Recon Squad. Also, I don't know the odds myself, but 15% seems absurdly low. When hunting Stakataka, most of my encounters were immediately Stakataka, so I don't know where you got that.

I don't mean to throw any accusations, especially because this is absurdly hard information to find for some reason, but did you use AI for this? Also I didn't mention shiny hunting, I just wanted the encounter rate.
This answer doesn't read as LLM-generated to me, but that second link has one of the most egregious AI-style UIs I've ever seen. There's no way that's a reliable source.
Fair, and looking at the second link, I see where some of the info came from. My bad for the accusations. Although that second link definitely has some incorrect information.
Taco those sites don’t even say anything about encounter rates
Also I didn’t use AI.
I know they don't say anything about encounter rates, that's why I said they disagree with the levels. My point is that if two of the most reliable sites for information regarding Pokemon have differing information than a far less known site, my bets are on the smaller one being wrong. Because I'm going to assume that Bulbapedia and Serebii are correct on the matter of level, it leads me to believe that dittobase is wrong for other things as well, and therefore is not a very reliable source for encounter rate. Also worth noting that in the comments on the question, Ditto did 100 counters and got Stakataka 80% of the time. The chances of that happening at a 15% encounter rate are incredibly low.

Given that the source you just added, Pokeos, has a pretty much identical layout to dittobase, I'm going to assume that one is a clone of the other.