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Should be self explanatory. Adaptability gives STAB moves a x2 boost instead of 1.5. Terastal also gives STAB moves a x2 boost. What is the interaction with the STAB boosts from Adaptability and Terastal? Do they stack to make it a total of a x4 boost to STAB? Does it stack, but not to a total of a x4 boost. Do the boosts from Adaptability and Terastal not stack?

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When the Tera type is different from the original types, does adaptability boost both the original types and the Tera type?
What is the resulting boost? Given that damage is partly random, I don't think you can answer this question just by using aqua jet twice.
I did some testing.
1. Tera does stack with Adaptability
2. When you terastalize into a new type, only the new type is boosted.
However, I don't know the boosts.
It just adds 1.5x with tera
How do you know this? In the replay, the aqua jet was boosted from 25% to 33%, and 33 is a lot less than 1.5 * 25.
Because according to the current information of terastal it should give a 1.5x boost otherwise I need to recheck but it 100% boosts the power if the Tera type is the same as the stab type.Also there's the possibility of a high damage roll.
https://replay.pokemonshowdown.com/gen9ou-1720658605
Here I did the calcs with basculin here(no EVs investment) and it matches perfectly with non tera
But when I tera its hard to say how much it boosted, the game probably havent know how to calculate the tera and Adaptability yet but I do think it still have STAB because for other mons they do get the type STAB for there tera.
If you did the calcs, then show us the calcs.
According to what "current information"? According to the information I have, after a type already gets STAB, both adaptability and Terestalizing boost it by 4/3. 3/2 * 4/3 * 4/3 = 8/3, which is roughly 2.667. How is your logic more correct than this argument?
How would one calculate the boosts for this question?
Ideally we can ask someone who looked at the code, but testing the same move many times and then averaging the damage would be better than what we have now.

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Tera Water + Adaptability does more damage than just Adaptability, though by how much is hard to say (I originally suggested 2.25x STAB multiplier, which would be 9216/4096 I think).

tl,dr;
Tera + Adaptability boosts damage more than regular Adaptability
Adaptability boosts moves of user's Tera type
Adaptability does not boosts moves of user's original type when Tera'd

You're right on this value, by the way! I saw this a few days ago and had to ask what causes Tera STAB to be upgraded from 8192 to 9216, because I am bad at Pokémon and forgot it existed.

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Interesting. Thanks!