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As far as my testing went this basic chance to create a new item happens only once at the start. If it did not change the first day you can keep it in there forever and it will not change.
However if you take it back and insert it into the pot again it will have a new chance to change the next day.
So think of it as two rolls. The first one happens when you insert it. It rolls *IF* the item will change at all, if that fails it won't do anything and you can just take it back the next day. If it succeeds it will roll what the changes are and you can decide between keeping the new item letting it brew another day or discarding it into the void.
First time I put something in it took me 5 days before I registered a change, haven't had this long a period repeat yet, but it's definitely a possibility it'll take a while.
This has the same occurence probability as my bracelet which did not change in 5 days. Going by the 1/3 chance, this would be a probability of ~13% is my math is correct ((2/3) ** 5, right ?). This is far from improbable. Don't fall for the gambler's fallacy, "loosing" several times in a row doesn't suddenly boost our chances of success. The probability will stay the same for our next roll, whether a change occured or not. ....unless the game's code is effectively boosting our chance of success on failure, but so far there is no reason to think so.