Hello everybody! I treated myself to a but now my pet is lacking in alchemy points. Where can I see how many I have already gained? And how many do I need to be able to use it? I have plenty of books stored in my vault, so that's not the problem. But I actually thought I could use them against the Morostide challengers. LOL

Your pet's AP is calculated by dividing intelligence by 16. Carcerus has 363 intelligence, which comes to 22 AP. It helps to read as many books as you can to increase your pet's intelligence. Higher intelligence/AP will allow you to equip more scrolls at once. Good luck!
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If you use stat boosters that raise intelligence, like tomes, you will need to read a book to get the AP owed you. You do not need to read a book on every 16th intelligence point though. For example, if you used 100 tomes on your pet and then read a book after it would give you all the back AP owed you.
Mentioned because some people don't know about intelligence boosters and reach a point where they are spending millions per book because they think it's the only way to keep raising intelligence.
to follow-up on this info, what are stat boosting tomes and how do you get them?
Alexandrite Stat Booster Guide: https://subeta.net/forums.php/read/903702/ The guide says it's not being updated but nothing has changed that I know of.
You can turn amulets into the Mage for a 1 in 7 or 1 in 9 chance of getting a tome. You can buy them from user shops. Or you can win them from beating challengers. Jess's guide is fantastic to see what each challenger drops and how many times you need to beat them to get the tome or if it's random for a site event challenger,: https://subeta.net/forums.php/read/893452 There is also this guide for a quick look: https://subeta.net/forums.php/read/935193