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I am new to high level play in Pathfinder, or rather, in RPGs in general. I found a little bit in the FAQ, but still have some questions. I am very interested in Wizard, and we are starting at level 8. When looking through equipment for my character, I found the Headband of Vast Intelligence and have the money for a +4. This, plus the racial mod for elf and +2 for the two times you can upgrade an ability score, equals 26 intelligence. Is this allowed for purchase, or do you have to craft it? As well, what book is it from? Will taking the headband off decrease the score, even after becoming permanent? Thanks!
You can purchase or craft it.
It's from the Core Rule Book.
If you take it off it will cease being permanent and lose the bonus.
All purchases should be verified with your GM before assuming they are allowed.
Apart from that, yes, it's a standard item all wizards should be wearing (of the highest enhancement you can afford).
Removing it also removes the benefit - your Int drops back down, losing you the bonus spell slots, along with any spells memorised in them, and the bonus skill tied to that item (it doesn't grant 'spare' skill points, it grants one specific skill at one rank per level of the wearer, chosen by the item crafter - or the GM).
it's allowed for purchase. It's from the Core Rulebook. Yes taking it off removes the bonus it's giving.
The permanent is for things like preparing spells for the day. You get bonus spell slots for having a high INT. But only permanent int counts. So the headband makes it permanent for that when you prepare your spells. But if you take it off then you lose the bonus and you have to wait a day before it's permanent again, meaning you'll have 1 day where you'll have less slots then when you do have the headband.
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Will taking the headband off decrease the score, even after becoming permanent?
Permanent doesn't mean "on you forever".
Instantaneous is the in-game word for "changes you".
Permanent things are true so long as not-dispelled and not altered. You would lose it when you stop wearing the headband.
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s this allowed for purchase, or do you have to craft it?
For these sorts of questions, you should consult your GM (since this doesn't sound like a PFS character).
If your GM allows you to spend that much wealth on a single item, it's not a bad idea. Just keep in mind you're shorting yourself on other items such as consumables and defensive items.
If your GM allows magic item crafting, you'd of course require the appropriate crafting feats.