
Atalius |

I plan on buying a Headband of Vast Intelligence +2 in my next game session, just wanted to know what "A headband of vast intelligence has one skill associated with it per +2 bonus it grants." and " the headband grants a number of skill ranks in those skills equal to the wearer’s total Hit Dice" means. I would like to improve my Perception skill rating. Finally it says "If no skill is listed, the headband is assumed to grant skill ranks in randomly determined Knowledge skills".

avr |

If the headband grants perception, then while wearing it you are treated as having the maximum ranks for your level in perception. If you already had that then it gives you nothing.
If you find a headband of vast intelligence +2 as random loot the skill it grants will be a random knowledge skill. If you buy one you may be able to get the skill you want instead.

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If you buy one you may be able to get the skill you want instead.
You might want to ask your GM first though. There's a 75% chance that you can buy a Headband of Vast Intelligence in a settlement that is big enough. That doesn't mean it has the skill you want. I'd make it another 75% chance because you're asking for something that is very specific.
Ofcourse, you could pay somebody for making a Headband of Vast Intelligence. In this case you could specify that you want ranks in Perception. It takes a little longer, but you get exactly what you want.
Edit: Bonus points for GMs: Add a Gnome tailor to your campaign who can make wondrous items (but only clothing). The tailor asks if the PC has any other wishes. If the player doesn't give some sort of description they will get a lime green fur cloak of resistance +1 or something like that.
The upside is that they get a +2 bonus on diplomacy checks with nobles for wearing something that was made by a designer, but you shouldn't tell them until they notice that all the nobles are wearing garish articles of clothing.