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Ill be a lvl 1 Water Oracle with the Obscuring Mist so that I can see through the mist with Water Sight.
Lets say I cast Ob. Mist and dont move. A goblin archer tries to 'guess' my square and fire an arrow at me. What are the rolls? Here are my guesses.
Perception vrs my Stealth at +20 for being 'invisible' to locate my square then if a hit is scored has a 50/50 miss chance from concealment?
If I actively Stealth as my move action after casting Ob Mist do I get the +40 Stealth bonus?
I find it helps, rather than "actively Stealth" as a verb, to use the older terms. What you want to do here is move silently. If you cast Obscuring Mist and don't move, the goblin knows where you were when he last saw you. If he tries to determine whether you're still there, he's listening for you, attempting Perception against your Stealth +40 (for trying to pinpoint you solely by sound when you're trying not to make a noise). If he fails, but guesses that you're still there, he will be right anyway, then he just has to take a 50% miss chance.
If, instead, you cast Obscuring Mist and then move away, you move silently using Stealth +20, opposed by his listening (Perception). If he fails by 20 or less, he heard you move but doesn't know where you are. If he fails by more than 20, he didn't hear you at all. The next round, if he didn't work out where you are and you don't move or make loud noises (such as spellcasting), he needs a Perception check against your Stealth as above to find what square you're in. Say you do cast a spell, you are no longer stealthy, he hears you and he gets a Perception check to pinpoint you (DC 0 + 20 + usual modifiers).
A Barbarian in the group wants to wield a two handed weapon with a Spiked Gauntlet on for back up. Is there any rule for or against that?
That's fine. He can't use his gauntlet for anything (such as threatening AoO) while wielding the 2H weapon. He can release one hand from the 2H weapon as a free action, which means he can only do it on his turn.
He also wants to take Heart of the Fields alternate Human ability that cancels an effect that causes fatigue or exhastion once per day. He then wants to sleep in heavy armor and use the ability to cancel the morning fatigue...?
Your GM must be rubbing his hands with glee at a player who wants to give up one of his racial abilities to avoid a situation (a night attack on your camp/inn room/palace bedchamber - did he specify the exact circumstances when he would do this?) that rarely comes up and where heavy armour might not save him anyway.
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Excellent, very helpful.
I guess my last question to make sure I have this right...
What if I cast Ob Mist and then Draw a weapon taking no active stealth action? Do I still oppose Perception with a +20 Stealth Roll?
Stealth is not an action, except for the special case of sniping. You can take a Stealth check as part of another action, or opposed to a Perception check, whenever you meet the requirements: you have an opportunity to be stealthy and you don't do anything that exposes you to the opponent.