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The following is the description of stealth from the Core Rulebook with clarifications given in italics and changes given in bold.
STEALTH (Dex; Armor Check Penalty)
You are skilled at avoiding detection, allowing you to slip past foes or strike from an unseen position. This skill covers hiding and moving silently.
Check: Your Stealth check is opposed by the Perception check of anyone who might notice you. Creatures that fail to beat your Stealth check are not aware of you and treat you as if you had concealment. You can move up to half your normal speed and use Stealth at no penalty, three-quarter speed at a –5 penalty, and normal speed at a -10 penalty. It’s impossible to use Stealth while attacking, running, or charging.
After you have entered Stealth, you must make a roll each round to remain in Stealth. If you attempt no movement and take no physical action during the round (such as manipulating an item), the check to remain in Stealth is made at +10. Some physical actions are so slight that remaining in Stealth may be done at +5 (unsheathing a dagger or pulling out a potion) or +2 (unsheathing a sword). If you make a successful Slight of Hand check against your foe’s Perception, you may manipulate an item silently so the +10 bonus can be retained.
Creatures gain a bonus or penalty on Stealth checks based on their size: Fine +16, Diminutive +12, Tiny +8, Small +4, Medium +0, Large -4, Huge -8, Gargantuan -12, Colossal -16.
If people are observing you using any of their senses (but typically sight), you cannot successfully use Stealth. Against most creatures, finding cover or concealment allows for the use of Stealth. If observers are momentarily distracted (such as by a Bluff check), you may attempt to use Stealth at a -10 penalty (you must move quickly to take advantage of the moment.)
Breaking Stealth: When you start your turn using Stealth, you can leave cover or concealment and remain unobserved until the end of your turn as long as you succeed at a Stealth check. Your Stealth will remain unbroken if you are able to end your turn in cover or concealment. Stealth will end if you end your turn outside of cover or concealment. It will also end immediately if you make an attack (if sniping, see below).
This means that a very stealthy rogue could do the following: In round 1, beginning in stealth, move to a target and sneak attack. In round 2, move out of combat into cover and stealth. In round 3, beginning in stealth, move to a target and sneak attack…and so on and so on. This could also be effective when used with the Spring Attack feat. However, sneaky characters should be careful when attempting the same maneuver too often on the same enemy. Savvy enemies may come up with an unexpected advantage against an uncreative rogue.
Multiple Stealth Challenges: No more than one Stealth check is usually needed per round. If during a round, more than one event occurs where Stealth checks are needed, only the most challenging DC should be used against the Stealth check (note that there may be some exceptions that require more than one check).
Sniping: If you’ve already successfully used Stealth at least 10 feet from your target, you can make one ranged attack and then immediately use Stealth again. )You are not required to move when using sniping_. You take a –20 penalty on your Stealth check to maintain your obscured location.
Creating a Diversion to Hide: You can use Bluff to allow you to use Stealth. A successful Bluff check can give you the momentary diversion you need to attempt a Stealth check while people are aware of you. Players will need to describe how they are attempting to bluff.
Action: Usually no additional action is needed. Normally, a Stealth check is made as part of movement. Movement is not needed if cover or concealment is immediately nearby and in-between the character and his foe. Note that a 5-foot step cannot be used to enter Stealth. If Stealth is used immediately after a ranged attack, see Sniping, above.
Special: If you are invisible, you gain a +40 bonus on Stealth checks if you are immobile, or a +20 bonus on Stealth checks if you’re moving.
If you have the Stealthy feat, you get a bonus on Stealth checks (see Feats).
HIDE IN PLAIN SIGHT (EX)
High level Rangers and Rogues can gain access to Hide in Plain Sight. When used, the character will visually look like they have melded into their surroundings until they disappear. Darkvision and many types of magical detection will not aid in finding the hidden character as this is a non-magical ability. Using Hide in Plain Sight does not require a diversion (using bluff).
HIDE IN PLAIN SIGHT (SU)
Assassins and Shadowdancers gain the supernatural ability to Hide in Plain Sight using shadows. When used, the shadows appear to magically envelope the character until they simply disappear. This ability is ineffective against Darkvision. Also, due to it’s magical nature, some types of magical detection could aid in finding the hidden character. Using Hide in Plain Sight does not require a diversion (using bluff).
CURSORY SEARCH FOR HIDDEN FOES (free action): As a creature first enters an area containing a hidden foe, they are granted a free Perception check to spot them. If a creature is already in an area with a hidden foe and they suspect someone is hiding nearby, each round they can choose to make a Perception check as a free action (DC equal to opponents’ last Stealth check). A successful check lets the creature see or hear some evidence of an unseen foe “over there somewhere”, but the foe continues to remain in Stealth. A low Perception result leads the creature to believe they see something that is not really there.
INTENTIONAL SEARCH FOR HIDDEN FOES (move action): Instead of using a free action, A creature may choose to make a Perception check as a move action (DC equal to opponents’ last Stealth check). A successful check means that the creature has detected the hidden foe. A low Perception result leads the creature to believe they see something that is not really there.