Sneak (Fallout 3)

Sneak is a skill $$ It determines the chance of being detected while sneaking.

Background
Allows the player character to move closer undetected and avoiding taking damage for the longest time possible, and maximizing the damage potential through the use of "sneak-attacks." The player character can both sneak and run at the same time (i.e. move faster while crouching) regardless of perks. However, without the Silent Running perk, they will suffer a detection penalty while running.

Initial level
\text{Initial level}=2+(2\times\text{Agility})+\left\lceil\frac{\text{Luck}}{2}\right\rceil Example: A starting Agility of 5 and Luck of 5. 2+(2\times5)+\left\lceil\frac{5}{2}\right\rceil=15

Sneak states
The sneaking state is displayed while crouching and alerts the player character to detection and possible detection.
 * [HIDDEN] means being undetected. In this state, attacking a target guarantees the sneak attack critical bonus, pickpocketing is available, and it is safe to steal, lockpick, or otherwise access "owned" property.
 * [DETECTED] means being in sight by one or more targets. Pickpocketing is enabled, but almost always fails. Attempting to steal, lockpick, or otherwise access "owned" property will fail, and may result in friendlies turning hostile or confiscating stolen goods. Sometimes an unfriendly target will see it and this will be shown instead of [CAUTION] because they haven't identified one as hostile or a target.
 * [CAUTION] means one or more unfriendly targets are suspicious of presence and are searching for the character. After a time the enemy will dismiss the disruption and the state will return to [HIDDEN]. Pickpocketing is disabled for the enemy searching for the player character. Attacking in this state will not cause a sneak-critical hit.
 * [DANGER] means hostile NPCs are aware of one's presence, but they do not know the current location. They will actively search at or around their last known location. If [DANGER] is flashing, it means that the enemy has the player character in sight and will engage them. The state can be returned to [HIDDEN] by moving away and staying out of sight for an extended period of time. As soon as the conditions are satisfied for any state, it replaces the one above it on the HUD even though one may still be in the [HIDDEN] state to several targets around them. Essentially, it reports the worst detection state towards the player character of all potential targets. Once all targets that satisfy the most-elevated state are dead (as in killing everyone actively pursuing the target in [DANGER]), the state will revert to the highest remaining state amongst the remaining targets.

Factors

 * Sneak skill: The sneak skill applies whenever the player character crouches. The higher the Sneak skill, the easier it is to remain undetected while attacking, stealing, or picking someone's pocket.
 * Cloaking fields: The Stealth Boy and Chinese stealth armor will wrap the user in a cloaking field that makes them more difficult to detect while sneaking, rendering the character virtually undetectable by visual sighting. The stealth field effect is extremely powerful, and its value matters very little, so the Chinese stealth armor's stealth field of 5 works almost (but not quite) as well as the Stealth Boy's 75. It should be noted that this field only increases one's sneaking ability, and the field will be negated if leaving sneak mode in any conventional manner, such as firing a loud gun, since the cloaking field does not mask sound-based detection. The stealth suit only has a +15 Sneak versus the Stealth Boy's +100, but its effects are not limited by time. Cloaking can also be stacked, so the stealth armor and Stealth Boy can give the player character a combined field of 80.
 * Enemy's Perception: Enemies with low Perception are easier to sneak around than enemies with high Perception. A target's Perception will be impaired (a -4 reduction) if they have a crippled head.
 * Line of sight: While out of sight an enemy can only detect the target through sound.
 * Light level: The target is more difficult to see in dark areas or at night if outdoors. If the Pip-Boy light is active, it will give away the position.
 * Distance: The farther away the target is from the seeker(s) the less likely they would be detected.
 * Movement: The player character is hardest to detect when motionless and easiest to detect when running. One can avoid the sound aspect of this by the Silent Running perk. Moving faster while within line of sight will still make it easier to be seen, but one will no longer get any penalty for movement speed to sound made. Note that looking around counts as movement, but not as much as movement over ground. If standing in shadows with a direct line of sight to a target not aware of the location, looking around may very well make the target investigate, or immediately end with being found.
 * Contact: Touching or running into targets while crouched will immediately alert them of position. Regardless of how hidden one is, bumping into a target, friendly or otherwise, will immediately result in detection. This also applies to robots that have been deactivated using the Robotics Expert perk.
 * Equipped weight: The total weight of all equipped items (weapons count only if they are in one's hands) makes footstep volume louder for non-player characters. Silent Running removes this penalty entirely, allowing full sneaking ability in any equipment. The footsteps are still audible while sneaking with the perk, but non-player characters will not hear it.
 * Sound: Most guns make noise. Louder guns make one easier to detect. The Silenced 10mm Pistol, BB gun, Dart Gun, Infiltrator, Perforator , all melee weapons and all unarmed weapons are considered entirely silent, and thus will not break sneak mode. Grenades will also not break sneak mode, as they only make noise at where they explode. Hitting but not killing an enemy with silent weapons still causes the [CAUTION] alert. All other weapons will most likely be heard, depending on one's distance from the target. Missile Launchers and Fat Man units make noise at the location and then at the impact point as well. The Pip-Boy's radio has no effect on sneaking.
 * Dead bodies: When an enemy spots a dead body, it will often enter the [CAUTION] state and move toward the dead body. This can often create a more or less perpetual [CAUTION] state while one remains in the area. If a dead enemy can be grabbed and dragged out of the way before it is found, the player character can retain their hidden state.

Sneak Attack Critical
A Sneak Attack Critical occurs in Fallout 3, Fallout: New Vegas, Fallout 4, and Fallout 76 when attacking while [HIDDEN]. Successfully hitting the target will result in a guaranteed critical strike (unless the weapon does not allow critical hits), while at the same time doubling (ranged) or quintupling (melee/unarmed) total damage.

Pickpocketing
While sneaking and [HIDDEN] using the "activate" function while facing a non-player character (when in touching range) will allow pickpocketing them. This will open the inventories of both the player character and the target. Items can be transferred either way, and thus items can also be planted on them, also known as reverse-pickpocketing.

Permanent

 * Leveling up (up to 10 + INT + 3 with Educated perk))
 * Bobblehead - Sneak (+10)
 * Chinese Army: Special Ops Training Manual (+1 or +2 with Comprehension)
 * Thief perk (+5 with each rank)
 * Tag! perk (+15)
 * Silent Running perk (+10, removes movement speed penalties to sneak)
 * Survival Expert perk (+0 - +6, depending on quest results)

Temporary

 * Fire Ant Nectar (+2-8 depending on current Agility, a perfect Agility of 10 will see no benefit.)
 * Recon armor (+5)
 * Shady Hat (+5)
 * Poplar's hood (+10, additional +2 if less than 10 Agility)
 * Stealth Boy (+100, +75 cloaking field)
 * Chinese stealth armor (+15, also adds +5 cloaking field while crouched)
 * Lag-Bolt's shades (+3)