A random encounter is a common RPG situation. It most often occurs when the player character is traversing a distance across the world map or a dungeon, resulting in a conflict with a randomly chosen opponent. In Fallout, random encounters are only encountered on the world map and can be as simple as a trader wishing to show you their wares, to finding a tin man who needs to be oiled...
Not every encounter is hostile. Not every dangerous encounter involves aggressively minded NPCs (such as "Stampede" or "Dehydration" encounters in Fallout). Not every encounter even has an NPC on its map ("Old battle" encounter). Some random encounters are unique, and happen only once during the course of the game (or not at all) - these are commonly known as Special encounters.
The kind of encounter depends on many factors. The main one is player's location on the World Map. Others may be the player character's Outdoorsman Skill, Karma level or Reputation, as well as their previous actions during the game.
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 Fallout 2
The random encounters in Fallout 2 are determined by the player's location on the worldmap, his level and global variables governing it and finally, the chances of encountering one, stored in WORLDMAP.TXT. They can be everything, from a number of molerats foraging in the area, through a press gang to and including merchant caravans.
 Fallout 3
A random element is the place where a given event will appear. Once a special encounter has been activated in a particular area no other random event will occur in this area. You can save outside the spawning area and keep reloading if you don't get the encounter you want.
In principle, there are two different types of special encounters in the game: unique encounters and repeatable ones. Unique encounters will only occur once per playthrough whereas repeatable ones can occur multiple times. Another difference is that repeatable events can happen in any of the random encounter locations but unique encounters do not; there are 2 sets of unique events, each of which occurs only in a certain set of locations.
 Fallout: New Vegas
 Fallout Tactics
|The following is based on Fallout Tactics and some details might contradict canon.|
The random encounters in Fallout Tactics are determined by the player's location on the worldmap and the chances of encountering one, stored in BOS.CAM campaign file. They can vary from a number of peaceful tribals or a bunch of mutated animals, through raiders, beastlords, super mutants, reavers to and including Calculator's robots. Sometimes random encounters include two rival groups fighting each other.