A Random Encounter or Random Event is a term used to describe when a random situation, quest, item, or NPC (ect.) appears while the player is traveling across the world map or in a metro station. Random Encounters have appeared in all of the games in the Fallout Series excluding Fallout: Brotherhood of Steel.
For a list of random events see Fallout 3 Random Events.
 Fallout 3
The following information is about Fallout 3 random encounters:
A random encounter can be as simple as a random enemy attacking, like a pack of Vicious Dogs, or as complex as a full on unmarked quest. Other examples include a trader coming and engaging you in dialogue, a group of Raiders attacking out of nowhere with a unique weapon, and special dialogue encounters such as a discussion with a Wasteland "Junkie".
These events can occur in special random event locations such as outside the Super Duper Mart, North or South of the Yao Guai Tunnels, and Temple of the Union. Unlike other RPG's random encounters aren't just scripted to happen anywhere in the Wasteland, they can happen in specific places as well, usually called spawning or encounter areas.
 Repeatable and Non-Repeatable
Random Encounters are put into two categories: repeatable and non repeatable. Repeatable encounters can happen more than once in the game with a different set of random NPC's, and can occur in different spawning grounds, and are repeatable. Non-repeatable events only happen one time during a playthrough (may happen more than once if DLC is installed) and can also happen in any spawning zone.
Usually Non-Repeatable random encounters offer better rewards or can be longer and more detailed, while repeatable ones might be shallow or seem short.
Usually random encounters can be manipulated if you are near a spawning zone. Say you're inside the Super Duper Mart and you know there's a random encounter outside, and you want the Alien Blaster event.
1). Turn auto-save off. 2). Save before you go outside, do not save afterwords except if you get the desired encounter 3). Step outside, and test you luck.
If you get an undesirable location, quit and save back to the Super Duper Mart. This will make the game spawn a new random encounter, not the same one you just saw. Rinsing and repeating can get you that favorite item or encounter you wish to have!
It should be noted that spawning grounds are split across the map. A set of spawning random encounters can only happen in one part of the map, while another group of spawning events can happen in the other. Please remember this when manipulating random events, because some events cannot just happen in some locations.
An example of a random encounter, the Wasteland Merchant.
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