Vault 21

 is one of the Vault-Tec Vaults, located in or near Las Vegas, Nevada.

Background
Its purpose in the Vault Experiment was gambling, reinforced by having only compulsive gamblers admitted as Vault residents, and all conflicts within the Vault were solved through a toss of the dice. Mitchell comes from here. At some point, Mr. House decided he wanted to have Vault 21, so he bet for it. And, of course, Mr. House won.

Layout
The Vault has been converted into another casino. The Vault is actually advertised with a big sign, unlike all the rest.

Appearances
Vault 21 appears in Fallout: New Vegas.

Behind the scenes
Vault 21 is a reference to the card game "Blackjack", where a player has to have the highest sum of card numbers, and 21 is the limit.