"A Link to the Past Randomizer", often abbreviated ALttPR, is a randomizer of the Super Nintendo Entertainment System game The Legend of Zelda: A Link to the Past. There are several games which have randomizers, including several others in The Legend of Zelda series, but A Link to the Past Randomizer is one of the most popular.
A Randomizer is a program that reads and rewrites a ROM file to change information about where items and enemies are placed, and sometimes the order that levels come in, or the terrain of the map. This allows a player to play the same game with some novelty, as the game is a little different each time. In ALttPR, the main change is in the placement of items, (although there is also a mode that allows the player to randomize the placement of enemies). A Link to the Past has about two dozen items that a player needs to gain to complete the game, and the randomizer works by putting them in random locations. The Fire Rod, which has a vanilla location of Skull Woods in the Dark World, might be the first item you pick up in your house, or might be carried by the very difficult boss of the sixth dungeon in the Dark World. Since there are hundreds of chests and locations that the two dozen vital items could be hiding in, the game theoretically has something like 255! possible combinations.
However, there are some combinations that are impossible. Since many locations are only accessible with certain items, those items can not be in those locations. Misery Mire is only accessible to a player that has The Titans Mitts and The Magical Flute. Therefore, the Randomizer makes sure that when it randomly generates a seed, that the game is logically clearable. This can be quite complicated: since the Titans Mitts and the Magical Flute can't be in Misery Mire, that means that if the Magic Mirror is in Misery Mire, that those items also can't be in Swamp Palace, since it requires the Magic Mirror to enter. And in fact, Swamp Palace can't have any item that would be necessary to get the Mitts and Flute, such as the Fire Rod to free them if they have been placed on the boss of Skull Woods...there are dozens of different interactions that logically dictate the order in which the items appear, and that the developers had to account for in their programming (which required many different versions to catch all these possible contradictions). Following this chain is also a challenge for players, and represents the test of real mastery of the game. This system of interactions, called "The Logic" is a subject of almost Talmudic study by the players and commentators of the game.
Ah yes, the commentators. Because this game was not just meant to be played. It is also played in races, both casually and as part of formal tournaments, where two or more runners will attempt to clear the same seed as quickly as possible, while commentators explain the sometimes confusing structure of the game to an audience. Most of these tournaments have been online, although recently there was a live tournament. There are a few dozen people who specialize in this game, and a community of hundreds of people are interested in it, and it is interesting following it for the community as well as for the game play. Soon, pieces of jargon like "Ice Rod on Laser Bridge", "Hammer in Lumberjack Cave" and "Good Routing on the Smith Chain" start to make sense. There are many of these games viewable on YouTube, and I find they have a bit of restful, hypnotic quality to them. They are predictable and comfortable enough to be soothing, but involve enough variation each time that I am interested in seeing how they turn out.