Pokémon Ruby Version, Sapphire Version, and Emerald Version - Trainer ID and OT Name
The Trainer ID is 32 bits long. The player as well as each Pokémon can have a 32-bit Trainer ID. A Pokémon’s 32-bit Trainer ID is set to the player’s as the Pokémon is created, if it’s owned by that player. A player’s 32-bit Trainer ID is set when a new game is started. However, the game only displays the lower 16 bits of a Trainer ID (here called called "public ID").
Many other Web sites use the term "ID number" or "Trainer ID" to mean the portion of the number visible on the Trainer Card, even though the Trainer ID, as used on this site, is 32 bits long. The "ID number" term used by those sites is 16 bits long and takes the lower 16 bits of the 32-bit ID number. These sites also use another term, "secret ID", which is the portion not shown of the ID and consists of the high 16 bits of the 32-bit ID number.
Each Pokémon also comes with an Original Trainer name ("OT name") and OT gender. (The OT gender is used primarily to color the OT name’s text blue (male) or red (female).) These two values, like the Trainer ID, are set to those of the player as a Pokémon owned by that player is created.
The way each game checks "ownership" of a Pokémon, however, can vary depending on the game and on the specific case, as detailed below.
To rename a Pokémon using the Name Rater in Slateport City or Lavender Town, a Pokémon’s 32-bit Trainer ID and OT name must match those of the player.
If a Pokémon’s 32-bit Trainer ID, OT name, or both (but not necessarily OT gender) are different from those of the player, it can disobey unless the player has the appropriate badges, and it will gain extra Exp. Points (see below).
Pokémon Ruby Version, Pokémon Sapphire Version, and Pokémon Emerald Version say that a Pokémon was "obtained from a trade" if its 32-bit Trainer ID, OT name, OT gender, any two, or all three are different from those of the player. Pokémon FireRed Version and Pokémon LeafGreen Version say that a Pokémon was "obtained from a trade" merely if its 32-bit Trainer ID, OT name, or both are different from those of the player. Pokémon Emerald Version, Pokémon FireRed Version, and Pokémon LeafGreen Version always say a Pokémon was "probably met" if it was met at a location in a different region not in the game, regardless of ID, OT gender, or OT name.
Shiny Pokémon
There is a 1/8192 chance that a Pokémon generated by the game will be shiny. Shiny Pokémon will have a different color from normal Pokémon.
To determine whether a Pokémon is shiny, the game splits the personality ID and 32-bit Trainer ID each into two 16-bit halves, resulting in four numbers, A, B, C, and D. Then the game calculates "A xor B xor C xor D", resulting in another number, E. ("Xor" is an "exclusive or" operation; see "Size Calculation" below.) If E is less than 8, the Pokémon is shiny.