In Gen 2 to Gen 5 the shiny Base Shiny Odds are 1/8192
In Gen 6 to Gen 9 the shiny Base Shiny Odds are 1/4096
This is only in Pokemon Crystal.
The Pokemon in the Odd Egg can only be Pichu, Cleffa, Igglybuff, Tyrogue, Smoochum, Elekid, or Magby.
In the Japanese Version of Pokemon Crystal the Odd Egg shiny odds are 1/2 or 50%.
In the International Version of Pokemon Crystal the Odd Egg shiny odds are 1/14 or 7%.
This method is only in the Gen 2 games and is because shinyness is determined by DVs.
If the Pokemon's gender ratio is 1/8 the odds would be 1/64.
If the Pokemon's gender ratio is 1/2 the odds would be 1/128.
Gen 4 introduced the Masuda Method where you breed a Pokemon with a Pokemon from a differnt language. Eg. An English Pokemon with a Japanese Pokemon.
In Gen 4 the odds for the Masuda Method are 1/1638.
In Gen 5 the Masuda Method odds were decreased to 1/1366.
In Gen 6 to Gen 9 the Masuda Method odds decreased to 1/682.
Poke Radar is a method where you catch a bunch of Pokemon in a row and that raises the odds of a shiny appearing.
In Gen 4 the odds for the Poke Radar are 1/200.
In Gen 6 the odds decreased to 1/100.
In Gen 8 (BD/SP) the odds decreased again to 1/99.
The Shiny Charm was released in Black 2 & White 2 and raises the odds of a shiny appearing.
In Gen 5 the odds for the Shiny Charm are 1/2048.
In Gen 6 to Gen 9 the odds were decreased to 1/512.
The Friend Safari is a online function of the X & Y games.
In Gen 6 the odds for the Friend Safari are 1/819.
Chain Fishing is a method where you fish a bunch of Pokemon in a row.
In Gen 6 the odds for Chain Fishing are 1/99
SOS Battles are battles were you battle Pokemon another Pokemon called to help them.
In Gen 7 the odds for SOS Battles are 1/315.
Dynamax Adventures are battles where you eventually battle a Legendary Pokemon.
In Gen 8 (SW/SH) the odds for Dynamax Adventures are 1/300.
In Gen 8 (BD/SP) the odds after something good happens are 1/2048.
In Gen 8 (PLA) the odds for Mass Outbreak Pokemon to be shiny are 1/158.
In Gen 8 (PLA) the odds for Massive Mass Outbreak Pokemon to be shiny are 1/315.
In Gen 8 (PLA) the shiny odds decrease to 1/2048 if that Pokemon's Pokedex level is 10.
In Gen 8 (PLA) the shiny odds decrease to 1/1024 if that Pokemon's Pokedex level is Perfect.
In Gen 9 the shiny odds decrease to 1/1365 after defeating 60+ Pokemon from a Mass Outbreak.
In Gen 9 the shiny odds decrease to 1/1024 after making a sandwich with Sparkling Power 3.