How many times can I finish the game and enter the Hall of Fame?
Every time you finish the game you join the Hall of Fame. After beating the game 20 times I was wondering if there is a limit to the amount of Pokémon that can be listed in the Hall of Fame.
Is there a limit of times one can beat the game and join the Hall of Fame? What happens if you beat the game again? Will it overwrite the first entrance or nothing will be added to the Hall of Fame?
Generation I games store the player's 50 most recent hall of fame records. If you were to beat the game a 51st time, your 1st record would be overwritten. (Source)