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Pokemon & Science - Did You Know Gaming? Feat. JonTron
Pokemon Part 2 - Did You Know Gaming? Feat. Rosanna Pansino
 
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In the game's code is evidence of an unused Event Pokémon. Event Pokémon are exclusive Pokémon throughout the franchise's history which usually have movesets or other unique properties that would not otherwise legitimately occur in normal gameplay.

A code string indicates that Diglett learns the move "Acid" at Lvl. 1, found at the end of Diglett's Generation 1 move pool, as this programming method was the manner in which the programmers ensured Event Pokémon transferred via the Game Pak to Stadium could function properly during gameplay.

To date, a Diglett with Acid being legitimately learned in it's moveset has never been released or distributed by an official Event by Nintendo nor Game Freak.
Contributed by Regen-33
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The game has unused animation of two Butterfrees holding a banner. As the animation is found within the main menu graphics, it may have been used to display the names of the locations in the menu.
Contributed by MeleeWaluigi
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Nidoqueen's entry stance was altered in the international release as her Japanese stance showed her cupping her breasts.
Contributed by RadSpyro
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If a Pokémon knows an attack it normally shouldn't be able to, the text changes color to purple.
However, even if someone teaches a Pokémon a legitimate move through Pokémon Gold/Silver or Pokémon Crystal, and then trades it back, if the move cannot be learned in Red, Blue or Yellow, the game will still show it as purple.
Contributed by RadSpyro
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The GB Tower can be upgraded by completing the Poke Cup and the Prime Cup. Completing one will unlock the Doduo Tower, which will change the background and allow the player to play their games at 2x speed, and completing both cups will unlock the Dodrio Tower, which will allow for 3x speed.
Contributed by Funland47
Transferring your starter Pikachu from Pokemon Yellow will have them say their name during battles (voiced by Pikachu's anime voice actress Ikue Ohtani), instead of the standard Pokemon growl.
Contributed by Funland47
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Transferring nicknamed Pokemon from Red & Blue can change their colors.
Contributed by Funland47
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Surf can legitimately be taught to any Generation I Pikachu by completing the Master Ball division of the Round 2 Prime Cup while meeting the following requirements:

• All of the Pokémon must be selected directly from a Game Pak. The Pikachu can come from any Generation I game.
• Continues may be used, but the game cannot be saved.
• Pikachu only has to be selected for the final battle and does not have to take part in the battle.
Contributed by Funland47
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If you successfully complete the Gym Leader Castle and Stadium modes, Pikachu, Blastoise, Charizard, Venusaur and Mewtwo will appear on the game's title screen.
Contributed by FUS RO DAH
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In Japan, this game is known as Pokemon Stadium 2. This is due to Japan having already released another version of the game, but with very limited Pokemon available.
Contributed by RadSpyro
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Electabuzz mistakenly has six fingers on each hand. This error was not corrected in Pokemon Stadium 2.
Contributed by DidYouKnowGaming