From the Super Mario Wiki
A Super Mushroom (also known as a Power-Up Mushroom) is a red Mushroom that serves a particular function depending on the game in which it is found. Its first and most common effect is causing Mario or Luigi to turn into their Super form, allowing them to smash through bricks and take an extra hit from enemies. An opposite can be considered as the Poison Mushroom, a mushroom item that hurts the player. Both this and the standard Mushroom are designed after the Amanita Muscaria mushroom, which is ironically poisonous.
The idea for Super Mushrooms were originally believed to have been inspired by the cake that Alice eats in Alice's Adventures in Wonderland that makes her grow after having been shrunk by a potion. However, Shigeru Miyamoto later corrected himself, saying that this was a misunderstanding; the mushrooms were actually inspired by the concept of mushrooms being associated with magical worlds in general, like the Wonderland of Alice's Adventures in Wonderland and the Mushroom Kingdom.
Super Mario series
Super Mario Bros.
Super Mario Bros. is the first Mario game to feature Super Mushrooms. They are the most common items found in the game and touching them will make Mario grow into Super Mario. When Mario is Super Mario, he can take one more hit from an enemy and revert back to normal Mario before losing a life, and gains the ability to break Brick Blocks. When Mario already has a Super Mushroom, usually a Fire Flower appears instead. Also, when Mario shrinks, he will be invisible and invincible temporarily. The mushroom's colors resemble those of a Mega Mushroom. Players can make Super Mushrooms change direction by hitting the blocks they move along.
Super Mario Bros.: The Lost Levels
Super Mushrooms return in Super Mario Bros.: The Lost Levels, working as they do in Super Mario Bros. Also, Super Mushrooms receive eyes in this game for the first time, unlike the Super Mushrooms in Super Mario Bros., and Super Mario Bros. 2, making them look even more like Mega Mushrooms. Poison Mushrooms look almost identical to Super Mushrooms, except they are slightly darker in color.
Super Mario Bros. 3
In Super Mario Bros. 3, Super Mushrooms again return, but still grant the player the same ability. The only changes that were made was the sprite's appearance. In the original Super Mario Bros. 3, Super Mushrooms are colored white with red spots. In the Super Mario All-Stars remake, those colors are changed to the as-of-Super Mario World standard: red cap with white spots. However, the map's item screen retains the error.
Super Mario World
Super Mushrooms reappear in Super Mario World and no changes had been made to them. However, Super Mushrooms tend to "leap" out of the bushes sometimes for the player to receive. However, in this game, grabbing one while in Super, Fire, or Caped form will put it in the Item Stock, regardless of any reserve items. It also marked the first appearance of the current color scheme of the Super Mushroom, with the colors of the cap and spots reversed (red cap with white spots).
Super Mario 64 DS
Super Mushrooms (called just Mushrooms in the manual) appear exclusively in Super Mario 64 DS, but this time, they make the characters grow extremely large for a limited time, similar to the effect of a Mega Mushroom. This allows the characters to destroy objects or enemies simply by touching them. They earn an extra life for each object or enemy that they destroy after the first seven.
New Super Mario Bros.
In New Super Mario Bros., Super Mushrooms return, working as they did in the classic 2D Mario games. Unlike in Super Mario World, however, they don't replace higher-tiered power-ups in the Item Stock (like the Fire Flower), instead simply giving 1000 points to the player.
New Super Mario Bros. Wii
In New Super Mario Bros. Wii, the Super Mushrooms got little or no change except the amount of Mushrooms that appear out of blocks depends on the amount of players there are. Also when a character obtains a Super Mushroom (or any power-up) the character will sparkle and glow for a few seconds.
Super Mario 3D Land
Super Mario 3D Land is the second 3D game, but first original 3D game to have Super Mushrooms included. They turn Mario from Small Mario to Super Mario, in the same way as in the side-scrollers. If Mario collects a Super Mushroom when the player already has an item stored, the player earns ten coins instead. They also are not as necessary since Mario starts out as Super Mario if he is to lose a life. Morty Moles also drop a Super Mushroom sometimes.
New Super Mario Bros. 2
Super Mushrooms appear in New Super Mario Bros. 2, acting the same as they did in previous side-scolling games.
New Super Mario Bros. U
The Super Mushrooms appear in New Super Mario Bros. U, acting the same as in other games.
Super Mario 3D World
Super Mushrooms return in Super Mario 3D World acting the same as in other games. However, like in Super Mario 3D Land, they aren't necessary, because Mario, Luigi, Princess Peach, Toad, Captain Toad, and Rosalina start off in their Super forms.
Goomba Towers sometimes carry Super Mushrooms and the player can touch the screen to pop the bubble to get them from the Goomba Towers.
Donkey Kong (Game Boy)
Super Mushrooms also make an appearance in Donkey Kong for the Game Boy. They are used by Donkey Kong during the final battle. He ends up using several of them to transform himself into a giant. A Super Mushroom is also briefly seen in the ending when Pauline gives one to Mario, so that he can change his size and catch Donkey Kong when he is falling.
The Super Mushroom appears in Hotel Mario. It doesn't make Mario big or small, but gives him the chance to take one hit and not lose a life. The only difference between the normal Mario and the one that ate the Super Mushroom is the color of his overalls.
Super Smash Bros. series
In Super Smash Bros. Melee, the Super Mushroom allows the player to grow to an incredible size, thus making them heavier and harder to knock off. In Super Smash Bros. Brawl and Super Smash Bros. for Nintendo 3DS / Wii U, the fighter's attack strength also increases. An attack that normally does 15% damage could do near 30% damage when the fighter is a giant. Specifically, those attacks deal nearly twice the normal damage.
Captain Toad: Treasure Tracker
Super Mushrooms also return in Captain Toad: Treasure Tracker. Like in the main series of games, Super Mushrooms turn Small Captain Toad and Small Toadette into their Super forms. If the player collects a Super Mushroom while the character is in Super form, they instead earn 10 coins like in Super Mario 3D Land.
Mario Kart 8
In the Animal Crossing × Mario Kart 8 DLC pack of Mario Kart 8, a Super Mushroom emerging from a block appears as a cameo in a Super Mario Bros.-styled grafitti on the underground wall in Super Bell Subway.
Super Smash Bros. Melee
Super Smash Bros. Brawl
Super Smash Bros. for Nintendo 3DS / Wii U
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