From the Super Mario Wiki
The Mushroom Cup consists of four (or five in Super Mario Kart) race courses of the Mario Kart games. It is represented by the Super Mushroom. The tracks in this cup are the least challenging in the game. It always begins with a circuit, often Luigi Circuit. The tracks have few hazards and gimmicks, and few turns. The tracks are shortest in all games.
List of Mario Kart Courses
Not only is this cup in the Mario Kart series but also in other Mario sports games like Mario Power Tennis and Mario Superstar Baseball. In Super Mario Strikers, the Mushroom Cup has four teams and three rounds. When the player places in the top three, the Flower Cup and the Konga Coliseum are unlocked. A similar cup is the Super Mushroom Cup. In Mario Sports Mix, it's the first cup to be played in the tournament.
The Mushroom Cup also makes an appearance in Mario Tennis Open as the first tournament of the World Open. It is played on the Mushroom Valley court, and the CPU difficulty is the easiest in the World Open. The cup is the only one to be unlocked from the start.
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