From the Super Mario Wiki
The Winkle Colosseum is a place in the Chucklehuck Woods where many Winkles compete. During the course of Mario & Luigi: Superstar Saga, one of the four pieces of the broken Beanstar lands inside the Colosseum.
Mario and Luigi comes to the Winkle Colosseum to look for the piece, and are forced to play a minigame for a fee of 500 Beanbean coins. After they complete the game, the Winkle guarding the door gives the brothers a Winkle Card, allowing them to pass to the Winkle Area, where the Beanstar piece is.
There they find Popple, who has already seized the Beanstar piece. Mario and Luigi battle him for it, and Popple is eventually defeated and forced to flee, leaving the Beanstar piece for the brothers.
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