From the Super Mario Wiki
During the course of Mario & Luigi: Superstar Saga, one of the four pieces of the broken Beanstar lands somewhere in the woods. Mario and Luigi come 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 (as well as Popple) is.
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