From the Super Mario Wiki
The Fourth-Degree Card is a collectible item in Paper Mario where Mario may obtain it by training at the Toad Town Dojo in Toad Town. After defeating the first two members of the dojo: Chan and Lee, Mario may fight The Master. If he defeats The Master the first time, he will change his costume and fight Mario again. If Mario defeats The Master in his new form, he will receive the Fourth-Degree Card. The card has no particular use in-game and is simply a collectible item.
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