From the Super Mario Wiki
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Stache (Horn for Bowser) is an unique statistic in the Mario & Luigi RPG series, similar to Luck in other RPGs. It usually gives Mario and Luigi or Bowser better chances at getting a "Lucky" or "Critical" hit in battle, doubling the damage of their attacks. In Mario & Luigi: Superstar Saga and Mario & Luigi: Partners in Time it gives discounts to items bought at shops, and lets the Mario Bros. sell items at higher prices. Baby Mario and Baby Luigi also have this stat in Mario & Luigi: Partners in Time, despite not having mustaches. In Mario & Luigi: Bowser's Inside Story and Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey, it affects the type of scratch card the player gets after purchasing items. Since none of these features are present in Mario & Luigi: Dream Team the stat is only used for critical or lucky hits and nothing else, while Mario & Luigi: Paper Jam it also increases the chances of enemies dropping items after battle. This stat can be increased through level ups (in Superstar Saga / + Bowser's Minions, Bowser's Inside Story / + Bowser Jr.'s Journey, Partners in Time, Dream Team and Paper Jam), Teehee Blends and Teeheespressos (only in Superstar Saga / + Bowser's Minions), and Stache/Flex Beans (introduced in Dream Team).
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