Lucky Day

Lucky Day is a badge in Paper Mario and Paper Mario: The Thousand-Year Door. It is a stronger version of the Pretty Lucky badge. In Paper Mario, it is the reward for completing a chain of sidequests that involve delivering a letter to a specific person (the chain starts with Goompapa), then being given another letter by that person to deliver to someone else, and so on until the final letter is delivered to Goompapa, who gives the badge to Mario. In Paper Mario: The Thousand-Year Door, it is the reward for reaching the ninetieth floor of the Pit of 100 Trials, found inside a treasure chest, as well as matching 3 numbers in a row at the Happy Lucky Lottery. It can also be rarely dropped after a battle by Swampires. If Mario equips the badge, all attacks from his enemies have a 25% chance of missing entirely. The chance of attacks missing is increased when multiples copies of the badge are equipped, as well as alongside other badges that reduce the chance of being hit, such as Pretty Lucky and Close Call.

Merluvlee's prediction in Paper Mario

 * "I see...a Lucky Day Badge. You are asked to deliver letters by many people and you receive the Badge when you complete your last delivery."