Power Bounce

Power Bounce is a badge in Paper Mario and Paper Mario: The Thousand-Year Door. In Paper Mario, it is at the Koopa Bros. Fortress' entrance, inside a jail cell accessed by using Bombette. It is also accessible through an opening in the back of the jail. In Paper Mario: The Thousand-Year Door, it is found at the entrance to Hooktail Castle. If Mario equips this badge, he is able to use the Power Bounce jump move at the cost of three FP. By timing the action commands correctly, Mario is able to continuously jump on a single enemy until the action command is failed. The first jump does the normal damage of a jump, and every subsequent jump does one less damage until every attack only deals one damage. After every bounce, the action becomes a little faster and the timing needs to be more precise as a result. The All or Nothing, Power Plus and P-Up, D-Down badges increase the first jump's damage and subsequently all further damage. Failing the action command with that badge equipped results in no damage being dealt in that jump, in addition to the attack stopping. Some bosses and stronger enemies have a bounce cap in which the game automatically stops Mario's Power Bounce. Auto-Caps have a slightly different animation than missing an action command in the first Paper Mario game, and do not count as a missed action command when using the All or Nothing badge.

Merluvlee's prediction in Paper Mario

 * "I see...a Power Bounce Badge. It lies inside a cage in the Koopa Bros. Fortress. You sneak through an opening in the back to reach it."