From the Super Mario Wiki
The Green Missile is Luigi's side special move in the Super Smash Bros. series, starting in Super Smash Bros. Melee. When executed, Luigi flies like a rocket across the stage, smashing into any other opponents and burning them. Luigi is able to charge this move up, which allows him fly farther and deal more damage to opponents. The move has a 1/8 (Melee and Brawl) or 1/10 (3DS / Wii U and Ultimate) chance of misfiring; a misfired Green Missile deals almost as much damage as a fully-charged Green Missile and it travels the farthest out of any Green Missile state. In the Super Smash Bros. games up until Super Smash Bros. for Nintendo 3DS and Super Smash Bros. for Wii U, Luigi enters a squatting position with a neutral expression while charging up, while in Super Smash Bros. Ultimate, he holds his shoulders forward and his arms back with a determined expression in a ready position.
Super Smash Bros. Brawl introduced a mechanic where misfiring a Green Missile into a wall causes Luigi to get stuck in between the bottom of the stage and its ledge, allowing him to use an extra jump to get out and recover. The animation shows Luigi's nose getting stuck in the stage, with him comedically wiggling it out to set himself free.
In Super Smash Bros. Melee, a CPU-controlled Luigi always uses this move to recover, and never tries to use the Super Jump Punch. If the CPU Luigi's are unable to grab on to the edge of the stage, they will continue going downward and be defeated. Since Super Smash Bros. Brawl, however, a CPU-controlled Luigi will hardly ever use this move in the easier difficulty levels.
In Super Smash Bros. for Nintendo 3DS and Super Smash Bros. for Wii U, the Green Missile can be changed into one of the two custom variants, although they are locked first. One is the Floating Missile, which flies sideways in a straight line, while the other one is the Quick Missile, which flies faster and farther than normal. Both custom variants appear to deal less damage than the original variant.
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