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1.
Specifically in the context of Super Smash Brothers and Super Smash Brothers: Melee, a deliberate attempt to ensure the death of an opponent, and gain points for the kill by several methods:

1. Waiting on the ground, by the edge that an opponent will try to grab after executing a saving jump and executing an attack whose range extends between the opponent and the ledge, resulting in kinetic damage propelling the opponent back over the edge, and certain death. Not only does the opponent have no opportunity for a counter attack, but even if the opponent could have successfully completed the saving jump, he/she is given no chance to recover. This is especially effective attack with Pikachu, Captain Falcon, Donkey Kong, Samus, and Link.

2. Waiting for an opponent to land on the area near a ledge, and grappling them before he/she has an opportunity to recover, allowing the player to throw his opponent out over the edge again (a likely death). Repeated grabs do not allow the player an opportunity to perform a block, or a counterattack. This is an especially effective attack with the N64 versions of Ness and Donkey Kong and on the Mushroom Kingdom level.

3. Using a character with a good hover or jumping ability to wait in the air for an opponent to attempt to land after a executing a saving jump and subsequently drilling or smashing smashing them straight downward, usually to certain death at the bottom of the level before he/she has the opportunity to land or recover. This is an especially effective attack with Kirby, Ness, Donkey Kong, and Samus.

4. Throwing an item, item crate, or item capsule over toward an opponent making a saving jump to return to game play. Usually this kinetic damage, applied so close to the edge of the map, is enough to instantly knock an opponent to certian death with no opportunity to land or recover. This is especially effective with a red or green shell, a bumper, a Beam Sword, a Home Run Bat, a Star Wand, a Bob-omb, a Poke Ball, or and explosive box or capsule, but can also be performed with a Proximity Mine.

5. Grabbing onto a ledge, either because one is also trying to make a saving jump/ledge grab, or because one jumps off and grabs the ledge intentionally, preventing an opponent from grabbing that ledge after his/her saving jump, when the opponent would have normally been able to save himself/herself by grabbing the unoccupied ledge. The former is more acceptable behavior, although both are discouraged. Waiting an extended period of time after grabbing onto a ledge, knowing an opponent will need the opportunity to grab is blatant edge camping.

All of these tactics are allowed by the game, and actively employed by high level computer players (CP), but strongly contradict the unwritten codes of conduct and sportsmanship that have been adopted by veteran players. New players or n00bs that edge camp are tolerated, but attempts to educate them in the rules of the duel are quickly made. Veteran players that actively edge camp, usually intentional, are usually called out by the other players and targeted in the current and subsequent games for this obnoxious behavior.

Edge camping is an exploit of the game's engine to unfairly defeat an opponent, and cannot be eliminated, although the dodge move in SSBM was added to combat the edge camping tactic.

Opponents who actively edge camp ruin the challenge between two players of approximately equal skill, and should be considered assholes. These players should be temporarily or permanently banned from playing, depending on their willingness to abide by the codes of conduct and sportsmanship, to preserve the game's enjoyment for other players.

As an alternative to edge camping, players that practice good sportsmanship back up, giving an opponent who has just completed a saving jump/edge grab time to recover before continuing to battle. When an opponent is clearly knocked to his/her death by an attack on a part of the map away from the edge, this is considered a fair kill.

The practice of juggling an opponent in the air with aerial attacks or up+A smashes is similar to the practice of edge camping, but is slightly more acceptable.
1. Damnit, Zach, you clearly used Pikachu's Side+A smash attack to kill me before I had the opportunity to grab the edgeback on, you douchebag. I'm suck and tired of you edge camping! I've had it with this bullshit! Learn to play fair, or don't play, assmunch!

2. Jason, you throw whore! That's edge camping, douche! I had no chance to recover after landing before you used Ness' overpowered throw on me. Thanks, jackass. Next time, why don't you give me some fucking recovery time? Or are you just too pussy to fight me.

3. I swear, if you use Kirby to drill me down into the lava one more time, I will go fucking ape shit on your ass!

4. *Loud Groan* Damn you and your throwing accuracy... Why didn't you just let Alex have the Beam Sword instead of throwing it at me?

5. You lousy son of a bitch. I saw you jump off and grab that ledge so that I would fall. You do it again, and you're fucking dead, you asshole! That is the epitome of edge camping, you fat fuck! Get that cheating motherfucker, guys!
by thewalex April 18, 2007
 
2.
while playing Supersmash Bros, to stay at the very edge of the solid ground and not allow someone who has been thrown off to return back and continue play, especially by shooting some sort of projectile weapon at them
also: edgecamper
I was about to win before Taylor started edgecamping all up in Kirby's grill.
by Kirbasaur February 03, 2007