Ditto match
A ditto match or a mirror match is a match where both players choose the same character. They are different from other matches in that neither player has a match-up or stage advantage over the other player. The name comes from the definition of 'ditto', which means 'the same'. Ditto matches occur at times during tournaments.
Strategies
Strategies for a ditto match often vary greatly from the character's normal strategy. An example would be a "Melee" Marth ditto match; as both players have access to Marth's long, far-reaching sword, neither player receives an advantage, as well as making approaching considerably more difficult. Another example would be in a Super Smash Bros. Captain Falcon ditto match; due to Captain Falcon's incredible combo ability along with his own vulnerability to combos, the match ends up taking advantage of player flaws more frequently than usual.
A general strategy is to be unpredictable at all times and use experience with a character (knowing combos or recovery strategies) against the other player. Snake is a good example of this; in a mirror match of the two, the players have to use projectiles in such ways to make the stage difficult to navigate for the other player.
Matchups
Ditto matches would appear to always be perfectly even matchups, allowing a 50/50 chance of winning between two evenly-skilled players. However, due to port priority, this is not always precisely the case. The most obvious imbalance regards simultaneous KOs and is overridden in tournaments by the "Suicide Rule". The remaining differences generally have little effect on practical tournament gameplay, though for some characters like Snake the imbalance can be noticeable.
