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A Smash hit (stylized as ) is an event that multiplies a regular attack's damage output. It is the EarthBound series's equivalent to a critical hit, a common feature in role-playing games. This can only occur when using a character's normal attack, such as Bash. Upon landing one, the game displays on the screen as the damage is being dealt, while the screen flashes green (red when an enemy lands a smash hit from EarthBound onwards).
Smash hits are determined by the character's Fight stat (in EarthBound Beginnings) or Guts stat (in EarthBound and Mother 3). The damage that is dealt is not consistent output, rarely it can do less than 2× normal damage, but oftentimes a Smash hit can do nearly triple the average damage.
Smash hit probability
In EarthBound Beginnings
Smash hits are determined by the Fight stat of a character, in other words, the higher the Fight stat the higher the chances of landing a smash hit. They essentially deal normal damage except that the target's Defense is ignored. A well-known glitch in the Famicom version is that instead of the being its normal color, it might accidentally use an enemy's color palette (e.g. a purple against a Mr. Bat).
(Information courtesy of Starmen.net) With the Bash command or Bash-like enemy/NPC attacks, the probability of a smash hit is equal to guts/500 or 1/20, whichever is greater. If a smash hit is successful, it deals 4×(Offense-Defense) damage. This damage is still affected by defending if applicable. If the target had a physical shield, it will be depleted. When a character in the player's party deals such an attack, the screen flashes green twice and appears in the text box on the upper side of the screen. If a character from the player's party receives a Smash hit, the screen will instead flash red once. Shoot weapons are incapable of Smash hits in the SNES and Super Famicom version which means that Jeff usually can't deal one. However, in what is most likely a bug or oversight, Shoot attacks can deal Smash hits in the Mother 1+2 port.
In Mother 3
Smash hits in Mother 3 work the same way that they do in EarthBound, except that it appears above the victim's sprite if dealt to an enemy, and above the character's HP meter if dealt to the player's party. Flint's Power Smash Skill is the only non-bashing attack for the playable characters that can enemies; this skill always results in a if it hits.
In other games
In the Super Smash Bros. series
When a Starman Assist Trophy (which is in Smash 4 and Ultimate) is defeated, it is sent flying with a graphic appearing. The graphic also appears if the Smash Run version of Starman is hit by its reflected PK Beam, which will defeat it in one hit.