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The 1975 role-playing game Empire of the Petal Throne introduced the concept of critical hits (though not the phrase). Using these rules a player who rolls a 20 on a 20 sided die does double the normal damage, and a 20 followed by a 19 or 20 counts as a killing blow: "this simulates the 'lucky hit' on a vital organ."
Critical hits are meant to simulate an occasional "lucky hit." The concept is realised as the effect of hitting an artery, or finding a weak point, such as a stab merely in the leg causing less damage than a stab in the Achilles tendon. Critical hits are almost always random, although character attributes or situational modifiers may come into play. For example, games in which the player characters have a "Luck" attribute will often base the likelihood of critical hits occurring on this statistic: a character with high Luck will deal a higher percentage of critical hits, while a character with low Luck may, in some games, be struck by more critical hits. In the tabletop RPG Dungeons & Dragons, each time a player character attacks an opponent with a weapon, the player rolls a 20-sided die; a roll of 20 (a 5% chance) results in a critical hit. In video games such as Final Fantasy or X-Men Legends the player character gets roughly the same chances for a critical hit, about 1% to 10% usually.
The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage). Critical hits also occasionally do "special damage" to represent the effects of specific wounds (for example, losing use of an arm or eye, or being reduced to a limp). Critical hits usually occur only with normal weapon attacks, but not with magic or other special abilities.
Many table-top and video games use "ablative" hit point systems. That is, wounded characters often have no game differences from unwounded characters other than a reduction in hit points. Critical hits originally provided a way to simulate wounds to a specific part of the body. These systems usually use lookup charts and other mechanics to determine which wound was inflicted. In RPGs with non-humanoid characters or monsters, unlikely or bizarre results could occur, such as a Beholder with a "lost leg". Most systems now simply award extra damage on a critical hit, trading realism for ease of play. The effect of a critical hit is to break up the monotony of a battle with high, unusual results.
Many games call critical hits by other names. For example, in Chrono Trigger, a double hit is a normal attack in which a player character strikes an enemy twice in the same turn. The EarthBound series refers to critical hits as a smash hit (known in-game as "SMAAAASH!!"). Gamers frequently use the abbreviation crit or critical for "critical hit". This usage has gained popularity due to verbing; when used as a verb, "crit" or "critical" is less cumbersome than "critically hit" or "score a critical hit". In the fighting game Super Smash Bros. Brawl, the maneuver "Marth's Final Smash" is called Critical Hit in reference to the concept's use in the Fire Emblem series, the games from which Marth originates.
In first person games such as Borderlands critical hits are only dealt if the player successfully hits an enemy's weak spot, such as an open mouth, or an unarmored spot.
Team Fortress 2 uses a Critical and "Mini-Crit" system. Criticals deal three times the normal damage (unscaled over distance) and "mini-crits" increase damage by 35%, but damage is still reduced over distances.
Critical miss 
The negative counterpart of the critical hit is variously known as the critical miss, critical fumble, or critical failure. The concept is less frequently borrowed than that of critical hits. Many tabletop role-playing games use some variation on this concept (such as a "botch" in the Storyteller System), but few computer role-playing games implement critical misses except where the game is directly based on a tabletop game in which such rules appear.
In first person shooter games such as Counterstrike: Source, Tactical Ops, and Unreal Tournament, the concept of a critical hit is often substituted by the headshot, where a player attempts to place a shot on an enemy player or NPC's head area which is generally fatal when successfully placed. Headshots require considerable dexterity and shot placement as players often have to compensate for target movement and a very specific area of the enemy's body. In some games even when stationary, the player may have to compensate for movement generated by scope drift.
See also 
- M.A.R. Barker, Empire of the Petal Throne, p34.