In Role-Playing Games, damage-dealing characters deal damage in a variety of ways. You have the wizard, who stands back and blasts away with fire (or other spells). You have the warrior, who gets in the enemy's face and starts hacking away. You have the damage-over-time class which uses set-and-forget spells to deal damage automatically. You have druids summoning the power of nature, monks using martial arts and Ki Attacks, and even wierder face-melting callings.
Then you have these guys. Usually a rogue or assassin, though gamblers qualify as well, the Critical Hit Class prefers the "one big hit" approach to dealing damage. Usually, this means one of two things (and sometimes both: increasing the chance of scoring a Critical Hit, or increasing the damage a Critical Hit does.
Commonly involves a crit-enhancing Infinity+1 Sword. See also For Massive Damage. Taken to its logical extreme, One-Hit Kill may be involved.
In The King of Fighters, Shingo's attacks have a higher chance of being critical than any other character on the game (with the possible exception of the bosses.
The Sniper in Team Fortress might count, since to do any real damage, you must be zoomed in and charged up. You don't NEED a "crit" to kill others, but if you're trying to use your sniper rifle without the scope, you'll do almost zero damage.
In Borderlands critical hits are dependant on where you hit your opponents rather than chance, but the Hunter class has a strong emphasis on accuracy (and thus hitting crit areas). Plus there are builds based around high crit damage.
In Border Lands 2, when Zero enters his Deception mode, all enemies are highlighted in blue, and his attacks will do more damage the closer the duration timer runs out. One of his abilities later on highlights the critical hit areas on enemies in red. Other abilities in the same skill tree increase damage for critical hits, increases accuracy and zoom on sniper rifles, and increases melee damage when backstabbing an enemy (not a critical hit area, but can be if you aim carefully.)
Massively Multiplayer Online Games
World of Warcraft: It's possible to reach absurd levels of critical hit chance through proper gearing, especially later in expansions when the gear improves but your level is not increasing to balance out the stat gains. Additionally, some classes have talents to get additional bonuses from critical hits or the ability to get a guaranteed critical hit every now and then.
The Stalker archetype in City of Heroes, which will always land critical hits with their single-target attacks when attacking while hidden, and a chance to do so even when not hidden that increases with team size. They even have an Assassin Strike power.
In Rohan Online, Dhan Avengers that focus on Agility and Human Guardians that focus on Dexterity do much of their damage through skills that increase crit damage.
League of Legends: In theory, you can build any of the champions this way. In practice however, it's not always the smartest thing to do, since abilities don't usually have the possibility to score a critical strike like autoattacks do. Gangplank's "Parrrley" does have this possibility, so he's one of the champions for whom this build is a valid option.
The Glass Cannon Blademaster from Warcraft III. His three non-ultimate abilities are a Critical Hit for double, triple and quadruple damage depending on level; a sneak attack that makes him move faster, turn invisible, and deal extra damage on his next attack; and creating illusions of himself to take damage. Inverted with the Mountain King, a Mighty Glacier whose Critical Hit has a chance of stunning the target and doing a little extra damage, but his attack speed is much lower (he has active abilities to stun and slow units, however).
Just about any unit with a passive ability (such as heroes with certain orbs or items) turns into this if their attack speed is high enough.
Role Playing Games
Chie from Persona 4 is geared towards this, especially in Golden. There, she has Black Spot and later Rainy Death, two physical attacks with very high critical rate. She also got a passive that increases chance for critical, as well as a buff that also increases critical chance. This is probably to compensate for her lower damage compared to fellow physical attacker Kanji.
Pokémon: Any Pokemon with Super Luck or Sniper abilities tends to have one of these. With moves like Slash, items like the Scope Lens, and other ways of increasing crit chances, these tend to make effective wall breakers, but lose to everything else since those high-critical-chance moves tend to be on somewhat weaker moves. The most common example is probably Absol, although its weakness in other areas makes it underpowered.
Chrono Trigger: Ayla (and in the remake, Robo) eventually get the ability to do 9999 damage on a critical hit. Combined with luck-enhancing equipment, can reach Game Breaking levels (although if Ayla's powerful enough to get the ability, you're probably overleveled anyway).
The odds for a critical in Dragon Quest IV are 1 in 64; that is, unless you're Alena, who has a 1 in 4 shot, making her perfect for Metal Slime hunting.
In the Wizardry series, the samurai, ninja, and monk classes are very reliant on critical hits and instant kills.
In Fire Emblem, the Swordmaster is the traditional critical-reliant class, but later games added Berserkers, Assassins, Snipers and Halberdiers into the mix, as they all have boosted critical hit chances (Except Assassins, but they can score an One-Hit Kill 50% the time they critical.)
The above Fire Emblem example is missing Myrmidons and Trueblades (FE10 only; they're a third-tier Myrmidon, promoting from Swordmasters).
It's one of the possible ways to build your character in Fallout3, as critical rates are determined by the player's Luck stat, weapons, and a good number of the game's perks.
This becomes very common in Gothic 2, where your weapon skill is a measure of 10-100% that also serves as your critical hit odds (in addition to determining how fluid the hero's attacks are and how likely he is to make fatal mistakes), so any character with a higher skill than strength/dexterity (depending on the weapon) will only do noticeable damage on a critical.
The Sniper class in Valkyria Chronicles can only shoot once per turn, but has very high accuracy and range, making them ideal for headshots.
In DiabloIII, this is mainly the only build viable in higher difficulty games. There are magical items with the ability to increase critical hit chance, others with the ability to increase the damage on a critical hit, and items with both (mainly the so-called Trifecta, if they also have increased attack speed). Accumulating these items, you can, for example, get a 50% chance of dealing 400% of damage. Also, the game incorpores some special effects that only activate when dealing a critical effect. With all these factors combined, this becomes a Game Breaker.
The Thief (1st and 2nd Edition) and Assassin (1E) classes were this. The thief could do up to 5 times normal damage with a backstab, and the Assassin could kill an opponent in 1 hit by performing an assassination attack. Neither class was as good as a fighter in normal combat, due to armor restrictions and a lower chance to hit.
Third edition had weapons with an increased critical hit range (chance to make a critical hit), due either to their physical nature or magical enhancements. There were spells and feats that did likewise (e.g. "Improved Critical"). A character could concentrate on gaining as large a critical hit range as possible.
In D&D 4th Edition, many players who play Avengers will choose weapons and feats to take advantage of the fact that Avengers roll twice for every attack and pick the highest roll in order to maximize the chance for a crit and maximize crit damage.
Paladog: The core game mechanic is that the units only unleash their Critical Hits while in Paladog's aura, ranging from more damage to knocking enemies back to hitting everything on the map. The easiest way to win is building nothing but archers, as a group of archers in the aura becomes less Death of a Thousand Cuts and more Wave Motion Gun.
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