In an RPG, a phenomenally successful hit in combat, typically landing in some vital region, hence the name. Typically critical hits do more damage than regular ones; in some systems, special side-effects are suffered depending on where you were hit, what you were hit with, etc.

Critical hits were introduced to D&D in the third edition. The 3rd Edition D&D critical hit system is as follows: when you roll a certain number naturally (usually limited to 20s, though some weapons have a better threat range), that's considered a threat. When you score a threat, you roll again; if you manage to score any successful hit against the target on this role, you've scored a critical hit. Most weapons deal double damage on a crit. However, some creatures, such as any undead, are immune to critical hits.

Feel free to explain critical hit systems from other role-playing games here.

In Diablo 2, critical hits are slightly different. Only (to my knowledge) the Barbarian and the Amazon have the ability to get critical hits without the use of items. Crits do 2x damage. When last I checked, the Barbarian's chance of a crit was his weapon mastery level times 2 over a hundred. Thus, if you have a maxed spear mastery and hit with your pike, you stand a 40% chance of doing double damage. Wow. That's a leeeeeeetle unbalanced, so I think they're turning it down in the expansion.
For the Amazon, the skill Critical Strike determines your chance of doing double damage. Especially useful with Multi-Shot and Jab.

A few uniques and, in the Expansion pack, which I've yet to buy, runes, will give your weapon (or boots, rings, crowns, pet hamsters, etc...) Deadly Strike. This is the same as a %chance to crit from weapon mastery or the skill Critical strike, however, AFAIK, it stacks differently. if you had a 21% crit from skills and a 25% crit from your weapon, they are both calculated differently and you stand a 5.25% chance of double critting, or doing quadruple damage. Multiple bonuses to Deadly Strike on weapons just improve the Deadly Strike percentage, they do not add a chance for 8x, 16x, etc... damage.

UPDATE: The Barbarian's weapon mastery level will now display the %chance of a crit, however it is lower since version 1.08.

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