Random roll system

random roll system, n. refers to any game in which character stats and abilities are generated by die rolls. See also point system. [MC]
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Addendum: Random roll systems were the method used to generate characters in all early games. It has since become less popular as it creates character of widely varying ability, and newer games tend to use some form of point system. Older games such as AD&D and Palladium Games still use the random roll method. [MC] 
Addendum #2: The first version of Traveller took this to an extreme level. With sufficiently unlucky rolls, it was actually possible to die during character generation. [RayDK]