Free-form role-playing

free-form role-playing, n., adj. a style of role-playing that eschews the use of a published or pre-arranged set of rules, in favor of conflict resolution through group consensus and/or the absolute judgment of a referee or referees; also diceless role-playing. See also LARP. [GJ1]
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Addendum: Often the most popular style of play on PBW or PBEM games, as lack of access to either rulebooks or dice often can cause an issue for playing.