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Pen and paper (PnP) refers to the regular (non-computer) Dungeons and Dragons game. The term refers to the ancient tools that were available to early roleplaying mankind. The "pencil" was a long piece of wood that contained a staining material called graphite. Early roleplaying man would scrape the "pencil" across the surface of "paper". "Paper" was the term used to describe an early form of Random Access Memory, consisting of pressed tree pulp that was smooth and designed to easily absorb the scrapings of pencil graphite.
These pen and paper implements were partially replaced by computer-driven input consoles running applications like Neverwinter Nights 2. However, no computer-driven RPG or MMORPG ever achieved (as of yet) the amount of flexibility of a PnP RPG. Either use of hypothetical Turing-compliant artificial intelligence or powerful human-driven GMing tools are considered pre-requisites for overcoming the challenge of flexibilty.
In PnP, players would roll polyhedral dice to generate random outcomes. While computers do use pseudo-random number generation algorithms, they have suffered criticism that, by their very nature, computers are incapable of returning a truly random number.