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In game theory, the combinatorial factor refers to the fact that in a simulated world, every object must potentially interact with every other object. The more objects there are, the more potential interactions there are.
If you create a book of matches in a game, you need to account for burnable objects and fireproof objects.
Now, If you create water in the game, the player might expect wet objects to behave slightly differently than dry ones -- and even flammable objects become temporarily fireproof when they are immersed in water, or perhaps they burn more slowly, and create more smoke.
One reason why the classic text-adventure games are often set in deserted areas, or areas in which the only inhabitants are hostile, is because creating meaningful interactions between simulated characters is a difficult programming task (and, based on the kind of games that are popular today, not a financially rewarding task).
The interactive fiction games and essays of Emily Short are a storyteller's serious attempt to apply at least a subset of the grandiose but so far artistically unproductive simulationist schemes advocated by Chris Crawford and Jorn Barger.
Hypertext fiction authors also run into the combinatorial factor problem. If you write a story that could continue in two different ways, and then each of those branches also has two branches, and so on, then very soon it takes a phenomenal amount of work to advance the story. (This is why plots and storytelling have lagged so far behind graphics in recent computer games.)
More about combinatorics (heavy math stuff): http://www.combinatorics.org
Dennis G. Jerz
Mar 2000 -- first posted
24 Apr 2001
-- last modified