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I guess, randomness makes AI more believable. Small, unpredictable variations, that force you to react and change your plan, instead of simply executing the best strategy over and over. But I wonder, how differently would Doom play, if it was built from ground up without the random gameplay elements? When I think of games, that deliberately avoid randomness, I'm thinking of platformers and shmups, that focus on high score, speed and memorization. Could be fun in an FPS too.