>If they knew what the next number to be pulled from the random number generator was, they could, for example, delay firing a weapon by a frame or two, to get more damage. Probably other more interesting things I can't think of immediately. If there was ever a bot vs bot Doom competition, this is something you'd definitely want to consider.

If you're interested in that kind of stuff, check out tasvideos.org, a community dedicated to beating old videogames as fast as possible using that type of knowledge. Since all videogame 'randomness' is really deterministic pseudo-randomness, the kind of RNG-knowing you described is ubiquitous

In fact, by coincidence, it looks like someone just recently published a DOOM (second episode) run: http://tasvideos.org/2825M.html