OP is wrong about Doom's determinism I guess, it is already deterministic, random values are predefined. He just set them to constant, so his random is literaly "int random() {return 4;}", still deterministic but not 'random'
Regular Doom may not be random in the mathematical sense, but it is as far as a player is concerned. In combat, pulls from the "random number" pool are happening fast enough that I don't believe it could be exploited in any meaningful way.
What I meant was, I hadn't thought that infighting target choice and player pain-noise referred to the "random" pool at all. I thought they were 100% predictable in the original game. I wonder where the randomness actually comes in.