Another trick in RPGs is to increase or decrease the odds of a successful hit according to recent hits and misses, bringing the short-term average much closer to the expected value. It's still "true random", but uses correlation between attacks to create an underdispersed distribution overall. (Basically, you want to make the variance lower to make people happy.)
Example: My hobby is that I'm a tournament judge for Magic: the Gathering. I also play a bit, because I like the game. And there's an online version... which has a shuffling system that's actually random (i.e., has reportedly been examined by the same folks who certify stuff for casinos, and passed).
But that causes a lot of complaining from players, because real random shuffling is very different from what human beings accomplish when shuffling pieces of cardboard, and is actually a different standard from what's enforced in tournament play (requirement there is that after shuffle, no player is able to know locations, relative orders or patterns within the deck, not that the deck is "random").
At any given time there are thousands of players online, and every deck gets shuffled at least once per game. With those numbers... unlikely results happen. They happen a lot. And they get players really, really angry, to the point that most forums have "complain about the shuffler" permathreads, because those results tend to absolutely screw you over when they happen.
DYWYPI?