Not sure if any of this is relevant to RPGs but
- Firaxis XCOM's designers secretly manipulated the accuracy RNG in favor of the player, ironically to prevent players from perceiving the game as having cheated. They did this in XCOM 2 as well.
- Long War 2 made many changes reducing the overall role of RNG in XCOM 2. Removing powerful random effects from the game, making most misses do damage etc. In general, their approach was to give the player as much agency as possible over the RNG.
- NEO Scavenger has RNG but it adds a layer of uncertainty over it. You never get explicit damage ranges or hit chances. In this way, RNG is made irrelevant to the player's decision making process entirely even though mechanically it still exists.
Intuition works against people when it comes to understanding probabilities. In short, we have no trouble understanding fully certain and impossible events, but when it comes to less than around 55% likely events their likelihood is exaggerated and more likely ones are underestimated. Here is a fancy formula behavioral economists have worked out from the empirical findings.
Black line is the objective probability and blue one is subjective.
What this means in practice is that if you code a fair random number generator, people will systematically bitch about missing too many hits and enemies getting too many crits in a row when the chances work as intended. The people who actually do the math are the most oblivious about it happening and it just so happens that the developers tend to be better at math than the average consumer.