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On the other hand, sometimes it turns out the players are right when they suspect something is biased against them.

In Everquest when you cast a spell, there was a chance the spell would fizzle.

Occasionally, someone would get a streak of fizzles. Many argued this was just the normal streakiness you expect when you are do repeated independent trials. Some insisted that fizzles streaks were more common than you'd expect based on that model.

Finally, a statistician who also played EQ spend some time gathering data, and determined that fizzling was not independent. Your fizzle chance was an increasing function of the length of your current fizzle streak, up to a cap.

Things like that give a game character.

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