[matsemann]

Same with Tetris: Don't randomly select the next tetramino (piece). Then you can get the same multiple times in a row, or long streaks without ever seeing a certain tetramino. Instead, make a "bag" holding one of each tetramino, shuffle it, and use that as the next 7 pieces. Still random, but it's bounded, and as you say not "too random".

[livrem]

Just don't lie to players. In Tetris it is well-known that a bag is used and that is part of the game rules that everyone but the most casual players will know about. Other games, unfortunately, secretly filter randomness behind the scenes to make Gambler's fallacy real, pretending that random events are independent when they're not.