Quick Answer: Good game design balances Input Randomness (randomness before you make a decision, like rolling dice at the start of your turn) against Output Randomness (randomness after you make a decision, like rolling dice to see if an attack hits).
In games like Catan or Dungeons & Dragons, variance creates the narrative. A critical miss on a 20-sided die generates a more memorable story than guaranteed success. However, Euro-style games prefer input randomness, presenting the player with random conditions and asking them to find the optimal strategic puzzle solution.