Yet if you give a player a set of dice to give them perceived control over the random number generator, they are much more happy.
Dungeons and Dragons and other dice-based RPGs are a great example. If they roll a 20, they are overjoyed with the results and feel incredibly lucky. If they roll a 1 they are sad or mad, but chalk it up to bad luck.
But if it's a random number generator that they have no control over, they feel it's "random" and there is no luck. And they blame the random number generator for bad results. Even if it's just the same as using dice, without the physical interaction.
I've always thought that even if you just let the player click a button to activate the random number generator, you give them a sense of control. Perhaps you let them hold the button down for a while just like how players rattle the dice for longer hoping for "luck" in the results.