I suspect this might get deeper in philosophy than I'm used to, but I'll go ahead and lay out my ideas: I think "random" is pretty much just an admission of ignorance. When I roll a die, the result isn't "random" because there's some metaphysical principle coming up with utterly unpredictable numbers. It's "random" because I didn't bother to collect detailed data on the die and my throwing technique necessary to predict the outcome beforehand. It's "random" because of a lack of data.
If I were to hand the die to Lt. Commander Data, he could probably weigh the die, feel the variation in density, and perform enough fine motor control to roll whatever he wanted. In fact, he did so in one episode at a craps table. The result is no longer random because he has all the information he needs to predict the roll under different circumstances and use his fine motor control to pick out the result he wants by matching the circumstances.
That's pretty well why I've been getting vocal about calling Creationism for what it is: Randomness. Whenever we find something that wouldn't make sense for an intelligent designer to do, they start making claims that we can't possibly know anything about the stone idol behind it all, and thus can't make predictions about its behavior.
Sounds just like the randomness I described.