The problem with "evolution is random" isn't the definition of "random." It's the definition of "evolution." I'll work my way back to that point.
I accept that "random" does correctly describe loaded dice and other processes with skewed non-uniform distributions of outcome.
So, if you're playing craps with loaded dice, the outcome of one throw, or one pass, is still accurately described by "random."
But with loaded dice the outcome of the game is no longer random. That is to say, the answer to the all-important question of who goes home with more money than they came with, and who with less, becomes entirely predictable once we know who's using the loaded dice, and it is therefore not random.
The movements and collisions of gas molecules are unpredictable and random. Pressure is the movement and collision of gas molecules. So pressure is random. True or false?
Obviously, false, as we can tell by the ability to precisely predict the pressure of a given system, and even how it changes as we change such variables as its temperature or volume. But the reason it's false is not that the movement of gas molecules isn't really truly random. It's because pressure isn't the movement and collision of gas molecules. It's the result of the movement and collision of gas molecules. That's an important distinction. Getting it wrong leads to the false conclusion that gas pressure is unpredictable.
A similar distinction that's equally important, though it's often missed: evolution is not random variation and natural selection. Evolution is the long-term result of random variation and natural selection. The game, not the dice. The pressure, not the trajectories of the gas molecules.
This distinction is rarely clearly made, to the detriment of understanding. We casually call a lion pouncing on a slow gazelle "evolution in action." It's not. It's a lion and a gazelle in action. It's, to some degree, selection in action. It's the event that acts on evolution (in a small way), not the other way around. "Evolution in action" cannot be observed on that scale.
Random processes can have random long-term outcomes (like a fair craps game), or completely predictable outcomes (like gas pressure). Thus, the randomness of random variation, and the randomness (however skewed) in the effect of natural selection on individuals, tells us nothing about whether evolution is random.
So, it's reasonable to ask, what is the evidence that evolution, the long-term result of random variation and natural selection, is random? For instance, repeatable laboratory studies can be performed observing the evolutionary changes to populations (e.g. of bacteria) over many generations under controlled selective pressures. Are the results of such studies consistent from one repetition to another, or are they random?
We do generally regard the history of life's evolution on earth as "unpredictable" in the sense that we generally hypothesize that it could have gone very differently if, say, a certain geophysical or astronomical event hadn't occurred. But that doesn't necessarily make it an intrinsically random process, it makes it a process (random or otherwise) perturbed by external random inputs. Is there any scientific evidence that evolution is random?
Respectfully,
Myriad