"Joe Sixpack" knows a roll of the dice produces a random result, but he also know it's more likely to produce a seven than a two, and that it's not going to produce a one. In the context of this conversation, I think we all understand that those same kinds of conditions apply when talking about genetic mutations and recombinations. It produces an unpredictable result, but the conditions and mechanisms involve dictate that not all results are possible, and some are much more probable than others.
We understand that in an absolute context it is a misnomer, yet we commonly and frequently do the same thing ourselves with that and other terms in different contexts. We understand those limitations and implicitly apply them to try and discern the correct meaning. In the context of evolution, I think there is some degree of "randmoness". If I say that genetically, I am a "random" child of my parents, I believe you would understand what I mean.
If you argued that if it was "random" I could have just as easily been a dalmation, so the idea of genetics is just wrong, I'd think you were being intentionally disingenuous.
betty boop wrote an excellent essay on the differences between combinatorix and Bayesian probability.
When scientists use the term "random mutations" in reference to the dogma of Darwin, they do not mean combinatorix - that the DNA content of the offspring of a human man and woman is as likely to be a cat as a human child.
They mean Bayesian probability, i.e. percentage of likelihood that the offspring will inherit certain traits of the parents - and then also the percentage of likelihood that the child will obtain a novel allele, etc. and survive to pass that along to future offspring.
In math, the term "random" literally means what Joe Six-Pack understands it to mean, i.e. combinatorix.
There is no auto-correlation in a random string. The string 123123123 is not random.
The digit at any position in a random string must be equally probable. In base ten the digit must be equally probable to be 0,1,2,3,4,5,6,7,8 or 9.
The extension of pi may appear random but it is not. It is only pseudo-random. The digit in any position of the extension of pi is caused by the calculation of a particular circle's circumference divided by its diameter. It will be the same digit in the same position no matter how many times it is calculated or on what circles.
And even if the digit at a position in the string is mostly unpredictable, it is still pseudo-random when it is caused, e.g. Chaitin's Omega random number generator. Indeed, most every random number generator uses a "seed" number thereby making the result only pseudo-random.
In the dogma of Darwin, Bayesian probability (not "randomness") makes sense once life exists in a biosphere because of the cause/effect relationship of inherited traits and variations.
However, in abiogenesis (life from non-life) combinatorix ("randomness") is always at issue. As Shroeder put it (quoting from betty boop's article):
But as Schröeder further describes the problem: