Evolution is random! Stop saying it isn't!

There is absolutely nothing in any theory of statistics that says that all possible outcomes must have the same probability of occurrence! In fact, the point of much of statistical theories is to determine the various probabilities of the various outcomes by means of analysis or experimentation. By letting yourself get hung up on this "equal probabilities" nonsense, you have gotten sidetracked away form the trust of your OP.Evolution is a process that has two key components, one random (mutation in its various forms) and one deterministic (natural selection). Not all mutations are equally probable, but the mutation process is still random (in Darwinian evolution) - it does not occur with a pre-planned outcome or teleological 'intent'.A card game is also a process with both a random component and a deterministic component: The shuffling and dealing of the cards is random, the rules of the game are deterministic. Who gets which cards is totally random, but once the players each get a set of cards, which player "survives" - acquires the most "resources", is completely determined by the rules. Even allowing for bluffing in poker, the winning player, which is only loosely coupled to the random set of cards dealt, is still determined by a set of rules, although these are now subtle, psychological rules that may not be well understood. Note that the fact that various hands and card draws are not equally probable is not relevant to the discussion or to any functional definition of random, chance, or statistical process.In fact, most processes that we encounter every day are combinations of random (or unpredictable sub-processes) and deterministic sub-processes: the weather, who we marry, what job we get, etc. People who have only a pedestrian acquaintance with quantum mechanics often get confused in thinking that QM says that everything is random and equally likely and that nothing is predictable. This is totally untrue. QM usually predicts that the outcome of a situation can only occur within a narrow range of possibilities, and it precisely predicts the probabilities for those outcomes in that range.

Your 'criterion' is that anything that is natural is random. Actually, this isn't a criterion, you are using this as a definition of "random". When an apple falls from a tree it falls directly towards the center of the earth until it hits the ground. This is a natural process but is not random. The orbits of the planets and their moons can be predicted thousands of years into the future with an extreme precision that is only limited by our patience to make observations and calculations. This natural process is not random. Your definition of random is your own and is not used in any field of mathematics or science. You can define your way into fantasy, but not into reality. I, of course, did not say these things are irrelevant, I said they are irrelevant to a formal definition of "random". I am merely saying that in random processes, the various possible outcomes can have the same or different probabilities. Note that there are only two ways to determine or estimate the probabilities for the various outcomes: 1) to have a quantitative model of the process from which you can analyze the probabilities - and you are conjecturing or theorizing that this model is a good representation of reality; or 2) to observe the process a large number of times and catalog the distribution of outcomes of the trials.Also note that a great many processes that we think of and treat as random are really deterministic. When you flip a coin, if you can measure the exact position of the coin on your finger, the exact dynamics of your thumb striking the coin, the exact interactions of all the air currents that interact with the coin, the exact mechanical properties of the floor where the coin lands and the geometry of that landing, etc., you can in principal determine exactly how that coin will land. Most point mutations in genes are caused by the thermal motions of the various molecules in the vicinity of the gene when it is being transcribed. If you knew all these motions exactly, you could again exactly predict the outcome of these mutations. (For the sake of this argument, I am ignoring quantum fluctuations which are, apparently, fundamentally stochastic in nature. But even including such quantum fluctuations, their influence on such macro objects as coins and cards would be small enough that the outcomes of coin flipping and card shuffling could in principal be predicted with almost total certainty.)The most precise way to describe these processes is that their behavior is such that they are well modeled as random processes. Whether such a description is appropriate is determined by observation - whether that behavior does in deed emulate the behavior of the stochastic model conjectured. In particular, even when considered as fundamentally deterministic processes, they do not act to produce some pre-planned outcome.