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You continue, "The error in the original post is the assumption that every attempt is a fresh attempt, where we throw everything out from the last run and make a random stab in the dark...". If order is derived by chance from nothing then mustn’t we assume that each try is completely unique and in no way connected with any other attempt? Isn’t this very meaning of randomness? I no statistician or mathematician but how can a process be both random yet retain and build upon previous data?

Because the theory of evolution is based on two processes: mutation (random) and natural selection (non-random).

You start with a group of organisms. Some number of them have random mutations. Most of those mutations are harmful, so those individuals die-- they don't reproduce. Only a tiny percentage of mutations are beneficial, but the individuals with those mutations survive longer and reproduce more. So the next generation has more individuals with the favorable mutation than the prior generation.

Some percentage of the next generation has mutations. Again, most of the mutations are harmful, but those individuals don't reproduce; the few with favorable mutations do reproduce, and in disproportionate numbers.

Each generation thus keeps the beneficial results, and only the beneficial results, from the previous generation's random mutations; and each set of favorable mutations builds on the prior successes.

Natural selection requres a thing that can replicate itself. The question then becomes what are the odds of that thing arising by chance? To answer this we need to know, among other things, what is the simplest thing that can replicate itself? Francis Crick, who ought to know something about this, says (in his book "LIFE ITSELF") that it would have to be something as complicated as an RNA molocule, and that, says Crick, is so complicated that he personally can't believe that it could have arisen by chance in the relatively-few years available in the history of the Earth. (Crick, by the way, is therefore left to assert that the first replicator came to Earth from outer space.)

I'm not saying (or meaning to say, at any rate) any more than this: Natural selection doesn't help your theory one bit until you have that first replicator, and at least one sure 'nuff expert on the subject says that the first replicator was VERY complicated-- a lot more so, I'll wager, than "To be or not to be."