But the vast majority of those 52! hands are nothing special, and there are only a few "extraordinary" hands. For example getting all the cards in strict order of suit and number would be an extraordinary hand, and would be astonishing retrospectively without being a fallacy.
This is similar to life. The vast majority of nucleotide combinations are no-results. A very few lead to functional proteins. So we could say there is an extraordinary hand in life.
But astonishment at this is another thing. It would be astonishing to think chemistry could have dealt such an extraordinary hand if chemistry was random. But it isn't, so there is no necessary reason to be astonished by it.
So I think the fallacy being committed is more like "fallacy of astronishment where no astonishment is necessarily due".
Right. Especially when organic compounds form so readily, thus before very long, the oceans are full of sub-assemblies that don't need to be "invented" all over again from ground zero.
Additionally, all these "the odds are against DNA" computations totally ignore the powerful effect of what me might call parallel processing. Each cubic meter of ocean has millions (billions?) of "experiments" going on all the time. So in a few hundred million years, an amazingly large number of combinations is possible.
I wonder about that. I've read of an observed mutation that enables metabolism of nylon. It is a frame shift mutation which means that the resulting protein is essentially random. Also, I am continually amazed by the amount of difference between the codes for functionally similar proteins between species. It seems to me that the genome is vastly more plastic wrt functionality than is usually portrayed.
According to your perception, because you value that particular combination. But it's not statistically any less likely than any other combination.