/*DNAunion*/ The paper I was addressing gave us this. But, the value it gave was overstated (as I already pointed out).
Sorry, I must have missed something. Did the paper limit the OoL to specific conditions or rule out others? What I am trying to get at is that Earth is a pretty big place, we're not talking about someone's backyard pool here.
*DNAunion*/ The two key things are (1) how improbable an event is, and (2) how many shots are available to hit the target. "Large numbers" of attempts don't do too much for us if the inverse of the probability is an even larger number.
Also, the number of shots are frequently based on unreasonable assumptions, such as the ignoring of side reactions, starting with "The Molecular Biologist's Dream: 'Once upon a time there was a prebiotic pool full of [beta]-D-nucleotides...'"*, and so on.
Unless you can quantitate the chances over say a 50 million year timespan you can't claim that the odds are against it. So, how does the inverse of the probability outweigh the chances? How many chances were there? Why do you feel they are unreasonable?
*DNAunion*/ But they do have fairly good ideas how long an RNA molecule would have to be in order to self-replicate. Orgel and Joyce estimated that it would have to be at least 40 monomers in length in order to be able to fold up into a complex enough shape to perform the required function. Experiments since have found that such is probably far too low: the closed thing yet to a self-replicator that has been designed was about 180 nucleotides long.
RNA as the catalyst for life is still a theory, although it has good backing it seems. The question is could a RNA 20mer plus a peptide 20mer be involved? How specific does the sequence have to be? The fact that pseudo self-replicating RNA has been observed at 180mers does not rule out anything.