Sure. Remember, this is a thought experiment, not a comprehensive theoretical treatise…
Since 3 of the 64 codons are stop codons, a round number for the frequency of a stop codon in a random sequence will be once every 21 codons or so. (3 divided by 64, throw away the remainder since I don’t want to clutter things up…)
For Axe’s per-residue “probability”, he assumes a uniform average probability, and raises it it to the power reflecting the length of the protein. Thus, for his number of 10^-77, this comes out to somewhere in the 0.33 or so range per residue. (Again, this is rough, off the top of my head. Precision here doesn’t change the final point.)
Thus, for a 20-mer (that is the expected size of a newly-occurring random polypeptide), the “probability” or function is 0.33 raised to the 20th power. Again, using round numbers, about 1 in 10^10.
I figure on about 10^30 cells in the biosphere. I forget where I got this from, but includes all bacteria, and the volumes of oceans, etc., etc. I figure that at least 1 in 10^20 of these will see a mutation that will create a new transcriptions start site. I am too lazy to provide a citation for this, but I am pretty sure that, given the known rates of mutation and the relatively uncomplicated nature of promoters, such a mutation will probably occur at least once with every round of replication, even in a bacterial genome. Certainly, using a value which is, in essence, 1 in 10^-10 for such mutations is pretty conservative here. (As has been seen elsewhere in this discussion, a new gene arises basically via “creation” of a promoter.)
Thus, if a function arises once in every 10^10 new proteins, and we have 10^20 new proteins with each passing generation, the probability of getting a new function is essentially 1. (I won’t show my work here - hopefully, readers can at least grasp this.)
Again - THIS IS JUST A THOUGHT EXPERIMENT!!!. I want to provoke some general discussion about the approach that ID proponents take when they talk about function, accessibility, sequence space, and the like. Do not take these rough estimates any more seriously than needed to see where I am trying to lead things (or be led, as the case may be). Please.