One major fallacy in the alpha-globin argument mentioned above, common to many others of this genre, is that it ignores the fact that a large class of alpha-globin molecules can perform the essential oxygen transfer function, so that the computation of the probability of a single instance is misleadingly remote. Indeed, most of the 141 amino acids in alpha-globin can be changed without altering the key oxygen transfer function, as can be seen by noting the great variety in alpha-globin molecules across the animal kingdom (see DNA). When one revises the calculation above, based on only 25 locations essential for the oxygen transport function (which is a generous over-estimate), one obtains 1033 fundamentally different chains, a enormous figure but incomparably smaller than 10183.
A calculation such as this can be refined further, taking into account other features of alpha-globin and its related biochemistry. Some of these calculations produce probability values even more extreme than the above. But do any of these calculations really matter? The main problem is that all such calculations, whether done accurately or not, suffer from the fatal fallacy of presuming that a structure such as human alpha-globin arose by a single all-at-once random trial event. But generating a molecule "at random" in a single shot is decidedly not the scientific hypothesis in question -- this is a creationist theory, not a scientific theory. Instead, available evidence from hundreds of published studies on the topic has demonstrated that alpha-globin arose as the end product of a long sequence of intermediate steps, each of which was biologically useful in an earlier context. See, for example, the survey article [Hardison2001], which cites 144 papers on the topic of hemoglobin evolution (note: this reference is now 17 years out of date -- many more have been published since then).
In short, the creationist-intelligent design argument claiming that scientists assert an all-at-once "at random" creation of various biomolecules, and then asserting that this is probabilistically impossible, is a classic "straw man" fallacy. Scientists do not believe this, so this line of argumentation is completely invalid. In other words, it does not matter how good or how bad the mathematics used in the analysis is, if the underlying model is a fundamentally invalid description of the phenomenon in question. Any simplistic probability calculation of evolution that does not take into account the step-by-step process by which the structure came to be is almost certainly fallacious and can easily mislead [Musgrave1998; Rosenhouse2018].
This is simply more obfuscation. You don't have a cosmos until you consider all the factors needed to make a cosmos. This line of reasoning does not prove anything other than that in a controlled environment, with in an induced model, certain aspects life of forms can propagate. This does not even come close to engaging with the real issues of spontaneous generation on a cosmic scale through random processes.
