No one knows the "relevant math", much less you.
That's incorrect. The entire scientific community understands and knows the relevant math for calculating the probabilities of unaided processes accurately sequencing data and/or instructions.
That's correct. The simplistic random sequencing model is completely inappropriate. No one has a model, only a collection of isolated parts and mechanisms. Without a model, there is no math. The math is the model. So if the math shows garbage that does not represent reality, then the model is rubbish.