Fred Hoyle, British mathematician and astronomer, said the probability of the formation of just one of the many proteins on which life depends is comparable to that of the solar system packed full of blind people randomly shuffling Rubik’s cubes all arriving at the solution at the same time.
Hoyle knew astronomy, astrophysics and mathematics well. Some people even like his SF. But here he was talking total bollocks. His entire output regarding evolution is complete and utter bollocks.
Yes, if you're talking about nothing but random chance, then the odds are astronomical. If you're talking about evolution, they're not. And if you don't understand why they're not then you don't understand evolution. Hoyle did not understand evolution.
Come to that, he didn't understand biochemistry, either. For example, haemoglobin isn't a unique molecule where you have to hit on that precise molecule or it's game over. Haemoglobin is different in each different species. Small differences, but it's not "everyone has to solve their Rubik's cube." Haemoglobin isn't even the best solution: in your last 7 months as an embryo you had foetal haemoglobin which is better at binding to oxygen than the adult type. Then there are the arthropods, which use copper-based haemocyanin instead of haemoglobin.
Hoyle calculated the odds of a perfect bridge hand. One where the hands are clubs, diamonds, hearts, spades in that order. Where the first cards dealt are the aces, then the twos, then the threes, etc. The odds against that happening are enormous. Fred knew how to calculate probabilities. What he didn't mention is that every possible deal has those same odds. And what he didn't understand is that the calculation he ought to have performed were the odds of you and your partner being dealt a winning hand (50/50).
No doubt somebody is already doing the maths. And coming up with the fact that the odds of hitting haemoglobin by nothing but random chance are mega-hyper-ultra-super-astronomical. And that even allowing for a million variants of haemoglobin/haemocyanin that still leaves the odds as hyper-ultra-super-astronomical. And that will be because they understand as little of evolution as Hoyle did.
Single-celled animals don't have haemoglobin or haemocyanin because diffusion carries sufficient oxygen. Small multi-cellular animals don't have haemoglobin or haemocyanin either because the square-cube law means they're more "surfacey" and diffusion suffices. Water can carry around 1/20th the oxygen of blood (at human body temperature) so animals that are small enough don't need anything better than water. There's even a species of antarctic fish without haemoglobin because water dissolves more oxygen at low temperature and they are so sedentary they can get by without it.
Up to a certain size, water is sufficient. Slightly larger than that and you need something better than water, but it doesn't need to be 20 times better (as haemoglobin is). It only needs to be fractionally better. Over time, your descendants may be slightly larger than you and need something slightly better to carry oxygen than you had. Enough time, and enough size increases and you need, and end up with, via a series of small improvements accumulating over time haemoglobin or haemocyanin. Never, at any stage, was there a jump from getting by with water to your children needing haemoglobin.
Hoyle made a straw man. Kicked the arse out of it. Set fire to it. Stamped the ashes into the ground. Then pissed on the ground. The creationists praise him for demolishing evolution, but he didn't. He destroyed a straw man. He probably sincerely thought what he was attacking was evolution, but it wasn't. Hoyle's comments regarding evolution are unmitigated bollocks.