Critics of evolution often claim that it is a purely random process, and that specific, complex structures do not have a chance of being produced by it. Hell would have to freeze over first.
This is what is known as a "straw-man" argument. You present a fake version of an idea in order to falsify it. Using straw-man arguments, if known to be such in order to mislead and deceive, is deeply dishonest.
According to evolutionary theory, the process that drives evolution is not entirely random. Rather, undirected mutations are selected according to their ability to get themselves replicated, quite naturally. This is the core insight of Darwin and Wallace that prompted Huxley, Darwin's friend, to declare that he was very stupid not to have have thought of that himself.
What is needed to get evolution off the ground and evolving is a system in which "replicators", be they individual molecules, or a bunch of interacting molecules, replicate with variations that are heritable. Do you know what the simplest and most probable replication system to arise naturally could be? Neither do I. Neither does anyone else, but there are some strong indicators as to what they may have looked like. Google "origin of life research".
But once you do have such a replicator or "evolver" there are some who claim that it still cannot evolve. One once-prominent cdesign proponentsist* is William Dembski. He would straw-man evolution as a blind trial-and-error "search" of an unlimited configuration space of possibilities, and he wrote a book that was popular at the time and made himself a number of shekels, named after the theorems of two respectable mathematicians, D.H. Wolpert and W.G. Macready, called the "No Free Lunch" or "NFL" theorems. The theorems basically say that in an environment that cannot allow a hill-climbing algorithm to work (because there are no consistent inclines) an evolutionary algorithm cannot work any more effectively than blind shooting in the dark. Of course it couldn't. Let me explain-
Once you have a simple replicator that produces variations, it makes variations that are more or less efficient at replicating themselves. In an environment that is not totally chaotic, some variations, the efficient replications, will become more numerous, increasing the probability that further, more elaborated variations will arise. The inefficient replicators will decline or disappear. But the environment is a key part of this. It must allow for new variations to find better solutions if there is to be any further evolution. These allowances are called gradients, or inclines, or hills. These features are abundant in the natural world, from physical gradients, to gradations in temperature, light levels, water abundance, you name it.
Here is a demonstration program I wrote to prove that many naïve and simplistic creationist approaches to probability are - naïve and simplistic - and wrong. https://barryhisblog.blogspot.com/p/probability-emo.html
And here is a book by a professor of mathematics at a major university who says the same things. https://www.amazon.com/Failures-Mathematical-Anti-Evolutionism-Jason-Rosenhouse/dp/1108842305
* cdesign proponentsist https://ncse.ngo/cdesign-proponentsists
Recommended further reading: Climbing Mount Improbable https://www.amazon.com/Climbing-Mount-Improbable-Richard-Dawkins/dp/0393354083/
and https://en.wikipedia.org/wiki/Hill_climbing
https://barryhisblog.blogspot.com/p/is-evolution-random.html
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