What is the road from a bunch of chemicals to the "simplest" molecules that can replicate themselves halfway reliably?
Let's - VERY optimistically - assume that a specific chain of 100 chemical reactions are enough to create this "simplest" molecule.
Now - Darwinian selection has no part in creating this molecule; for Darwinian selection, you need self-replication, which you do not yet have.
Which leaves probability in charge. For a very rough approximation, calculate factorial 100. It gives a number so close to 0 as the chance of this "simplest" molecule emerging, that the chances are life on Earth is alone in the observable universe (and a huge chunk of the unobservable one).
Conclusion - abiogenesis is rare. VERY rare. Even if my factorial 100 approximation is exceedingly rough and even if there are hundreds of billions of Earth-like worlds in our galaxy, the chances are only ours ever gave birth to life.
Two objections to this argument. First, chemical reactions are highly sensitive to conditions. If the right conditions exist, they can easily drive a particular product from 1% to 99%. We aren't entirely sure what the right conditions are for ambiogenesis, of course.
Indeed - the conditions needed for the first of 100 chemical reactions must exist; followed by the conditions needed for the second of 100 chemical reactions; etc; etc. Throughout the process, conditions that destroy the fledgling molecule-to-become-self-replicating must not come to pass.
The chances of 100 such conditions existing in the right succession are - very roughly - approximated as factorial 100.
One more thing - abiogenesis is not a case of 'all roads lead to Rome'; we have tried to create life in the laboratory mimicking primordial Earth conditions or not, etc, etc - and failed.
We can be quite sure that there are only a limited number of '100 chemical reactions'* chains that lead to life. Only one such chain is confirmed to exist - the one that lead to life on Earth, to us.
*Realistically, a LOT more than 100 chemical reactions are necessary in order to create a self-replicating molecule. Such a molecule is so complex, we have trouble even theoretically designing it.
I was just being highly optimistic in my 100 steps estimate.
Second, even an exceptionally unlikely event becomes probable when there are enough chances. Winning the lottery is exceptionally unlikely, yet someone seems to win every few weeks because there are so many players. Similarly, there could be trillions of ambiogenesis precursor molecules out there. Granted, 100! is much larger than one trillion, but the odds are at least improved somewhat.
100! is 9.3326215444×10ˆ157.
That means there is a chance in 9.3326215444×10ˆ157 for life to come into being.
Lindley, the number of atoms in the observable universe is generously estimated at 10ˆ80. And only a small fraction of these are amenable to giving birth to life.
This means that, in order to win the 'lottery' of life, you need more than the atoms in the observable universe. A LOT more.
As I already said, 100! gives a number so close to 0 as the chance for the "simplest" self-replicating molecule to emerge, that the chances are life on Earth is alone in the observable universe (and a huge chunk of the unobservable one).
Even considering the abyss of time (6-7 billions of years), of space, considering Earth-like planets as a dime a dozen and taking my 100! only as a very rough/high estimate.