How improbable is it that proteins can form by "chance"?

A common trait of scientists who work on the origins of life, is not to attempt to estimate the probability macromolecules (like peptide chains) will form. A common trait of creationists who don't, is estimating such probabilities.  This typically produces astronomical odds against such macromolecules forming.

For instance, suppose we are told there is a 50:50 chance that two amino acids will bond.  A peptide-chain (protein) 150 amino-acids long, will thus have the probability of (0.5)*(0.5)^2*(0.5^3)*...(0.5)^150.  This gives a cumulative probability of well, a really really big number against (1 in 10⁴⁵ IIRC).  Thus the number of trials needed to make this peptide seem up there in many billions of trillions.

The problem above is simple. It ignores the fact that macro-molecules form in a modular fashion. (There's also some assumptions about the chemistry also, but we'll put those aside).  Macromolecules don't form one molecule at a time, in one go.  If we just add one correction to the calculation above- that the peptide chains form in a modular way, it takes just 5 trials to make a chain 150 amino-acids long.  That's right. Just 5.  The Creationist result above are entirely produced by unrealistic assumptions.

Let me demonstrate.  We start with a large pool of amino-acids.  There's a 50:50 chance in the first round, they bond to another amino acids (using SIPF chemistry, dipeptides are found within a week).  This is merely the assumption from the creationist maths above.

So after trial 1:
Half the amino-acids have formed dipeptides (a chain of 2 amino acids)
Half the amino acids are still unpaired to anything.

We then carry these into trial 2:
Some of the amino acids will still not have bonded.  Some will form dipeptides.
Some of the dipeptides will bond to one other single amino acids (making a tripeptide)
Some of them will bond to another bipeptide, or to two single amino acids.  (Bonding can occur at either end of the chain, it doesn't have to be at just one end).  That's an oligopeptide 4 amino-acids long.
Importantly, some of the dipeptides will bond to two other dipeptides.  After two trials, we will find peptide chains 6 amino-acids long.

On to trial 3:
Some of the peptide chains 6 amino-acids long, will bond to two other 6 amino-acid peptides.  Some of the peptide chains are now 18 amino-acids long.  The distribution of peptide chains in the pool will range from 1 to 18 amino-acids long.

On to trial 4:
Some of the 18 amino-acid chains will bond to two other 18 amino acids.  We will find in the sample, anything between 1 amino acid to chains 54 amino-acids long.  

On to trail 5:
If 3 peptide chains that are 50-54 amino-acids long bond, then we've got our 150 amino-acid peptide chain.  We didn't need trillions of trials. It's that simple.

Ok.  This is a gross simplification.  The chemistry of peptide formation is a lot more complex than just two molecules randomly bonding.  That's why people who actually work in this topic, don't try to calculate probabilities.  There are too many variables and too many permutations to make any estimate meaningful.  The point is to show how utterly devious and dishonest it is, to drop the modular assumption of macro-molecule formation.  And why you actually need to use a Markov probability function, not an IID.  What happens in each trial is not independent of previous trials. The reason creationists use an IID is because it's the one function everyone knows, and it wildly inflates the improbability of anything happening.