Let’s be a bit less ambitious: how about just one sonnet, a short poem, rather than the Complete Works?

Israeli physicist Gerry Shroeder writes:

‘All the sonnets are the same length. They’re by definition fourteen lines long.

I picked the one I knew the opening line for: ”Shall I compare thee to a summer’s day?” I counted the number of letters; there are 488 letters in that sonnet. What’s the likelihood of hammering away and getting 488 letters in the exact sequence as in “Shall I compare thee to a summer’s day”? What you end up with is 26 multiplied by itself 488 times… or, in other words, 10 to the 690th." (note: these calculations don’t allow for the need for spaces between words or punctuation of any sort).

One followed by 690 zeros. That is what 10 to the 690th means.

One billion is 10 to the power of 9 – one followed by 9 zeros – 1,000,000,000. Do you have the faintest idea how big a number one followed by 690 zeros is? Is there perhaps another big number we can compare it with? Gerry Shroeder again:

‘Now the number of particles in the universe – not grains of sand, I am talking about protons, electrons, and neutrons – is 10 to the 80th – one with 80 zeros after it. 10 to the 690th is one with 690 zeros after it. There are not (not even close! ) enough particles in the universe to write down the trials…’ quoted by Prof. Antony Flew, author of ‘There is a God’  2007.

Various ways of getting round this conclusion have been publicised, but all involve intelligent intervention – such as selecting each short segment that happens to match the target text and then assembling them together to match the complete text. Evolution of course has no such short cuts – no intelligence allowed.

Others have approached the problem from a slightly different angle: how long would it take to acheive this formidable task? 

"If the monkey could type one keystroke every nano second, the expected waiting time until the monkey types out Hamlet is so long that the estimated age of the universe is insignificant by comparison... this is not a practical method for writing plays."  Gian Carlo Rota

What seems on the face of it to be a piece of unremarkable common sense, is in reality complete nonsense. A story which was designed to prove one thing in fact proves the absolute opposite. Some mathematicians regard anything above 1 chance in 10 to the 50th as in effect zero probability: it’s never going to happen, ever.

For the record, the text of ‘Hamlet’, just one of Shakespeare’s plays, has not 488 but well over 132,000 letters.

In his book 'God's Undertaker', John Lennox quotes the astrophysicist Chandra Wickramasinghe:

"No matter how large the environment one considers, life cannot have had a random beginning. Troops of monkeys thundering away at random on typewriters could not produce the works of Shakespeare, for the practical reason that the whole observable universe is not large enough to contain the necessary monkey hordes, the necessary typewriters and certainly not the waste paper baskests required for the deposition of wrong attempts.  

The same is true for living material. The likelihood of the spontaneous formation of life from inanimate matter is one to a number with 40,000 noughts after it... it is enought to bury Darwin and the whole theory of evolution. There was no primeval soup, neither on this planet nor on any other, and if the beginnings of life were not random, they must therefore have been the product of purposeful intelligence."                           'Evolution from Space'

Sadly, he preferred the idea of life being seeded on earth by intelligent aliens ('panspermia') rather than admit a divine creator.

The real question of course is not about the possible productivity of hordes of mythical monkeys, but the likelihood for example of a single molecule of the protein haemoglobin assembling itself by chance. The odds against arranging the 20 amino acids involved in 4 chains each 146 links long is about 10 to the power of 170 – so says Isaac Asimov.