Never? How so? You’re telling me if I had a computer shuffling one million decks of cards per second it would never see a repeat? What if it could do 10^500 per second?
10^500 is a large number. Too large to represent what the universe could do randomly. See the probabilistic resources of the universe below.
Signature in the Cell goes into this.
There are various calculations spread throughout the book. On page 213 is the following (my paraphrasing):
"Assuming that a minimally complex cell needs at least 210 proteins of, on average 150 amino acids and that the probability of producing just one such protein is 10 raised to the 14th power as calculated above, then the probability of a pre-biotic soup producing all the necessary proteins needed to service a minimally complex cell is …10 raised to the 41,000th power.
This number is close to an estimate done by Fred Hoyle who estimated the chances of a one-celled organism coming about by chance at 10 raised to the 40,000th power."
The number above needs to be compared to the total “probabilistic resources” of the universe, which is calculated as 10 raised to the 139th power. (on page 216)."
These probabilistic resources assume the following:
10^80 elementary particles in the universe.
Planck time (the fastest that anything can interact with anything else, limited by the speed of light) - 10^43 events per second.
Time since the big bang - 10^16 seconds.
If you multiply these together you get the total number of “interactions” that can have taken place since the big bang - 10^139.
The use of all of the probabilistic resources of the universe assume the “best possible case” for the utilization of matter - it assumes that everything in creation is part of the “pre-biotic” soup. This of course is not realistic since most of the matter is contained in stars (or perhaps even in dark matter). So it actually biases the calculation in you favor.
If both the chance of the one-celled organism and the probabilistic resources were both e.g. 10^139, then you could say there’s a 50/50 chance of it happening strictly by chance. But the bottom line is you’re comparing 10^40,000 to 10^139 so it’s not even close.
Note: I’ve probably not done the above discussion justice. But you can always read the book yourself.
