# How long will it take to sort a deck of cards by trial and error?

Inside the cell, things like proteins and DNA are formed by sequencing parts together in just the right way so that the sequence will have biological function. If the sequence is wrong, because some component of the sequence is the wrong piece or is in the wrong place, the sequence has no function. It’s just like writing English or computer instructions.

To calculate the probabilities, you have to use a rule called “The Product Rule”, because the order of the parts in the sequence (“permutation”) is important. For example, the odds of getting the sequence “ABC” just by choosing three random letters is 1/26 x 1/26 x 1/26 = 1/17576. Things get very unlikely quite quickly, don’t they?

So, take a look at Neil Simpson’s latest post, where he uses cards instead of letters or amino acids, but the principle is exactly the same. His calculation is a little different because the odds actually go down a little each time you choose a card. So, for the first card, it’s 1/52, but the second card is only 1/51, and so on…

Excerpt:

This is by no means a definitive argument against evolution, but I offer it to put the “time, chance and random mutation” theory in perspective.

Everyone knows that micro-evolution occurs, such as dog breeding and bacteria becoming resistant to antibiotics.  But macro-evolutionists believe that with enough time an amazingly complex single cell of unknown origin could make lots and lots of small changes, develop reproductive capacities and eventually become humans, elephants, caterpillar/butterflies, chameleons and so much more.

Let’s consider something very simple.  Imagine that you shuffle a deck of cards.  If you shuffled it one time per second, how often would all the cards go back into their original order? (Ace of spades, King of spades, etc.)  The math is simply 1/52 (the odds of the Ace of spades being on top) times 1/51 times 1/50, etc. I left out the Jokers to make it easier.

Guess how many years it takes?

Click through to see his calculations, or do them yourself! It’s easy and fun! Neil has a pretty fun discussion going on with the angry atheists who frequent his site, too.

This is everyone should learn probabilities in school, because then we can really talk about these things with our neighbor. Shalini can even do biochemistry, so she can actually explain it even better than I can!

Remember, we are looking for a specific sequence of cards – the sequence that the cards originally came in. In this example, it’s that sequence and that sequence alone that has biological function. The other sequences are just junk – they have no biological function. And most importantly, you don’t get to save any of the cards that are in the right spots because the sequence as a whole has no present function that would allow it to be “saved” for later. You have to re-select all 52 cards each time at random!

A typical protein isn’t made of 52 parts, it’s made of around 200, and there are 80 possible amino acids, not just 26! And in the case of proteins,the vast majority of the possible sequences that you can make won’t have any biological function at all! (And there are many more problems besides, such as chirality, cross reactions, and bonding type). Even if you filled the whole universe with reactants and reacted it all at Planck time, for the entire history of the universe, you still wouldn’t be likely to get even one protein!