I often encounter creationists who say that evolution is unbelievable because it is a random process. It cannot be true because something so complex as, say, the human brain could not possibly have come into being by "chance". The problem with such statements is that they are born of ignorance. These people fail to understand (or choose to willingly dismiss) the mechanism of natural selection. If you encounter a creationist who trots out this old, stale argument, here is an analogy you can use that will hopefully explain.

To understand how natural selection works, let’s look at something where chance plays an important role and is easily measured: poker. We can calculate that the chance of being dealt a spade royal flush, in order (10 of spades, jack of spades, queen of spades, king of spades, ace of spades), from a freshly shuffled deck of 52 cards is .0000000320641%. This means that if you were quick enough to shuffle a deck of cards and deal off the first five every second, you would expect to deal a spade royal flush, in order, about once every 9.9 years or so. It is pretty well improbable.

Now, lets say that we’ve set up a thousand decks of cards, shuffled them, and dealt one card off the top of each of them and laid it face up in front of its respective deck. The chances that at least one of those decks would flip the first card in our spade-royal-flush-in-order sequence (the 10 of spades) are quite good. In fact, we should expect that around 19 of those cards will be the 10 of spades. In our illustration, this represents a mutation that is favorable for survival and so is naturally selected to propagate in the population. To represent this, we will now go to every deck that did not deal a 10 of spades and replace the dealt card with a 10 of spades. Now we have 1000 decks of cards and each of them has a 10 of spades lying in front of it.

Now we flip another card from each of the decks. The chances that we will see at least one instance of the next card in our spade-royal-flush-in-order sequence (the jack of spades) is even better than before. We should expect to see between 19 and 20 instances of it. This represents another mutation that is beneficial for survival (perhaps building upon the previous one, but not necessarily), so it too will spread throughout the population over successive generations. To represent this, we replace the non-jack-of-spade cards dealt on the other piles with a jack of spades. Now we have a thousand decks of cards, each with the first two cards in our spade-royal-flush-in-order sequence laying in front of them.

If we repeat the process three more times, we will end up with 1000 spade-royal-flushes-in-order, none of which occurred purely by chance. You may say "But you cheated!" and you would be absolutely right! Natural selection is not random. It cheats. It propagates those changes that are beneficial for survival to a greater degree than other changes. Over time, if the change is differentially beneficial enough, every member of the species will have it. In the example of the cards it was I who SELECTED the changes that would propagate throughout the decks. In nature we constantly observe NATURE SELECTING mutations and instances of genetic drift to propagate throughout the species because they help the species to survive and pass them on. We are not guessing that natural selection happens. We KNOW natural selection happens. We have observed it.

And that is how complex structures like the human brain evolved. NOT BY RANDOM CHANCE, but by NATURAL SELECTION rigging the game and determining which random, incremental change would get to survive.