I have encountered many people who justify their belief that no intelligent Creator was needed, with the assumption that evolution has had a near-infinite number of trials to produce the full diversity of life. It is helpful, therefore, to figure out what the upper limit actually is, then we can be in a better position discuss whether it makes a Creator utterly unnecessary.
One mistake Darwinists make when discussing the probability of functional protein sequences is to spread out a deck of cards and point out how improbable that sequence of cards was. The reasoning seems to be that since improbable events happen all the time, therefore there is no problem finding a functional 3D protein sequence. Upon thinking critically about this, most people suspect there is a problem with this assumption. Here I explain why.