There are many illegitimate critiques of Intelligent Design (the hypothesis that some features of the world are best explained in terms of an intelligent cause rather than undirected natural processes).  One example is the charge often leveled against ID that it improperly uses probability statistics to infer design. For example, in a BBC documentary titled The War on Science, Ken Miller accused IDers of making the mistake of calculating probabilities after-the-fact, making the unlikely seem impossible:

One of the mathematical tricks employed by intelligent design involves taking the present day situation and calculating probabilities that the present would have appeared randomly from events in the past. And the best example I can give is to sit down with four friends, shuffle a deck of 52 cards, and deal them out and keep an exact record of the order in which the cards were dealt. We can then look back and say ‘my goodness, how improbable this is. We can play cards for the rest of our lives and we would never ever deal the cards out in this exact same fashion.’ You know what; that’s absolutely correct. Nonetheless, you dealt them out and nonetheless you got the hand that you did.

Miller is arguing that even the most mundane of events—events we know are truly random—can be made to seem impossible in the absence of an intelligent agent to order that event if we look at the probability of that event taking place after-the-fact.  The problem with this analysis is that it attacks a straw man.  As Barry Arrington has written in response to Miller:

Miller blatantly misrepresents ID theory, because…no ID proponent says that mere improbability denotes design. Suppose, however, your friend appeared to shuffle the cards thoroughly and dealt out the following sequence: all hearts in order from 2 to Ace; all spades in order from 2 to Ace; all diamonds in order from 2 to Ace; and then all clubs in order from 2 to Ace.  As a matter of strict mathematical probability analysis, this particular sequence of 52 cards has the exact same probability as any other sequence of 52 cards. But of course you would never attribute that sequence to chance. You would naturally conclude that your friend has performed a card trick where the cards only appeared to be randomized when they were shuffled. In other words, you would make a perfectly reasonable design inference. What is the difference between Miller’s example and my example? In Miller’s example the sequence of cards was only highly improbable. In my example the sequence of cards is not only highly improbable, but also it conforms to a specification. ID proponents do not argue that mere improbability denotes design. They argue that design is the best explanation where there is a highly improbable event AND that event conforms to an independently designated specification.[1]

See also Signature in the Cell, Part 1: Information

[1]Barry Arrington, “Ken Miller’s Strawman No Threat to ID”; available from http://www.uncommondescent.com/intelligent-design/ken-millers-strawman-no-threat-to-id/; Internet; accessed 14 December 2011.