The example is given of flipping a presumably fair coin 500 times and observing it come up heads each time. The ID advocates say this is clear evidence of "design", and those arguing against them (including the usually clear-headed Neil Rickert) say no, the sequence HH...H is, probabilistically speaking, just as likely as any other.
This is an old paradox; it goes back as far as Samuel Johnson and Pierre-Simon Laplace. But neither the ID advocates nor their detractors seem to understand that this old paradox has a solution which dates back more than 15 years now.
The solution is by my UW colleague Ming Li and his co-authors. The basic idea is that Kolmogorov complexity offers a solution to the paradox: it provides a universal probability distribution on strings that allows you to express your degree of surprise on enountering a string of symbols that is said to represent the flips of a fair coin. If the string is compressible (as 500 consecutive H's would be) then one can reject the chance hypothesis with high confidence; if the string is, as far as we can see, incompressible, we cannot. It works because the proportion of compressible strings to noncompressible goes to 0 quickly as the length of the string increases.
So Rickert and his defenders are simply wrong. But the ID advocates are also wrong, because they jump from "reject the fair coin hypothesis" to "design". This is completely unsubstantiated. For example, maybe the so-called "fair coin" is actually weighted so that heads come up 999 out of 1000 times. Then "chance" still figures, but getting 500 consecutive 1's would not be so surprising; in fact it would happen about 61% of the time. Or maybe the flipping mechanism is not completely fair -- perhaps the coin is made of two kinds of metal, one magnetic, and it passes past a magnet before you examine it.
In other words, if you flip what is said to be a fair coin 500 times and it comes up heads every time, then you have extremely good evidence that your prior belief about the probability distribution of flips is simply wrong. But ID advocates don't understand this and don't apply it to biology. When they view some biological structure, calculate the probability based on a uniform distribution, claim it is "specified", and then conclude "design", they never bother to consider that using the uniform distribution for probabilities is unfounded, because the causal history of the events has not been taken into account. Any kind of algorithmic bias (such as happens when random mutation is followed by selection) can create results that differ greatly from the uniform distribution.
Elsberry and I discussed this in great detail in our paper years ago, but it seems neither side has read or understood it.