Iris recognition has legendary resistance to False Matches, and the tools of information theory can help to explain why. The concept of entropy is fundamental to understanding biometric collision avoidance. This paper analyses the bit sequences of IrisCodes computed both from real iris images and from synthetic “white noise” iris images whose pixel values are random and uncorrelated. The capacity of the IrisCode as a channel is found to be 0.566 bits per bit encoded, of which 0.469 bits of entropy per bit is encoded from natural iris images. The difference between these two rates reflects the existence of anatomical correlations within a natural iris, and the remaining gap from one full bit of entropy per bit encoded reflects the correlations in both phase and amplitude introduced by the Gabor wavelets underlying the IrisCode. A simple two-state Hidden Markov Model is shown to emulate exactly the statistics of bit sequences generated both from natural and white noise iris images, including their “imposter” distributions, and may be useful for generating large synthetic IrisCode databases.