Blackbody radiation contains (on average) an entropy of 3.9 +/- 2.5bits per photon. If the emission process is unitary, then this entropy is exactly compensated by " hidden information" in the correlations.
We extend this argument to the Hawking radiation from GR black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget. The key technical aspect of our calculation is a variant of the "average subsystem" approach developed by Page, which we extend beyond bipartite pure systems, to a tripartite pure system that considers the influence of the environment.