quad statistics

As my loyal readers know (both of them, I hope), the astrometry.net project, among other things, will use an index of quadrangles of stars to identify fields blind, ie, even when the user doesn't remember the image pointing, rotation, or scale. I spent quite a bit of time this weekend working out (and recalling) the statistics of such quadrangles: How many are there on the sky? How many unique quads can we index, given finite positional errors? How many quads do we expect in a finite, rectangular image of given dimensions? What fraction of fields will we fail to solve, given the need for redundant successes? Etc. The goal is to re-solve all of the SDSS images blind.