Reassembling unknown broken objects from a large collection of fragments is a common problem in archaeology and other fields. Computer tools have recently been developed by the authors and by others, which try to help by locating pairs of fragments with matching outline shapes. These tools have been succesfully tested on small collections of fragments. Here we address the question of whether such tools can be expected to work for practical instances of the problem (103 to 105 fragments). To that end, we describe here a method to measure the average amount of information contained in the shape of a fracture line of given length. This parameter tells us how many false matches we can expect to find for that fracture among a given set of fragments; and we show that outline comparison should give useful results even for large instances.