Several example-based systems for shape retrieval and shape classification directly match input shapes to stored shapes, without using class membership information to perform the matching. We propose a method for improving the accuracy of this type of system. First, the system learns a set of chance probability functions (CPFs). The CPFs estimate the probabilities of obtaining a query shape with particular distances from each training example by chance. The learned CPFs are used at runtime to rapidly estimate the chance probabilities of the observed distances between the actual query shape and the database shapes. These estimated probabilities are then used as a dissimilarity measure for shape retrieval and/or nearest-neighbor classification. The CPF learning method is parameter-free. Experimental evaluation demonstrates that: (1) chance probabilities yield higher accuracy than Euclidean distances; (2) the learned CPFs support fast matching; and (3) the CPF-based system outperforms prior systems on a standard benchmark test of retrieval accuracy.