It has been proposed that the development of verbal counting is supported by a more ancient preverbal system of estimation, the most widely canvassed candidates being the accumulator originally proposed by Gibbon and colleagues and the analogue magnitude system proposed by Dehaene and colleagues. The aim of this chapter is to assess the strengths and weaknesses of these models in terms of their capacity to emulate the statistical properties of verbal counting. The emphasis is put on the emergence of exact representations, autoscaling, and commensurability of noise characteristics. We also outline the modified architectures that may help improve models' power to meet these criteria. We propose that architectures considered in this chapter can be used to generate predictions for experimental testing and provide an example where we test the hypothesis whether the visual sense of number, ie, ability to discriminate numerosity without counting, entails enumeration of objects.