Consider an experiment in which a subject guesses repeatedly at a randomly chosen target on a continuum. To guarantee a positive probability of success, the continuum is partitioned into a finite but large number of segments. The subject is given directional feedback. General guessing strategies are characterized, and an optimal strategy is identified. The hypothesis that the subject's performance can be explained by “chance alone” is of interest in such experiments. A test is developed based on comparing the subject's performance to expected performance using the optimal strategy. A “skill-scoring” procedure is developed for assessing a subject's performance in light of the strategy used, and a test based on skill-scoring is advanced.