Visual ambiguity plays a key role in the perceptual experience of art and has been much exploited by modernist and contemporary artists for aesthetic effects. But it remains unclear how aesthetic judgments are affected by visual ambiguity, and the subjective nature of aesthetic experience makes it difficult to measure. Wang et al. (2020) piloted a methodology in which a large collection of free-form textual descriptions of artworks were gathered from participants. The variability of these descriptions was then quantified computationally with Shannon entropy; ambiguous images tended to generate a greater number and wider diversity of descriptive terms. In the present study, we evaluated how well these measures can predict aesthetic preference for ambiguous images. We designed three crowdsourcing tasks in order to measure aesthetic preferences. The first was a simple rating task, and the other two required the participants to engage more actively with the images. We hypothesized that the number of associations evoked by ambiguous works of art, when computationally measured by entropy and description lengths, is a factor in judgments of their aesthetic value. Following this hypothesis, we made and tested a number of predictions. Our results provide broad support for the hypothesis, but with some interesting caveats and exceptions. We find that the form of the task significantly affects preference ratings and that participants’ responses can be clustered into two categories: those that prefer simple, recognizable imagery, and those that prefer more complex, ambiguous imagery. When taking this clustering into account, we find that our measures of entropy are correlated with aesthetic ratings. We conclude that these computational methods are useful for investigating the variable subjective responses to ambiguous artworks.