No natural language is known to have contrafactive attitude verbs, yet factives are common across natural languages. Several experiments by Strohmaier and Wimmer (2022; 2023; 2025) use transformers as model learners to investigate whether this asymmetry is due to a difference in how easy it is to learn contrafactives and factives. But they do not explore empirically-founded data distributions. We fill this gap, further improving the overall quality of training data distributions using linear programming.Our results confirm Strohmaier and Wimmer’s 2025 conclusion that there is no learnability difference in production, while establishing the impact of differences in data distributions.