Previous experimental studies on concessive connectives have only looked at their local facilitating or predictive effect on discourse relation comprehension and have often viewed them as a class of discourse markers with similar effects. We look into the effect of two connectives, but and although, for inferring contrastive vs. concessive discourse relations to complement previous experimental work on causal inferences. An offline survey on AMTurk and an online eye-tracking-while-reading experiment are conducted to show that even between these two connectives, which mark the same set of relations, interpretations are biased. The bias is consistent with the distribution of the connective across discourse relations. This suggests that an account of discourse connective meaning based on probability distributions can better account for comprehension data than a classic categorical approach, or an approach where closely related connectives only have a core meaning and the rest of the interpretation comes from the discourse arguments.