Previous experimental studies on concessive connectiveshave only looked at their local facilitating or predictive ef-fect on discourse relation comprehension and have oftenviewed them as a class of discourse markers with simi-lar effects. We look into the effect of two connectives,but and although, for inferring contrastive vs. concessivediscourse relations to complement previous experimentalwork on causal inferences. An offline survey on AMTurkand an online eye-tracking-while-reading experiment areconducted to show that even between these two connec-tives, which mark the same set of relations, interpretationsare biased. The bias is consistent with the distribution ofthe connective across discourse relations. This suggeststhat an account of discourse connective meaning based onprobability distributions can better account for compre-hension data than a classic categorical approach, or an ap-proach where closely related connectives only have a coremeaning and the rest of the interpretation comes from thediscourse arguments.