Empirical studies of ambiguity attitudes to date have focused on events of moderate likelihood. Extrapolation to rare events requires caution. In an Ellsberg-like experiment with very unlikely events, we measured ambiguity attitudes with neither assumptions on subjects' beliefs nor restrictions to specific ambiguity models. Very unlikely events were overweighted, being weighted more strongly in isolation than when part of larger events. Using latent profile analysis, we classified the subjects in terms of deviations from ambiguity neutrality. One third behaved close to ambiguity neutrality. The others exhibited overweighting of rare events. Such behavior can lead to money-pump situations.