When two scatterers intersect tangentially in a planar dispersing billiard domain, the particle can be trapped in the cuspoidal region. These phenomena are known to cause slow decay of correlations and non-standard limit theorems. In joint work with N. Chernov and D. Dolgopyat we have shown that the second moments of the appropriately normalized Birkhoff sums converge to a value which is twice the second moment of the limit distribution. In my talk I would like to describe this doubling effect and show that it arises in many other situations, in particular in an entirely probabilistic setting.