Improbable differential cryptanalysis is a recent attack technique that generalizes impossible differential cryptanalysis for block ciphers. In this paper, we give the most effective attacks known to date on the CLEFIA cipher using improbable differential cryptanalysis. Moreover, we provide a general data complexity calculation that can guide the cryptanalyst to choose the optimal improbable differential. On a related account, we consider the probability calculations used for improbable differential cryptanalysis. Recently, some examples were given where certain assumptions in these calculations do not hold. Although such cases exist, especially on small toy ciphers with insufficient diffusion, we provide experimental evidence which supports that the improbable differential attacks on CLEFIA and PRESENT are valid. (C) 2015 Elsevier B.V. All rights reserved.