We consider a model of randomness for self-similar Cantor sets finite and positive 1-Hausdorff measure. find the sharp rate decay probability that Buffon needle lands δ-close to set this particular randomness. Two quite different models sets, by Peres Solomyak, Shiwen Zhang, appear have same order probability: clog1δ. In note, we prove third randomness, which asserts vague feeling any “reasona...