  The notion of Kolmogorov randomness fits well with the intuitions about the disorderliness of random sequences we derived from the Martin-Löf account. It also fits well with other intuitions about randomness—random sequences don’t have a short description, so there is no sense in which they are produced in accordance with a plan. As such, Kolmogorov randomness also supports von Mises’ intuitions about randomness being linked to the impossibility of gambling systems, as there will be no way of effectively producing a given random sequence of outcomes using a set of initially given data any smaller than the sequence itself. There is no way of predicting a genuinely random sequence in advance because no random sequence can be effectively produced, yet every predictable sequence of outcomes can (intuitively) be generated by specifying the way in which future outcomes can be predicted on the basis of prior outcomes. Moreover, because for increasing \(k\) the number of strings of length \(n\) which are random increases, and because for increasing \(n\) we can choose larger and larger \(k\), there is some sense in which the great majority of sequences are random; this matches well the desiderata in the infinite case that almost all sequences should be random. Finally, it can be shown that the Kolmogorov randomness of a sequence is equivalent to that sequence passing a battery of statistical tests, in the Martin-Löf sense—indeed, that the Kolmogorov random sequences are just those that pass a certain universal test of non-randomness (Martin-Löf 1969a:  §2).[11]