  The universal test does define an effective measure one property, but (unlike normality, or having no biased admissible subsequences), it is far from a naturally graspable property. Nevertheless, Martin-Löf’s result does establish that there are random sequences that satisfy all the properties of stochasticity, and that in fact almost all binary sequences are random in that sense. Returning to  Ville’s theorem  2,  it can be shown that all ML-random sequences satisfy the law of symmetric oscillations (van Lambalgen 1987a: §3.3). Hence the kind of construction Ville uses yields vM-random sequences which are not ML-random. All the ML-random sequences have the right limit relative frequencies, since they satisfy the effective measure one property of large numbers. So Martin-Löf random sequences satisfy all the intuitive properties we would expect of a sequence produced by tosses of a fair coin, but are characterised entirely by reference to the effectively specifiable measure one sets of infinite sequences. We have therefore characterised random sequences entirely in terms of the explicit features of the product, and not of the process that may or may not lie behind the production of these sequences.