  As the bias in a chance process approaches extremal values, it is very natural to reject the idea that the observed outcomes are random. (As an example, we may consider human behaviour—while people aren’t perfectly predictable, and apparently our behaviour doesn’t obey non-probabilistic psychological laws, nevertheless to say that people act randomly is incorrect.) Moreover, there is a relatively measure-independent notion of disorder or incompressibility of sequences, such that biased sequences really are less disorderly. We can define a measure-dependent notion of disorder for biased sequences only by ignoring the availability of better compression techniques that really do compress biased sequences more than unbiased ones. To generalise the notion of randomness, as proposed above, permits highly non-random sequences to be called random as long as they reflect the chances of highly biased processes. So there is at least some intuitive pull towards the idea that if randomness does bifurcate as Earman suggests, the best deserver of the name is Kolmogorov randomness in its original sense. But this will be a sense that contrasts with the natural generalisation of ML-randomness to deal with arbitrary computable probability measures, and similarly contrasts with the original sense of randomness that von Mises must have been invoking in his earliest discussions of randomness in the foundations of probability.