  That conclusion may well be justified. But we can largely sidestep the dispute over whether there is a single precise notion of randomness that answers perfectly to our intuitive conception of random sequence. Kolmogorov-Martin-Löf randomness is a reasonable and representative exemplar of the algorithmic approach to randomness, and it overlaps almost everywhere with any other plausible definition of randomness. It is adopted here as a useful working account of randomness for sequences. None of the difficulties and problems I raise below for the connection between random sequences and chance turns in any material way on the details of which particular set of sequences gets counted as random (most are to do with the mismatch between the process notion of chance and any algorithmic conception of randomness, with differences amongst the latter being relatively unimportant). So while the observations below are intended to generalise to Schnorr randomness and other proposed definitions of random sequences, I will explicitly treat only KML randomness in what follows.