  Von Mises’ original proposals were deliberately imprecise about what kinds of procedures count as admissible place selections. This imprecision did not concern him, as he was disposed to regard the ‘right’ set of place selections for any particular random collective as being fixed by context and not invariantly specifiable. But his explicit characterisation is subject to counterexamples. Since ‘any increasing sequence of natural numbers \(n_1 \lt n_2 \lt \ldots\) defines a corresponding selection rule, … given an arbitrary sequence of 0s and 1s … there is among the selection rules the one which selects the 1s of the given sequence, so the limit frequency is changed’ (Martin-Löf 1969b: 27). This clearly violates von Mises’ intentions, as he presumably intended that the place selections should be constructively specified, yet the notion of vM-randomness remains tantalisingly vague without some more concrete specification.