  We can use these constructions to come up with counterexamples to RCT. Let a dome system be prepared, and left for a period of 5 seconds. If the ball remains at rest on the apex, call the outcome ‘0’. If the ball moves, and so is at the end of 5 seconds somewhere on the dome other than the apex, call the outcome ‘1’. Both outcomes are physically possible final states of the system after 5 seconds. If the system is repeatedly prepared in this state, it is physically possible to get a random sequence of outcomes of these repeated trials. Certainly the outcomes cannot be produced by some finite algorithm, since the indeterministic dynamics permits as physically possible every sequence of outcomes, including those that differ at some place from every algorithmically compressible sequence. In the infinite future case, it is physically possible for the system to produce every infinite binary sequence, but at most countably many of these are non-random. So it is physically possible for these setups to produce a random sequence of outcomes in the KML sense. But we then have randomness without a chance distribution over the outcomes. Randomness only requires two distinguishable possible outcomes and the possibility of production of arbitrary sequences of such outcomes. Chance requires two distinguishable outcomes, each of which has some chance. These cases show that chance and possibility come apart—there are cases where there are two possible outcomes of a process, neither of which has any chance at all (not even a chance of zero).