  But unlike a sequence of fair coin tosses, supposing them to involve genuine chance, the baker’s transformation is entirely deterministic. Given a particular point \((p, q)\) as an initial condition, the future evolution of states of the system at each moment is time \(t\) is determined to be \(\phi^t (p, q)\). So while the product produced is random, as random as a genuine chance process, these outcomes do not happen by chance; given the prior state of the system, the future evolution is not at all a matter of chance. So we have a random sequence without chance outputs. (Indeed, given the symbol shift dynamics, the evolution of the system over time in \(\{L, \overline{L}\}\) simply recapitulates successive digits of the starting point.) To be perfectly precise, the trial in this case is sampling the system at a given time point, and seeing which cell of the coarse grained partition it is in at each time. This is a sequence of arbitrarily repeated trials which produces a random sequence; yet none of these outcomes happens by  chance.[18]  To put the point slightly differently: while the sequence of outcomes is random, there is a perfectly adequate theory of the system in question in which probability plays no role. And if probability plays no role, it is very difficult to see how chance could play a role, since there is no probability function which serves as norm for credences, governs possibility, or is non-trivial and shared between intrinsic duplicate trials. In short, no probability function that has the features required of chance plays a role in the dynamics of this system, and that seems strong reason for thinking there is no chance in this system.