Change level
At what level should we explain what happens, and act on it?
An explanation can sit at many levels – a person, a circle, a whole network. A small system of states, with the chance of moving from each to each, makes the choice precise. Group the states, and see whether the grouped description tells you more about what follows, and whether it predicts itself.
Your prediction
Grouped, the system is deterministic: the shuffling no longer counts as noise, so each intervention says more about what follows – 0.19 bits more here.