A characteristic of a binary Markovian process is its ability to imitate a random process (in certain ways), even when the time series of records it has generated exhibits inherent memory of its previous states.  The two self-transition probabilities would simply need to be equal although different from 50%. Then, the long term statistical average of these records resembles that from a random process, i.e. it is 50%. Variance Modulating Factor Variance effect in a first-order, two-state Markovian process with equal self-transition probabilities, p. Variance