Consider a system that is always in one of two states, 1 or 2. Every time a clock ticks, the system updates itself according to a 2×2 matrix of transition probabilities, the entry of which gives the probability that the system moves from state to state at any clock tick. A two‐state Markov chain is a system like this, in which the next state depends only on the current state and not on previous states. Powers of the transition matrix approach a matrix with constant columns as the power increases. The number to which entries in the column converge is the asymptotic fraction of time the system spends in state .