  Suppose that $\mathcal C$ is a finite collection of patterns. Observe a
Markov chain until one of the patterns in $\mathcal C$ occurs as a run. This
time is denoted by $\tau$. In this paper, we aim to give an easy way to
calculate the mean waiting time $E(\tau)$ and the stopping probabilities
$P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time
until the pattern $A$ appears as a run.
