  In the study of Markov chain mixing times, analysis has centered on the
performance from a worst-case starting state. Here, in the context of Glauber
dynamics for the one-dimensional Ising model, we show how new ideas from
information percolation can be used to establish mixing times from other
starting states. At high temperatures we show that the alternating initial
condition is asymptotically the fastest one, and, surprisingly, its mixing time
is faster than at infinite temperature, accelerating as the inverse-temperature
$\beta$ ranges from 0 to $\beta_0=\frac12\mathrm{arctanh}(\frac13)$. Moreover,
the dominant test function depends on the temperature: at $\beta<\beta_0$ it is
autocorrelation, whereas at $\beta>\beta_0$ it is the Hamiltonian.
