  Holroyd, Liggett, and Romik introduced the following probability model. Let
$C_1, C_2,...$ be independent events with probabilities $\P_s(C_n)= 1-e^{-ns}$
under a probability measure $\P_s$ with $0<s<1$. Let $A_k$ be the event that
there is no sequence of $k$ consecutive $C_i$ that do not occur. We given an
asymptotic for $\P_s(A_k)$ with a relative error term that goes to 0 as $s\to
0$. This establishes a conjecture of Andrews.
