  In this paper we consider a variant of Conway's sequence (OEIS A005150,
A006715) defined as follows: the next term in the sequence is obtained by
considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is
the digit and $a$ is the maximum of $b$ and the run's length. We dub this the
"look-and-say the biggest" (LSB) sequence. Conway's sequence is very similar
($b$ is just the run's length). For any starting value except 22, Conway's
sequence grows exponentially: the ration of lengths converges to a known
constant $\lambda$. We show that LSB does not: for every starting value, LSB
eventually reaches a cycle. Furthermore, all cycles have a period of at most 9.
