  Erd\H{o}s and Graham found it conceivable that the best $n$-term Egyptian
underapproximation of almost every positive number for sufficiently large $n$
gets constructed in a greedy manner, i.e., from the best $(n-1)$-term Egyptian
underapproximation. We show that the opposite is true: the set of real numbers
with this property has Lebesgue measure zero. [This note solves Problem 206 on
Bloom's website "Erd\H{o}s problems".]
