Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59–111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in
L
(
R
)
L(\mathbb {R})
is
U
\mathcal {U}
-Ramsey with respect to every selective ultrafilter
U
\mathcal {U}
. In this paper, we show that the large cardinal assumption cannot be weakened.