  The branching fraction of the $B_s\to K^0\bar K^0$ decay has been recently
measured by the LHCb and Belle experiments. We study the consistency of the
measured value with three relations to other decay rates and CP asymmetries
which follow from the Standard Model, and from the approximate flavor $SU(3)$
symmetry of the strong interactions. We find that each of these relations is
violated at a level of above $3\sigma$. We argue that various subleading
effects -- rescattering, electroweak penguins and $SU(3)$ breaking -- if larger
than theoretically expected, can account for some of these puzzles, but not for
all of them simultaneously.
