  A longstanding problem in galactic simulations is to resolve the dynamical
friction (DF) force acting on massive black hole particles when their masses
are comparable to or less than the background simulation particles. Many
sub-grid models based on the traditional Chandrasekhar DF formula have been
proposed, yet they suffer from fundamental ambiguities in the definition of
some terms in Chandrasekhar's formula when applied to real galaxies, as well as
difficulty in evaluating continuous quantities from (spatially) discrete
simulation data. In this work we present a new sub-grid dynamical friction
estimator based on the discrete nature of $N$-body simulations, which also
avoids the ambiguously-defined quantities in Chandrasekhar's formula. We test
our estimator in the GIZMO code and find that it agrees well with
high-resolution simulations where DF is fully captured, with negligible
additional computational cost. We also compare it with a Chandrasekhar
estimator and discuss its applications in real galactic simulations.
