  In recent work, Hollands, Kov\'acs and Reall have built on previous work of
Wall to provide a definition of dynamical black hole entropy for gravitational
effective field theories (EFTs). This entropy satisfies a second law of black
hole mechanics to quadratic order in perturbations around a stationary black
hole. We determine the explicit form of this entropy for the EFT of 4d vacuum
gravity including terms in the action with up to 6 derivatives. An open
question concerns the gauge invariance of this definition of black hole
entropy. We show that gauge invariance holds for the EFT of vacuum gravity with
up to 6 derivatives but demonstrate that it can fail when 8 derivative terms
are included. We determine an entropy for Einstein-Gauss-Bonnet theory by
treating it as an EFT with vanishing 6 derivative terms.
