  We describe a controllable and unbiased strong-coupling diagrammatic Monte
Carlo technique that is applicable to a wide range of fermionic systems and
spin models. Unlike previous strong coupling methods that generally rely on the
Grassmannian Hubbard-Stratonovich transformation, our construction is based on
Wick's theorem and a recursive procedure to group contractions into effective
connected vertices that are non-perturbative in all local physics and can be
calculated exactly. The resulting expansion is described by simple diagrammatic
rules that make it suitable for systematic treatment via stochastic sampling.
Benchmarks against numerical linked cluster expansion display excellent
agreement.
