  Given a finite structure $M$ and property $p$, it is a natural to study the
degree of satisfiability of $p$ in $M$; i.e. to ask: what is the probability
that uniformly randomly chosen elements in $M$ satisfy $p$? In group theory, a
well-known result of Gustafson states that the equation $xy=yx$ has a finite
satisfiability gap: its degree of satisfiability is either $1$ (in Abelian
groups) or no larger than $\frac{5}{8}$. Degree of satisfiability has proven
useful in the study of (finite and infinite) group-like and ring-like algebraic
structures, but finite satisfiability gap questions have not been considered in
lattice-like, order-theoretic settings yet.
  Here we investigate degree of satisfiability questions in the context of
Heyting algebras and intuitionistic logic. We classify all equations in one
free variable with respect to finite satisfiability gap, and determine which
common principles of classical logic in multiple free variables have finite
satisfiability gap. In particular we prove that, in a finite non-Boolean
Heyting algebra, the probability that a randomly chosen element satisfies $x
\vee \neg x = \top$ is no larger than $\frac{2}{3}$. Finally, we generalize our
results to infinite Heyting algebras, and present their applications to
point-set topology, black-box algebras, and the philosophy of logic.
