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The essential variety is an algebraic subvariety of dimension $5$ in realprojective space $\mathbb R\mathrm P^{8}$ which encodes the relative pose oftwo calibrated pinhole cameras. The $5$-point algorithm in computer visioncomputes the real points in the intersection of the essential variety with alinear space of codimension $5$. The degree of the essential variety is $10$,so this intersection consists of 10 complex points in general.  We compute the expected number of real intersection points when the linearspace is random. We focus on two probability distributions for linear spaces.The first distribution is invariant under the action of the orthogonal group$\mathrm{O}(9)$ acting on linear spaces in $\mathbb R\mathrm P^{8}$. In thiscase, the expected number of real intersection points is equal to $4$. Thesecond distribution is motivated from computer vision and is defined bychoosing 5 point correspondences in the image planes $\mathbb R\mathrmP^2\times \mathbb R\mathrm P^2$ uniformly at random. A Monte Carlo computationsuggests that with high probability the expected value lies in the interval$(3.95 - 0.05,\ 3.95 + 0.05)$.

Average degree of the essential variety