The number complex zeros of a system of sparse polynomial equations is an invariant from algebraic geometry that is linked to theory of mixed volumes in convex geometry. We present average number of real zeros of sparse polynomial systems with a similar geometric interpretation and obtain estimates on this quantity. The real case has a combinatorial nature unlike its convex geometric counterpart in complex case, and this brings a collection of open problems: this talk is meant to be an invitation to the participants of the workshop to this widely open field. Joint work with Josue Tonelli-Cueto, Mate Telek, and Peter Burgisser.