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Let ${\mathbb F}$ be an arbitrary field. We consider a commutative,non-associative, $4$-dimensional algebra ${\mathfrak M}$ of the rock, the paperand the scissors with unit over ${\mathbb F}$ and we prove that the image over${\mathfrak M}$ of every non-associative multilinear polynomial over ${\mathbbF}$ is a vector space. The same question we consider for two subalgebras: analgebra of the rock, the paper and the scissors without unit, and an algebra oftrace zero elements with zero scalar part. Moreover in this paper we considerthe questions of possible evaluations of homogeneous polynomials on thesealgebras.

The images of multilinear non-associative polynomials evaluated on a rock-paper-scissors algebra with unit over an arbitrary field