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